gauge-gravity duality and its applicationsqpt.physics.harvard.edu/talks/kac3.pdfization group...
TRANSCRIPT
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Gauge-gravity dualityand its applications
HARVARD
Talk online: sachdev.physics.harvard.edu
Marc Kac Memorial Lectures, May 5 2011
Thursday, May 5, 2011
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1. Quantum criticality and conformal field theories in condensed matter
2. The AdS/CFT correspondence Quantum criticality and black holes
3. Quantum transport and Einstein-Maxwell theory on AdS4
4. Compressible quantum matter Fermi surfaces
Outline
Thursday, May 5, 2011
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1. Quantum criticality and conformal field theories in condensed matter
2. The AdS/CFT correspondence Quantum criticality and black holes
3. Quantum transport and Einstein-Maxwell theory on AdS4
4. Compressible quantum matter Fermi surfaces
Outline
Thursday, May 5, 2011
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Ground state has long-range Néel order
Square lattice antiferromagnet
H =
ij
JijSi · Sj
Order parameter is a single vector field ϕ = ηiSi
ηi = ±1 on two sublattices
ϕ = 0 in Neel state.
Thursday, May 5, 2011
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Square lattice antiferromagnet
H =
ij
JijSi · Sj
J
J/λ
Weaken some bonds to induce spin entanglement in a new quantum phase
Thursday, May 5, 2011
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Square lattice antiferromagnet
H =
ij
JijSi · Sj
J
J/λ
Ground state is a “quantum paramagnet”with spins locked in valence bond singlets
=1√2
↑↓−
↓↑
Thursday, May 5, 2011
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λλc
Quantum critical point with non-local entanglement in spin wavefunction
=1√2
↑↓−
↓↑
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λλc
=1√2
↑↓−
↓↑
Conformal field theory in 2+1 dimensions (CFT3)
Thursday, May 5, 2011
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S =
d2rdτ
(∂τ ϕ)
2 + c2(∇r ϕ)2 + (λ− λc)ϕ
2 + uϕ2
2
Z =
Dϕ(r, τ) exp(−S)
λλc CFT3
=1√2
↑↓−
↓↑
Thursday, May 5, 2011
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Classicalspin
waves
Dilutetriplon
gas
Quantumcritical
Neel orderPressure in TlCuCl3
S. Sachdev and J. Ye, Phys. Rev. Lett. 69, 2411 (1992).A. V. Chubukov, S. Sachdev, and J. Ye, Phys. Rev. B 49, 11919 (1994).
Thursday, May 5, 2011
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S. Sachdev and J. Ye, Phys. Rev. Lett. 69, 2411 (1992).A. V. Chubukov, S. Sachdev, and J. Ye, Phys. Rev. B 49, 11919 (1994).
Classicalspin
waves
Dilutetriplon
gas
Quantumcritical
Neel order
CFT3 at T>0
Pressure in TlCuCl3Thursday, May 5, 2011
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S. Sachdev and J. Ye, Phys. Rev. Lett. 69, 2411 (1992).A. V. Chubukov, S. Sachdev, and J. Ye, Phys. Rev. B 49, 11919 (1994).
Classicalspin
waves
Dilutetriplon
gas
Quantumcritical
Neel order
CFT3 at T>0
Pressure in TlCuCl3Thursday, May 5, 2011
![Page 13: Gauge-gravity duality and its applicationsqpt.physics.harvard.edu/talks/kac3.pdfization group equation u dg du = β(g) where u is the energy scale. The RG equation is local in energy](https://reader033.vdocuments.mx/reader033/viewer/2022042300/5ecb081edb57f746241d8858/html5/thumbnails/13.jpg)
S. Sachdev and J. Ye, Phys. Rev. Lett. 69, 2411 (1992).A. V. Chubukov, S. Sachdev, and J. Ye, Phys. Rev. B 49, 11919 (1994).
