Holographic Interface
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Transcript of Holographic Interface
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