Holographic Interface

Collaboration with

K. NagasakiH. Tanida

K. Nagasaki, SY, arXiv:1205.1674 [hep-th]K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012) 139

谷田君

長崎君

共同研究者

Main achievement

(Gauge theory calculation)

(Gravity calculation)

主要な結果

ゲージ理論の計算

重力の計算

（ゲージ理論）＝（重力理論） の証拠(Gauge theory)=(Gravity)

Evidence for

Interface ?

QFT QFT

Interface

CFT

Point of view―Extension of boundary CFT

CFTBoundary CFTInterface CFT

BoundaryInterface

境界のある CFT の拡張

Point of view － test membrane

Test particle(Wilson loop, ’t Hooft loop,...)

Test membrane(Interface)

4 dim

試験粒子

試験膜

試験膜

Statistical mechanics統計力学

Extra dimensionsin particle physics

素粒子論で余剰次元

String worldsheet弦の世界面

AdS/CFT correspondence

AdS/CFT 対応

Motivations

Holography ?

Holography

Holography (AdS/CFT correspondence)

(Gravity) = (Lower dimensional non-gravitational QFT)重力 低次元の重力でない場の理論

AdS/CFT Correspondence

Certain gravitytheory(String theory)

Quantum field theory without gravity

Interface Brane, etc

Want to check

Physical quantities

One point function of local operators

ｘ

Strategy

QFT

Gauge theoryGravity

Prescription

Result in gravity

Classical calculation

Result in gauge theory

CompareQFT

One point function

Result

Agree nontrivially非自明な一致

Gravity Gauge theory

①②

Why agree ？なぜ一致？

重力 ゲージ理論

Gauge theory side

N=4 Super Yang-Mills

Fields

Adjoint rep. of the gauge group SU(N)

Action

ゲージ群 SU （ N ）の随伴表現

Large N limit

: gauge coupling

Large N limitFix

ゲージ結合定数

固定

: ’t Hooft coupling

is the loop expansion parameterがループ展開のパラメータ

1/2 BPS Interface

Fuzzy funnel background[Constable, Myers, Tafjord], [Gaiotto, Witten]

Use

Junction condition (boundary condition) hereここで接続条件（境界条件）

1/2BPS Nahm equation

Solution

k dim irrep of SU(2)SU(2) の k 次元既約表現

Path integral with the boundary conditionthat fields approach to the solution in

でこの解に近づくような境界条件の元で経路積分を行う

One point function

Traceless symmetric

Chiral primary operator

Evaluate one point function classically

Just substitute代入するだけ

１点関数を古典的に評価する

Example 　例

= ?

Quiz 　小テスト

k dim irrep of SU(2) 　の k 次元既約表現

The answer

The correct answer

One point function --- result

Gravity side

AdS/CFT correspondence

IIB SuperstringAdS5 x S5

4dim N=4 SYMSU(N)

Interface ??

D3 system

N D3-branes0123 direction

AdS5 x S5

Near horizon

4dim N=4 SYM

open stringlow energy

type IIB string

D3-D5 system

AdS5 x S5+

D5-brane probeAdS4 x S2

(with magnetic flux)

Near horizon

SU(N-k) SU(N)Interface

Low energyN D3-brane0123 direction

1 D5-brane 012 456 direction

N-k

Description in the gravity side

D5-brane

magnetic flux

[Karch, Randall]

One point function

GKPW

source

Scalar field

Result

Comparison to the gauge theory side

（　： Large ）

Gauge

（　： Large ）Gravity

Agree

Summary

One point function

One point function

N=4 SYMAdS5 x S5

Classical calculation

SU(N-k)

probe D5-brane

SU(N)

Agree

GKPW

Why agree?

Calculation in gauge theory sideValid in

Calculation in gravity sideValid in

？

Gravity side

Positive power series in

cf [Berenstein, Maldacena, Nastase]

since k is large.

Future problem

Can reproduce from the perturbative calculation in the gauge theory side?

Thank you