Classicalspin
waves
Dilutetriplon
gas
Quantumcritical
Neel order
CFT3 at T>0
Pressure in TlCuCl3
Strongly coupled dynamics andtransport with no
particle/wave interpretation,and relaxation thermalequilibration times are
universally proportional to/kBT
Thursday, May 5, 2011
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M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature 415, 39 (2002).
Ultracold 87Rbatoms - bosons
Superfluid-insulator transition
Thursday, May 5, 2011
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Insulator (the vacuum) at large U
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Excitations:
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Excitations:
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Excitations of the insulator:
S =
d2rdτ|∂τψ|2 + v2|∇ψ|2 + (g − gc)|ψ|2 +
u
2|ψ|4
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g
T
gc
0
InsulatorSuperfluid
Quantumcritical
TKT
CFT3
ψ = 0 ψ = 0
S =
d2rdτ|∂τψ|2 + v2|∇ψ|2 + (g − gc)|ψ|2 +
u
2|ψ|4
Thursday, May 5, 2011
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g
T
gc
0
InsulatorSuperfluid
Quantumcritical
TKT
Thursday, May 5, 2011
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g
T
gc
0
InsulatorSuperfluid
Quantumcritical
TKT
CFT at T>0
Thursday, May 5, 2011
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1. Quantum criticality and conformal field theories in condensed matter
2. The AdS/CFT correspondence Quantum criticality and black holes
3. Quantum transport and Einstein-Maxwell theory on AdS4
4. Compressible quantum matter Fermi surfaces
Outline
Thursday, May 5, 2011
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1. Quantum criticality and conformal field theories in condensed matter
2. The AdS/CFT correspondence Quantum criticality and black holes
3. Quantum transport and Einstein-Maxwell theory on AdS4
4. Compressible quantum matter Fermi surfaces
Outline
Thursday, May 5, 2011
![Page 24: Gauge-gravity duality and its applicationsqpt.physics.harvard.edu/talks/kac3.pdfization group equation u dg du = β(g) where u is the energy scale. The RG equation is local in energy](https://reader033.vdocuments.mx/reader033/viewer/2022042300/5ecb081edb57f746241d8858/html5/thumbnails/24.jpg)
Field theories in D spacetime dimensions are char-
acterized by couplings g which obey the renormal-
ization group equation
udg
du= β(g)
where u is the energy scale. The RG equation is
local in energy scale, i.e. the RHS does not depend
upon u.
Thursday, May 5, 2011
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Field theories in D spacetime dimensions are char-
acterized by couplings g which obey the renormal-
ization group equation
udg
du= β(g)
where u is the energy scale. The RG equation is
local in energy scale, i.e. the RHS does not depend
upon u.
Key idea: ⇒ Implement u as an extra dimen-sion, and map to a local theory in D+1 dimensions.
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At the RG fixed point, β(g) = 0, the D dimen-sional field theory is invariant under the scale trans-formation
xµ → xµ/b , u→ b u
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At the RG fixed point, β(g) = 0, the D dimen-sional field theory is invariant under the scale trans-formation
xµ → xµ/b , u→ b u
This is an invariance of the metric of the theory in
D + 1 dimensions. The unique solution is
ds2=
u
L
2dxµdxµ + L2 du2
u2.
Or, using the length scale z = L2/u
ds2= L2 dxµdxµ + dz2
z2.
This is the space AdSD+1, and L is the AdS radius.
