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The dual of Janus -:- an interface CFT

A. B. Clark, D. Z. Freedman, A. Karch, M. Schnabl

TL;DR

The paper constructs and tests an interface CFT dual to the smooth Janus AdS/CFT solution, modeling it with N=4 SYM on two half-spaces separated by a planar interface that induces a jump in the gauge coupling through a marginal operator ${\cal L}'$. Using conformal perturbation theory, the authors show that quantum-level SO(3,2) symmetry is preserved and derive protected results, obtaining agreement with gravity for quantities like $\langle {\cal L}'\rangle$ and the vanishing of $\langle T_{\mu\nu}\rangle$. They also analyze two-point functions and operator dimensions in the presence of the defect, demonstrating Cardy-form behavior and protected correlators, consistent with an ICFT. An alternate D3-brane–inspired approach yields a perturbative framework with jump conditions for the gauge field across the interface, providing a complementary verification of the duality. Overall, the work provides nontrivial cross-checks of AdS/CFT in a defect/interface setup and clarifies how a position-dependent coupling realizes a stable, conformal interface theory.

Abstract

We propose and study a specific gauge theory dual of the smooth, non-supersymmetric (and apparently stable) Janus solution of Type IIB supergravity found in hep-th/0304129. The dual field theory is N=4 SYM theory on two half-spaces separated by a planar interface with different coupling constants in each half-space. We assume that the position dependent coupling multiplies the operator L' which is the fourth descendent of the primary Tr(X^I X^J) and closely related to the N=4 Lagrangian density. At the classical level supersymmetry is broken explicitly, but SO(3,2) conformal symmetry is preserved. We use conformal perturbation theory to study various correlation functions to first and second order in the discontinuity of g^2_{YM}, confirming quantum level conformal symmetry. Certain quantities such as the vacuum expectation value <L'> are protected to all orders in g^2_{YM}N, and we find perfect agreement between the weak coupling value in the gauge theory and the strong coupling gravity result. SO(3,2) symmetry requires vanishing vacuum energy, <T_{μν}>=0, and this is confirmed in first order in the discontinuity.

The dual of Janus -:- an interface CFT

TL;DR

The paper constructs and tests an interface CFT dual to the smooth Janus AdS/CFT solution, modeling it with N=4 SYM on two half-spaces separated by a planar interface that induces a jump in the gauge coupling through a marginal operator . Using conformal perturbation theory, the authors show that quantum-level SO(3,2) symmetry is preserved and derive protected results, obtaining agreement with gravity for quantities like and the vanishing of . They also analyze two-point functions and operator dimensions in the presence of the defect, demonstrating Cardy-form behavior and protected correlators, consistent with an ICFT. An alternate D3-brane–inspired approach yields a perturbative framework with jump conditions for the gauge field across the interface, providing a complementary verification of the duality. Overall, the work provides nontrivial cross-checks of AdS/CFT in a defect/interface setup and clarifies how a position-dependent coupling realizes a stable, conformal interface theory.

Abstract

We propose and study a specific gauge theory dual of the smooth, non-supersymmetric (and apparently stable) Janus solution of Type IIB supergravity found in hep-th/0304129. The dual field theory is N=4 SYM theory on two half-spaces separated by a planar interface with different coupling constants in each half-space. We assume that the position dependent coupling multiplies the operator L' which is the fourth descendent of the primary Tr(X^I X^J) and closely related to the N=4 Lagrangian density. At the classical level supersymmetry is broken explicitly, but SO(3,2) conformal symmetry is preserved. We use conformal perturbation theory to study various correlation functions to first and second order in the discontinuity of g^2_{YM}, confirming quantum level conformal symmetry. Certain quantities such as the vacuum expectation value <L'> are protected to all orders in g^2_{YM}N, and we find perfect agreement between the weak coupling value in the gauge theory and the strong coupling gravity result. SO(3,2) symmetry requires vanishing vacuum energy, <T_{μν}>=0, and this is confirmed in first order in the discontinuity.

Paper Structure

This paper contains 16 sections, 74 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The Janus solution.
  3. Gravity predictions for the dual gauge theory.
  4. Proposed gauge theory dual
  5. Calculations using conformal perturbation theory
  6. $1$-point function of ${\cal L}'$
  7. $\langle\, T_{\mu\nu}(z) \,\rangle_{{\rm Janus}}$
  8. Two point functions
  9. $\langle\, \mathop{\rm Tr}\nolimits X^{k_1}\, \mathop{\rm Tr}\nolimits X^{k_2}\dots \mathop{\rm Tr}\nolimits X^{k_n} \,\rangle_\gamma$ in gauge theory and gravity
  10. An alternate approach to the Janus dual
  11. $\langle\, {\cal L}' \,\rangle$ and $\langle\, T_{\mu\nu} \,\rangle$ again
  12. ${\cal N} =1$ interface SUSY and its failure for ${\cal N} =4$
  13. N=1 supersymmetry with chiral multiplet
  14. N=1 supersymmetry with vector multiplet
  15. ${\cal N} =4$ SYM theory
  16. ...and 1 more sections

Figures (1)

  • Figure 1: Conformal spatial geometries of a 2+1 dimensional version of the Janus solution for (a) global coordinates and (b) for Poincaré patch coordinates on the $AdS_2$ slices. The boundary is indicated by bold lines on which the dilaton takes values $\phi_{\pm}$. In (a) the spatial geometry is the larger "half" of a 2-sphere. In (b) it is the larger "half" of the plane, and the boundary is the set of two half lines, which meet at the defect. The coordinate $z$ in (\ref{['mink']}) is the radial coordinate in (b), with origin at the defect.