holographic interface

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Holographic Interface. Collaboration with. . K. Nagasaki. . H. Tanida. . K. Nagasaki, SY , arXiv:1205.1674 [ hep-th ] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012) 139. Main achievement. . (Gauge theory calculation). . (Gravity calculation). . - PowerPoint PPT Presentation

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One point functions in 1/2 BPS interface CFT

Holographic InterfaceCollaboration withK. NagasakiH. TanidaK. Nagasaki, SY, arXiv:1205.1674 [hep-th]K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012) 139Main achievement(Gauge theory calculation)

(Gravity calculation) (Gauge theory)=(Gravity)Evidence forInterface ?QFTQFTInterfaceCFTPoint of viewExtension of boundary CFTCFTBoundary CFTInterface CFTBoundaryInterfaceCFTPoint of view test membraneTest particle(Wilson loop, t Hooft loop,...)Test membrane(Interface)4 dimStatistical mechanicsExtra dimensionsin particle physicsString worldsheetAdS/CFT correspondenceAdS/CFTMotivationsHolography ?

HolographyHolography (AdS/CFT correspondence)(Gravity) = (Lower dimensional non-gravitational QFT)

AdS/CFT CorrespondenceCertain gravitytheory(String theory)Quantum field theory without gravityInterface Brane, etcWant to checkPhysical quantitiesOne point function of local operators

14StrategyQFTGauge theoryGravityPrescriptionResult in gravityClassical calculationResult in gauge theoryCompareQFTOne point functionResultAgree nontriviallyGravityGauge theory

Why agreeGauge theory sideN=4 Super Yang-MillsFields

Adjoint rep. of the gauge group SU(N)

ActionSUNLarge N limit

: gauge coupling

Large N limit

Fix

: t Hooft coupling

is the loop expansion parameter1/2 BPS InterfaceFuzzy funnel background[Constable, Myers, Tafjord], [Gaiotto, Witten]

UseJunction condition (boundary condition) here1/2BPS Nahm equation

Solutionk dim irrep of SU(2)

SU(2)kPath integral with the boundary conditionthat fields approach to the solution in

One point functionTraceless symmetricChiral primary operator

Evaluate one point function classicallyJust substitute

Example

= ?Quiz

k dim irrep of SU(2)k

The answer

The correct answer

One point function --- result

Gravity sideAdS/CFT correspondenceIIB SuperstringAdS5 x S54dim N=4 SYMSU(N)Interface ??D3 systemN D3-branes0123 directionAdS5 x S5Near horizon 4dim N=4 SYMopen stringlow energytype IIB stringD3-D5 systemAdS5 x S5+D5-brane probeAdS4 x S2(with magnetic flux)Near horizon SU(N-k) SU(N)InterfaceLow energyN D3-brane0123 direction1 D5-brane 012 456 directionN-kDescription in the gravity side

D5-brane

magnetic flux[Karch, Randall]

One point functionGKPW

sourceScalar field

Result

Comparison to the gauge theory side

LargeGaugeLargeGravity

Agree

SummaryOne point functionOne point functionN=4 SYMAdS5 x S5Classical calculationSU(N-k)probe D5-braneSU(N)Agree

GKPW

Why agree?

Calculation in gauge theory sideValid inCalculation in gravity sideValid in

Gravity sidePositive power series in cf [Berenstein, Maldacena, Nastase]since k is large.

Future problemCan reproduce from the perturbative calculation in the gauge theory side?

Thank you