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J. McGreevy, arXiv0909.0518
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AdS/CFT correspondenceThe quantum theory of a black hole in a 3+1-dimensional negatively curved AdS universe is
holographically represented by a CFT (the theory of a quantum critical point) in 2+1 dimensions
Maldacena, Gubser, Klebanov, Polyakov, Witten
3+1 dimensional AdS space
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AdS/CFT correspondenceThe quantum theory of a black hole in a 3+1-dimensional negatively curved AdS universe is
holographically represented by a CFT (the theory of a quantum critical point) in 2+1 dimensions
Maldacena, Gubser, Klebanov, Polyakov, Witten
3+1 dimensional AdS space A 2+1
dimensional system at its
quantum critical point
Thursday, May 5, 2011
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AdS/CFT correspondenceThe quantum theory of a black hole in a 3+1-dimensional negatively curved AdS universe is
holographically represented by a CFT (the theory of a quantum critical point) in 2+1 dimensions
Maldacena, Gubser, Klebanov, Polyakov, Witten
3+1 dimensional AdS space Quantum
criticality in 2+1
dimensionsBlack hole temperature
= temperature of quantum criticality
Thursday, May 5, 2011
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AdS/CFT correspondenceThe quantum theory of a black hole in a 3+1-dimensional negatively curved AdS universe is
holographically represented by a CFT (the theory of a quantum critical point) in 2+1 dimensions
Strominger, Vafa
3+1 dimensional AdS space Quantum
criticality in 2+1
dimensionsBlack hole entropy = entropy of quantum criticality
Thursday, May 5, 2011
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AdS/CFT correspondenceThe quantum theory of a black hole in a 3+1-dimensional negatively curved AdS universe is
holographically represented by a CFT (the theory of a quantum critical point) in 2+1 dimensions
3+1 dimensional AdS space Quantum
criticality in 2+1
dimensionsQuantum critical
dynamics = waves in curved space
Maldacena, Gubser, Klebanov, Polyakov, WittenThursday, May 5, 2011
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AdS/CFT correspondenceThe quantum theory of a black hole in a 3+1-dimensional negatively curved AdS universe is
holographically represented by a CFT (the theory of a quantum critical point) in 2+1 dimensions
3+1 dimensional AdS space Quantum
criticality in 2+1
dimensionsFriction of quantum
criticality = waves
falling into black hole
Kovtun, Policastro, SonThursday, May 5, 2011
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AdS/CFT correspondenceThe quantum theory of a black hole in a 3+1-dimensional negatively curved AdS universe is
holographically represented by a CFT (the theory of a quantum critical point) in 2+1 dimensions
3+1 dimensional AdS space Quantum
criticality in 2+1
dimensionsFriction of quantum
criticality = waves
falling into black hole
Kovtun, Policastro, SonThursday, May 5, 2011
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AdS/CFT correspondenceThe quantum theory of a black hole in a 3+1-dimensional negatively curved AdS universe is
holographically represented by a CFT (the theory of a quantum critical point) in 2+1 dimensions
3+1 dimensional AdS space Quantum
criticality in 2+1
dimensionsFriction of quantum
criticality = waves
falling into black hole
Kovtun, Policastro, Son
Strong coupling problem:General solution of spin and
magneto-thermo-electric transportin quantum critical region.
C. P. Herzog, P. K. Kovtun, S. Sachdev, and D. T. Son,
Phys. Rev. D 75, 085020 (2007).
S. A. Hartnoll, P. K. Kovtun, M. Muller, and S. Sachdev,
Phys. Rev. B 76, 144502 (2007).
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1. Quantum criticality and conformal field theories in condensed matter
2. The AdS/CFT correspondence Quantum criticality and black holes
3. Quantum transport and Einstein-Maxwell theory on AdS4
4. Compressible quantum matter Fermi surfaces
Outline
Thursday, May 5, 2011
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1. Quantum criticality and conformal field theories in condensed matter
2. The AdS/CFT correspondence Quantum criticality and black holes
3. Quantum transport and Einstein-Maxwell theory on AdS4
4. Compressible quantum matter Fermi surfaces
Outline
Thursday, May 5, 2011
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g
T
gc
0
InsulatorSuperfluid
Quantumcritical
TKT
CFT at T>0
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Quantum critical transport
S. Sachdev, Quantum Phase Transitions, Cambridge (1999).
Quantum “nearly perfect fluid”with shortest possiblerelaxation time, τR
τR = C kBT
where C is a universal constant
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Transport co-oefficients not determinedby collision rate, but by
