![Page 1: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/1.jpg)
Holographic Interface
![Page 2: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/2.jpg)
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
![Page 3: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/3.jpg)
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
![Page 4: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/4.jpg)
(ゲージ理論)=(重力理論) の証拠(Gauge theory)=(Gravity)
Evidence for
![Page 5: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/5.jpg)
Interface ?
![Page 6: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/6.jpg)
QFT QFT
Interface
![Page 7: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/7.jpg)
CFT
Point of view―Extension of boundary CFT
CFTBoundary CFTInterface CFT
BoundaryInterface
境界のある CFT の拡張
![Page 8: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/8.jpg)
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
![Page 9: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/9.jpg)
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
![Page 10: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/10.jpg)
Holography ?
![Page 11: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/11.jpg)
Holography
![Page 12: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/12.jpg)
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
![Page 13: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/13.jpg)
AdS/CFT Correspondence
Certain gravitytheory(String theory)
Quantum field theory without gravity
Interface Brane, etc
Want to check
![Page 14: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/14.jpg)
Physical quantities
One point function of local operators
x
![Page 15: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/15.jpg)
Strategy
QFT
Gauge theoryGravity
Prescription
Result in gravity
Classical calculation
Result in gauge theory
CompareQFT
One point function
![Page 16: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/16.jpg)
Result
Agree nontrivially非自明な一致
![Page 17: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/17.jpg)
Gravity Gauge theory
①②
Why agree ?なぜ一致?
重力 ゲージ理論
![Page 18: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/18.jpg)
Gauge theory side
![Page 19: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/19.jpg)
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
![Page 20: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/20.jpg)
Large N limit
: gauge coupling
Large N limitFix
ゲージ結合定数
固定
: ’t Hooft coupling
![Page 21: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/21.jpg)
is the loop expansion parameterがループ展開のパラメータ
![Page 22: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/22.jpg)
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)
![Page 23: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/23.jpg)
1/2BPS Nahm equation
Solution
k dim irrep of SU(2)SU(2) の k 次元既約表現
![Page 24: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/24.jpg)
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
![Page 25: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/25.jpg)
One point function
Traceless symmetric
Chiral primary operator
![Page 26: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/26.jpg)
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
![Page 27: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/27.jpg)
Example 例
= ?
Quiz 小テスト
k dim irrep of SU(2) の k 次元既約表現
![Page 28: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/28.jpg)
The answer
![Page 29: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/29.jpg)
The correct answer
![Page 30: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/30.jpg)
One point function --- result
![Page 31: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/31.jpg)
Gravity side
![Page 32: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/32.jpg)
AdS/CFT correspondence
IIB SuperstringAdS5 x S5
4dim N=4 SYMSU(N)
Interface ??
![Page 33: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/33.jpg)
D3 system
N D3-branes0123 direction
AdS5 x S5
Near horizon
4dim N=4 SYM
open stringlow energy
type IIB string
![Page 34: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/34.jpg)
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
![Page 35: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/35.jpg)
Description in the gravity side
D5-brane
magnetic flux
[Karch, Randall]
![Page 36: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/36.jpg)
One point function
GKPW
source
Scalar field
![Page 37: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/37.jpg)
Result
![Page 38: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/38.jpg)
Comparison to the gauge theory side
( : Large )
Gauge
( : Large )Gravity
Agree
![Page 39: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/39.jpg)
Summary
![Page 40: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/40.jpg)
One point function
One point function
N=4 SYMAdS5 x S5
Classical calculation
SU(N-k)
probe D5-brane
SU(N)
Agree
GKPW
![Page 41: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/41.jpg)
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.
![Page 42: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/42.jpg)
Future problem
Can reproduce from the perturbative calculation in the gauge theory side?
![Page 43: Holographic Interface. Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv:1205.1674 [hep-th] K. Nagasaki, H. Tanida, SY, JHEP 1201 (2012)](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649c775503460f9492c27f/html5/thumbnails/43.jpg)
Thank you