miami miami 2012 tirtho biswas stringy nonlocal theories
TRANSCRIPT
My Collaborators• N. Barnaby (University of Minnesota)• R. Brandenberger (McGill)• J. Cembranos (Madrid)• J. Cline (McGill)• M. Grisaru (McGill)• J. Kapusta (U of M)• T. Koivisto (Utrecht)• A. Kosheylev (Brussels)• A. Mazumdar (Lancaster)• A. Reddy (U of M)• W. Siegel (Stony Brook)• S. Vernov (Moscow)
• TB, J. Cembranos and J. Kapusta, PRL 104, 021601 (2010) [arXiv:0910.2274 [hep-th]]
• TB, E. Gerwick, T. Koivisto and A. Mazumdar, PRL 108, 031101 (2012) [arXiv:1110.5249 [gr-qc]]
OutlineNonlocal Scalar Field Theory
Stringy Motivations Ghostfree higher derivative theories Finite Loops & some results
Nonlocal Gravity The problem of Ghosts Nonsingular Black Holes? Nonsingular Cosmology?
String Field Theory Tachyons [Witten, Kostelecky &
Samuel, Sen]
Mass square has the wrong sign
p-adic string theory [Volovich, Brekke, Freund, Olson, Witten,
Frampton]
An inifinte series of higher derivative kinetic operators, mildly nonlocal
)()(2
11 2
2
222
Vemxdg
S MD
o
Open string coupling string tension
Nonlocal Actions in String Theory
1
2
2
2 1
1exp
2
1 pD
p
Ds
pMxd
g
mS
Interesting PropertiesGhostfree
But SFT/padic type theories have no extra states!
Quantum loops are finite UV under better control, like usual HD theories
Linear Regge Trajectories [TB, Grisaru & Siegel]
Thermal duality [TB, Cembranos & Kapusta, 2010 PRL]
Can there be any phenomenological implications for LHC? [Moffat et al]
2222222
222222
11~
)(
1~)(
0)()(2
1~
mppmppp
mmxdS D
)(2
11
T
mZTZ s
22
222 )exp()(
mp
Mpp
Applications
Insights into string theory Brane Physics & Tachyon condensation [Zwiebach & Moeller;
Forini, Gambini & Nardelli; Colleti, Sigalov & Taylor; Calcagni…]
Hagedorn physics [Blum; TB, Cembranos & Kapusta]
Spectrum [TB, Grisaru & Siegel, Minahan]
Applications to Cosmology Novel kinetic energy dominated non-slow-roll
inflationary mechanisms [TB, Barnaby & Cline; Lidsey…]
Large nongaussianities [Barnaby & Cline]
Dark Energy [Arefeva, Joukovskaya, Dragovich, ...]
Applications to Particle Physics [Moffat et.al.]
Nonlocal Gravity
Can Nonlocal higher derivative terms be free from ghosts?
Can they address the singularity problems in GR ?
What about quantum loops? Stelle demonstrated 4th order gravity to be renormalizable
(1977), but it has ghosts
Ghosts
From Scalars to Gravity The metric has 6 degrees (graviton, vector, and
two scalars)
Gauge symmetry is subtle, some ghosts are allowed
Several Classical (time dependent) backgrounds.
Linearized GravityFree from ghosts in Minkowski vacuum Only interested in quadratic action [with Mazumdar, Koivisto,
Gerwick, 2012 PRL]
Only 6 linearly independent combinations using BI
Covariant derivatives must be Minkowski, most general form
''''''''4 ˆ
)(~
RORRgxdS
hORhg
...)()()( 23
22
21
4
RFRRFRRRFRgxdS
hf
hhhd
hhchbhhahxdS
2
222
22224
)()(
2
1
)()()(2
1
Covariant to Minkowski
We noticed rather curious relations
They in fact follow from Bianchi identity! By inverting Field equations we obtain the
propagators Decouple the different multiplets using projection
operators: [van Nieuwenhuizen]
Precisely because of the above relations, the dangerous w-scalar ghost and the Vector ghost vanishes
)(2)(2
11)( 32 xxFxxFxa
0
0
0
fac
dc
ba
0012 ,,, ws PPPP
General Covariance dictates the propagator is of the form
At low energies, p 0, we automatically recover GR In GR a = c = 1, scalar ghost cancels the longitudinal
mode a has to be an entire function, otherwise Weyl ghosts a-3c can have a single zero -> f(R)/Brans-Dicke theory Exponential non-local Gravity,
2
0
2
2
222
0
22
22
2
1
)](3)([)()(
p
P
p
P
ppcpa
P
ppa
Pp sGRs
2
2exp
Mca
2
2
2
0
2
22 exp
2
1)(
M
p
p
P
p
Pp s
Newtonian Potentials
Large r, reproduces gravity; small r, asymptotic freedom
No small mass black holes, no horizon and no singularity!
Gravity Waves Similar arguments imply nonsingular Green’s
functions for quadrupole moments
)()21()21( 00222 rmanddxdtds
r
Mr
p
eepdrr
ripMp )(erf~~)()(
2
./3
22
M
Mm p
2
Exact SolutionsBouncing Solutions deSitter completions, a(t) ~ cosh(Mt)
Stable attractors, but there are singular attractors.
Can provide a geodesically complete models of inflation.
Perturbations can be studied numerically and analytically, reproduces GR at late times… can provide geodesic completion to inflation
RRFRgxdS )( 21
4
Conclusions
Nonlocal gravity is a promising direction in QG
It can probably solve the classical singularities
How to constrain higher curvatures? New symmetries Look at ghost constraints on (A)dS – relevant for
DE Can we implement Stelle’s methods?
Emergent Cosmology Space-time begins with pure vacuum
You cannot find a consistent solution for GR There must be a scalar degree of freedom
0 ttandg
1)(1)( tt taeta
0)(3)( 22 ca
mandpawithmpac ~)exp()/1( 222
t’ Hooft dual to string theory Polyakov action:
Strings on Random lattice [Douglas,Shenker]
Dual Field theory action
Motivation Standard Models of Particle Physics &
Cosmology have been remarkably successful
Too successful, no experimental puzzles Hints at new meV physics (Dark energy &
Neutrinos) Fall back on theoretical prejudices
Hierarchy problem, Unification - GUT, SUSY, String Theory
Nonsingularity – can we use this to guide us?