universal constants of nature
Spin/charge conductivity
Quantum critical transport
K. Damle and S. Sachdev, Phys. Rev. B 56, 8714 (1997).
σ =Q2
h× [Universal constant O(1) ]
(Q is the quantum of spin/charge)
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Quantum critical transport Transport co-oefficients not determined
by collision rate, but byuniversal constants of nature
Momentum transportη
s≡
viscosityentropy density
=
kB× [Universal constant O(1) ]P. Kovtun, D. T. Son, and A. Starinets, Phys. Rev. Lett. 94, 11601 (2005)
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Structure of conductivity for complex frequencies
ω
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Structure of conductivity for complex frequencies
ω
ω = i2πnkBT/,n integer:computable in pertur-bative analysis ofconformal field theoryabout free field theory
Thursday, May 5, 2011
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Structure of conductivity for complex frequencies
ω
ω kBT/,hydrodynamic regime:requires computationin dual gravity theory
Thursday, May 5, 2011
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Structure of conductivity for complex frequencies
ω
ω kBT/,hydrodynamic regime:requires computationin dual gravity theory
Thursday, May 5, 2011
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Boltzmann theory of quantum critical transport
K. Damle and S. Sachdev, Phys. Rev. B 56, 8714 (1997).
ωkBT
1
; Σ → a universal functionσ =Q2
hΣ
ωkBT
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Boltzmann theory of quantum critical transport
K. Damle and S. Sachdev, Phys. Rev. B 56, 8714 (1997).
ωkBT
1
; Σ → a universal functionσ =Q2
hΣ
ωkBT
O(N)
O(1/N)
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Boltzmann theory of quantum critical transport
K. Damle and S. Sachdev, Phys. Rev. B 56, 8714 (1997).
ωkBT
1
; Σ → a universal function
Collisionless“critical”dissipation
σ =Q2
hΣ
ωkBT
Thursday, May 5, 2011
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Boltzmann theory of quantum critical transport
K. Damle and S. Sachdev, Phys. Rev. B 56, 8714 (1997).
ωkBT
1
; Σ → a universal function
Collision-dominatedhydrodynamics
σ =Q2
hΣ
ωkBT
Thursday, May 5, 2011
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AdS4 theory of strongly interacting “perfect fluids”
To leading order in a gradient expansion, an infinite set ofstrongly-interacting CFT3s can be described by Einstein-Maxwell gravity/electrodynamics on AdS4
SEM =1
g24
d4x
√−g
−1
4FabF
ab
.
This theory is self-dual under Fab → abcdF cd, and thisleads to some artifacts in the properties of the CFT3
C. P. Herzog, P. K. Kovtun, S. Sachdev, and D. T. Son,
Phys. Rev. D 75, 085020 (2007).
Thursday, May 5, 2011
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AdS4 theory of strongly interacting “perfect fluids”
To leading order in a gradient expansion, an infinite set ofstrongly-interacting CFT3s can be described by Einstein-Maxwell gravity/electrodynamics on AdS4
SEM =1
g24
d4x
√−g
−1
4FabF
ab
.
This theory is self-dual under Fab → abcdF cd, and thisleads to some artifacts in the properties of the CFT3
C. P. Herzog, P. K. Kovtun, S. Sachdev, and D. T. Son,
Phys. Rev. D 75, 085020 (2007).
Thursday, May 5, 2011
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AdS4 theory of strongly interacting “perfect fluids”
To leading order in a gradient expansion, an infinite set ofstrongly-interacting CFT3s can be described by Einstein-Maxwell gravity/electrodynamics on AdS4
SEM =1
g24
d4x
√−g
−1
4FabF
ab
.
This theory is self-dual under Fab → abcdF cd, and thisleads to some artifacts in the properties of the CFT3
We include all possible 4-derivative terms: after suitablefield redefinitions, the required theory has only one dimen-sionless constant γ (L is the radius of AdS4):
S =1
g24
d4x
√−g
−1
4FabF
ab + γ L2CabcdFabF cd
,
where Cabcd is the Weyl curvature tensor.Stability and causality constraints restrict |γ| < 1/12.
