Holographic Interface

Collaboration with K. Nagasaki H. Tanida K. Nagasaki, SY, arXiv: [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 Interface

CFT Point of view―Extension of boundary CFT CFT Boundary CFTInterface CFT Boundary Interface 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

Statistical mechanics 統計力学 Extra dimensions in 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 gravity theory (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 Compare QFT One point function

Result Agree nontrivially 非自明な一致

GravityGauge 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 limit Fix 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 condition that 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 Superstring AdS5 x S5 4dim N=4 SYM SU(N) Interface ? ? ?

D3 system N D3-branes 0123 direction AdS5 x S5 Near horizon 4dim N=4 SYM open string low energy type IIB string

D3-D5 system AdS5 x S5 + D5-brane probe AdS4 x S2 (with magnetic flux) Near horizon SU(N-k) SU(N) Interface Low energy N D3-brane 0123 direction 1 D5-brane 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 N=4 SYMAdS5 x S5 Classical calculation SU(N-k) probe D5-brane SU(N) Agree GKPW

Why agree? Calculation in gauge theory side Valid in Calculation in gravity side Valid 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