R. C. Myers, S. Sachdev, and A. Singh, arXiv:1010.0443Thursday, May 5, 2011
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AdS4 theory of strongly interacting “perfect fluids”
R. C. Myers, S. Sachdev, and A. Singh, arXiv:1010.0443
Γ 0
Γ 1 12
Γ 1 12
0.0 0.5 1.0 1.5 2.0
Ω
4 Π T0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Σ
h
Q2σ
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AdS4 theory of strongly interacting “perfect fluids”
R. C. Myers, S. Sachdev, and A. Singh, arXiv:1010.0443
Γ 0
Γ 1 12
Γ 1 12
0.0 0.5 1.0 1.5 2.0
Ω
4 Π T0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Σ
h
Q2σ
Note: exact determination ofthe transport co-efficient of
an interactingmany-body quantum system!
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AdS4 theory of strongly interacting “perfect fluids”
R. C. Myers, S. Sachdev, and A. Singh, arXiv:1010.0443
Γ 0
Γ 1 12
Γ 1 12
0.0 0.5 1.0 1.5 2.0
Ω
4 Π T0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Σ
h
Q2σ
Note: exact determination ofthe transport co-efficient of
an interactingmany-body quantum system!Also note: no diffusion and
hydrodynamics for CFT2 and AdS3.
Thursday, May 5, 2011
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AdS4 theory of strongly interacting “perfect fluids”
R. C. Myers, S. Sachdev, and A. Singh, arXiv:1010.0443
Γ 0
Γ 1 12
Γ 1 12
0.0 0.5 1.0 1.5 2.0
Ω
4 Π T0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Σ
h
Q2σ
• Stability constraints on the effectivetheory allow only a limited ω-dependencein the conductivity
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AdS4 theory of strongly interacting “perfect fluids”
R. C. Myers, S. Sachdev, and A. Singh, arXiv:1010.0443
Γ 0
Γ 1 12
Γ 1 12
0.0 0.5 1.0 1.5 2.0
Ω
4 Π T0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Σ
h
Q2σ
• The γ > 0 result has similarities tothe quantum-Boltzmann result fortransport of particle-like excitations
Thursday, May 5, 2011
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AdS4 theory of strongly interacting “perfect fluids”
R. C. Myers, S. Sachdev, and A. Singh, arXiv:1010.0443
Γ 0
Γ 1 12
Γ 1 12
0.0 0.5 1.0 1.5 2.0
Ω
4 Π T0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Σ
h
Q2σ
• The γ < 0 result can be interpretedas the transport of vortex-likeexcitations
Thursday, May 5, 2011
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AdS4 theory of strongly interacting “perfect fluids”
R. C. Myers, S. Sachdev, and A. Singh, arXiv:1010.0443
Γ 0
Γ 1 12
Γ 1 12
0.0 0.5 1.0 1.5 2.0
Ω
4 Π T0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Σ
h
Q2σ
Fab → abcdF cd dualityof theory on AdS4
maps ontoparticle-vortex duality
of CFT3
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L. W. Engel, D. Shahar, C. Kurdak, and D. C. Tsui,Physical Review Letters 71, 2638 (1993).
Frequency dependency of integer quantum Hall effect
Little frequency dependence,
and conductivity is close to self-dual
value
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Outline
1. Coupled dimer antiferromagnets Quantum criticality and conformal field theories
2. The AdS/CFT correspondence Quantum criticality and black holes
3. Quantum transport and Einstein-Maxwell theory on AdS4
4. Compressible quantum matter Fermi surfaces
Thursday, May 5, 2011
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Outline
1. Coupled dimer antiferromagnets Quantum criticality and conformal field theories
2. The AdS/CFT correspondence Quantum criticality and black holes
3. Quantum transport and Einstein-Maxwell theory on AdS4
4. Compressible quantum matter Fermi surfaces
Thursday, May 5, 2011
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Graphene
Semi-metal withmassless Dirac fermions
Brillouin zone
Q1
−Q1
Thursday, May 5, 2011
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Turn on a chemical potential on a CFT
µ = 0
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Turn on a chemical potential on a CFT
Electron Fermi surface
Thursday, May 5, 2011
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• Consider a continuum quantum system with a globallyconserved U(1) charge Q (the “electron density”) inspatial dimension d > 1.
• We are interested in zero temperature phases whereQ varies smoothly as a function of any external pa-rameter µ (the “chemical potential”). For simplicity,we assume µ couples linearly to Q.
• We will also restrict our attention to phases where thisglobal U(1) symmetry is not spontaneously broken,and translational symmetry is preserved.
Compressible quantum matter
Thursday, May 5, 2011
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• Consider a continuum quantum system with a globallyconserved U(1) charge Q (the “electron density”) inspatial dimension d > 1.
• We are interested in zero temperature phases whereQ varies smoothly as a function of any external pa-rameter µ (the “chemical potential”). For simplicity,we assume µ couples linearly to Q.
• We will also restrict our attention to phases where thisglobal U(1) symmetry is not spontaneously broken,and translational symmetry is preserved.
Compressible quantum matter
Thursday, May 5, 2011
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• Consider a continuum quantum system with a globallyconserved U(1) charge Q (the “electron density”) inspatial dimension d > 1.
• We are interested in zero temperature phases whereQ varies smoothly as a function of any external pa-rameter µ (the “chemical potential”). For simplicity,we assume µ couples linearly to Q.
• We will also restrict our attention to phases where thisglobal U(1) symmetry is not spontaneously broken,and translational symmetry is preserved.
Compressible quantum matter
Thursday, May 5, 2011
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Compressible quantum matter• Consider a continuum quantum system with a globally
conserved U(1) charge Q (the “electron density”) inspatial dimension d > 1.
• We are interested in zero temperature phases whereQ varies smoothly as a function of any external pa-rameter µ (the “chemical potential”). For simplicity,we assume µ couples linearly to Q.
• We will also restrict our attention to phases where thisglobal U(1) symmetry is not spontaneously broken,and translational symmetry is preserved.
There are only a few established examples of such phases in condensed matter physics.
However, they appear naturally as duals of gravitational theories, and we want to interpret them in the gauge theory.
Thursday, May 5, 2011
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Compressible quantum matter• Consider a continuum quantum system with a globally
conserved U(1) charge Q (the “electron density”) inspatial dimension d > 1.
• We are interested in zero temperature phases whereQ varies smoothly as a function of any external pa-rameter µ (the “chemical potential”). For simplicity,we assume µ couples linearly to Q.
• We will also restrict our attention to phases where thisglobal U(1) symmetry is not spontaneously broken,and translational symmetry is preserved.
Thursday, May 5, 2011
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Compressible quantum matter• Consider a continuum quantum system with a globally
conserved U(1) charge Q (the “electron density”) inspatial dimension d > 1.
• We are interested in zero temperature phases whereQ varies smoothly as a function of any external pa-rameter µ (the “chemical potential”). For simplicity,we assume µ couples linearly to Q.
• We will also restrict our attention to phases where thisglobal U(1) symmetry is not spontaneously broken,and translational symmetry is preserved.
All known examples of such phases have a Fermi Surface
(even in systems with only bosons in the Hamiltonian)Thursday, May 5, 2011
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The Fermi surface
Area A
This is the locus of zero energy singularities in momentum spacein the two-point correlator of fermions carrying charge Q.
G−1fermion(k = kF ,ω = 0) = 0.
Luttinger relation: The total “volume (area)” A enclosed byFermi surfaces of fermions carrying charge Q is equal to Q. Thisis a key constraint which allows extrapolation from weak to strongcoupling.
Thursday, May 5, 2011
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Aharony-Bergman-Jafferis-Maldacena (ABJM) CFT3
• U(N)×U(N) gauge field.
• 4N2 Weyl fermions carrying fundamental chargesof U(N)×U(N)×SU(4)R.
• 4N2 complex bosons carrying fundamentalcharges of U(N)×U(N)×SU(4)R.
• N = 6 supersymmetry
• Add a chemical potential µ coupling to aglobal SU(4)R charge Q.
Thursday, May 5, 2011
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Adding a chemical potential coupling to a SU(4) charge breaks supersymmetry and SU(4) invariance
• U(N)×U(N) gauge field.
• 4N2 Weyl fermions carrying fundamental chargesof U(N)×U(N)×SU(4)R.
• 4N2 complex bosons carrying fundamentalcharges of U(N)×U(N)×SU(4)R.
• N = 6 supersymmetry
• Add a chemical potential µ coupling to aglobal SU(4)R charge Q.
Aharony-Bergman-Jafferis-Maldacena (ABJM) CFT3
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Phases of ABJM-like theories
Ac
Fermi liquid (FL) of gauge-neutral particlesGauge theory is in confining phase
2Ac = Q
Fermi surface of gaugeneutral particles, c, whichcarry 2 units of Q charge.
Thursday, May 5, 2011
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2Ac + 2Af = Q
Phases of ABJM-like theories
Ac
Fractionalized Fermi liquid (FL*)Gauge theory is in deconfined phase
Af
Fermi surface of gaugecharged particles, f , which
quench gauge forcesand lead to deconfinement
Thursday, May 5, 2011
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Phases of ABJM-like theories
Ac Af
Fermi surface of gaugecharged particles, f , which
quench gauge forcesand lead to deconfinement
Fractionalized Fermi liquid (FL*)Gauge theory is in deconfined phase
2Ac + 2Af = Q
Thursday, May 5, 2011
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Phases of ABJM-like theories
Ac Af
Fermi surface of gaugecharged particles, f , which
quench gauge forcesand lead to deconfinement
Fractionalized Fermi liquid (FL*)Gauge theory is in deconfined phase
Claim: this is the phase underlying recent holographic theories of compressible metallic states.
However, a number of artifacts appear in the classical gravity approximation.
2Ac + 2Af = Q
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Begin with a CFT e.g. the ABJM theory with a SU(4) global symmetry
The CFT is dual to a gravity theory on AdS4 x S7
Gauge-gravity duality
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Begin with a CFT e.g. the ABJM theory with a SU(4) global symmetry
Add some SU(4) charge by turning on a chemical potential (this breaks the SU(4) symmetry)
The CFT is dual to a gravity theory on AdS4 x S7
In the Einstein-Maxwell theory, the chemical potential leads at T=0 to an extremal Reissner-Nordtrom black hole in the AdS4 spacetime.
Gauge-gravity duality
T. Faulkner, H. Liu, J. McGreevy, and D. Vegh, arXiv:0907.2694Thursday, May 5, 2011
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Begin with a CFT e.g. the ABJM theory with a SU(4) global symmetry
Add some SU(4) charge by turning on a chemical potential (this breaks the SU(4) symmetry)
The CFT is dual to a gravity theory on AdS4 x S7
In the Einstein-Maxwell theory, the chemical potential leads at T=0 to an extremal Reissner-Nordtrom black hole in the AdS4 spacetime. The RN black hole describes compressible quantum matter with Fermi surfaces, but with infinite range hopping: this leads to numerous artifacts.
Gauge-gravity duality
Thursday, May 5, 2011
![Page 83: Gauge-gravity duality and its applicationsqpt.physics.harvard.edu/talks/kac3.pdfization group equation u dg du = β(g) where u is the energy scale. The RG equation is local in energy](https://reader033.vdocuments.mx/reader033/viewer/2022042300/5ecb081edb57f746241d8858/html5/thumbnails/83.jpg)
Compressible quantum matter is characterized by Fermi surfaces.
Phases of a strongly-coupled gauge theory: Fermi liquids (FL) and fractionalized Fermi liquids (FL*)
Fermi liquids are everywhere.
There is evidence that FL* phases have been recently been observed in some intermetallic compounds. The FL* and related phases are attractive candidates for “strange metals” in the higher temperature superconductors
Summary
Thursday, May 5, 2011
![Page 84: Gauge-gravity duality and its applicationsqpt.physics.harvard.edu/talks/kac3.pdfization group equation u dg du = β(g) where u is the energy scale. The RG equation is local in energy](https://reader033.vdocuments.mx/reader033/viewer/2022042300/5ecb081edb57f746241d8858/html5/thumbnails/84.jpg)
Compressible quantum matter is characterized by Fermi surfaces.
Phases of a strongly-coupled gauge theory: Fermi liquids (FL) and fractionalized Fermi liquids (FL*)
Fermi liquids are everywhere.
There is evidence that FL* phases have been recently been observed in some intermetallic compounds. The FL* and related phases are attractive candidates for “strange metals” in the higher temperature superconductors
Summary
Thursday, May 5, 2011
![Page 85: Gauge-gravity duality and its applicationsqpt.physics.harvard.edu/talks/kac3.pdfization group equation u dg du = β(g) where u is the energy scale. The RG equation is local in energy](https://reader033.vdocuments.mx/reader033/viewer/2022042300/5ecb081edb57f746241d8858/html5/thumbnails/85.jpg)
Compressible quantum matter is characterized by Fermi surfaces.
Phases of a strongly-coupled gauge theory: Fermi liquids (FL) and fractionalized Fermi liquids (FL*)
Fermi liquids are everywhere.
There is evidence that FL* phases have been recently been observed in some intermetallic compounds. The FL* and related phases are attractive candidates for “strange metals” in the higher temperature superconductors
Summary
Thursday, May 5, 2011
![Page 86: Gauge-gravity duality and its applicationsqpt.physics.harvard.edu/talks/kac3.pdfization group equation u dg du = β(g) where u is the energy scale. The RG equation is local in energy](https://reader033.vdocuments.mx/reader033/viewer/2022042300/5ecb081edb57f746241d8858/html5/thumbnails/86.jpg)
Compressible quantum matter is characterized by Fermi surfaces.
Phases of a strongly-coupled gauge theory: Fermi liquids (FL) and fractionalized Fermi liquids (FL*)
Fermi liquids are everywhere.
There is evidence that FL* phases have been recently been observed in some intermetallic compounds. The FL* and related phases are attractive candidates for “strange metals” in the higher temperature superconductors
Summary
Thursday, May 5, 2011
![Page 87: Gauge-gravity duality and its applicationsqpt.physics.harvard.edu/talks/kac3.pdfization group equation u dg du = β(g) where u is the energy scale. The RG equation is local in energy](https://reader033.vdocuments.mx/reader033/viewer/2022042300/5ecb081edb57f746241d8858/html5/thumbnails/87.jpg)
Compressible quantum matter is characterized by Fermi surfaces.
Phases of a strongly-coupled gauge theory: Fermi liquids (FL) and fractionalized Fermi liquids (FL*)
Fermi liquids are everywhere.
There is evidence that FL* phases have been recently been observed in some intermetallic compounds. The FL* and related phases are attractive candidates for “strange metals” in the higher temperature superconductors
Summary
Gauge-gravity duality is a very promising approach to solving strong-coupling problems associated with FL*-like phases.
Thursday, May 5, 2011
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New insights and solvable models for diffusion and transport of
strongly interacting systems near quantum critical points
The description is far removed from, and complementary to, that of
the quantum Boltzmann equation which builds on the quasiparticle picture.
Conclusions
Thursday, May 5, 2011
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The AdS/CFT correspondence offers promise in providing a new
understanding of strongly interacting quantum matter at non-zero density
Conclusions
Thursday, May 5, 2011