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Holography and Defect Conformal Field Theories

Oliver DeWolfe, Daniel Z. Freedman, Hirosi Ooguri

TL;DR

The paper constructs and analyzes a holographic dual for a defect conformal field theory realized by a D3/D5-brane system: AdS_5×S^5 with an AdS_4×S^2 defect is dual to 4D N=4 SU(N) SYM in R^4 coupled to a 3D N=4 defect hypermultiplet. It provides a complete defect action via the superspace boundary method, derives the KK spectrum of D5 open-string modes and matches them to gauge-invariant defect operators with integer conformal dimensions, and computes defect and mixed correlators from gravity to compare with weak-coupling field theory predictions. The study reveals plenty of structure from defect conformal symmetry, including one-point and mixed correlators, and discusses the (partial) quantum conformality results, highlighting differences from the standard N=4 SYM non-renormalization theorems. It also identifies open questions, such as proving non-Abelian conformality, exploring generalizations, and understanding backreaction and nonperturbative aspects of the dCFT holography.

Abstract

We develop both the gravity and field theory sides of the Karch-Randall conjecture that the near-horizon description of a certain D5-D3 brane configuration in string theory, realized as AdS_5 x S^5 bisected by an AdS_4 x S^2 "brane", is dual to N=4 Super Yang-Mills theory in R^4 coupled to an R^3 defect. We propose a complete Lagrangian for the field theory dual, a novel "defect superconformal field theory" wherein a subset of the fields of N=4 SYM interacts with a d=3 SU(N) fundamental hypermultiplet on the defect preserving conformal invariance and 8 supercharges. The Kaluza-Klein reduction of wrapped D5 modes on AdS_4 x S^2 leads to towers of short representations of OSp(4|4), and we construct the map to a set of dual gauge-invariant defect operators O_3 possessing integer conformal dimensions. Gravity calculations of <O_4> and <O_4O_3> are given. Spacetime and N-dependence matches expectations from dCFT, while the behavior as functions of lambda = g^2 N at strong and weak coupling is generically different. We comment on a class of correlators for which a non-renormalization theorem may still exist. Partial evidence for the conformality of the quantum theory is given, including a complete argument for the special case of a U(1) gauge group. Some weak coupling arguments which illuminate the duality are presented.

Holography and Defect Conformal Field Theories

TL;DR

The paper constructs and analyzes a holographic dual for a defect conformal field theory realized by a D3/D5-brane system: AdS_5×S^5 with an AdS_4×S^2 defect is dual to 4D N=4 SU(N) SYM in R^4 coupled to a 3D N=4 defect hypermultiplet. It provides a complete defect action via the superspace boundary method, derives the KK spectrum of D5 open-string modes and matches them to gauge-invariant defect operators with integer conformal dimensions, and computes defect and mixed correlators from gravity to compare with weak-coupling field theory predictions. The study reveals plenty of structure from defect conformal symmetry, including one-point and mixed correlators, and discusses the (partial) quantum conformality results, highlighting differences from the standard N=4 SYM non-renormalization theorems. It also identifies open questions, such as proving non-Abelian conformality, exploring generalizations, and understanding backreaction and nonperturbative aspects of the dCFT holography.

Abstract

We develop both the gravity and field theory sides of the Karch-Randall conjecture that the near-horizon description of a certain D5-D3 brane configuration in string theory, realized as AdS_5 x S^5 bisected by an AdS_4 x S^2 "brane", is dual to N=4 Super Yang-Mills theory in R^4 coupled to an R^3 defect. We propose a complete Lagrangian for the field theory dual, a novel "defect superconformal field theory" wherein a subset of the fields of N=4 SYM interacts with a d=3 SU(N) fundamental hypermultiplet on the defect preserving conformal invariance and 8 supercharges. The Kaluza-Klein reduction of wrapped D5 modes on AdS_4 x S^2 leads to towers of short representations of OSp(4|4), and we construct the map to a set of dual gauge-invariant defect operators O_3 possessing integer conformal dimensions. Gravity calculations of <O_4> and <O_4O_3> are given. Spacetime and N-dependence matches expectations from dCFT, while the behavior as functions of lambda = g^2 N at strong and weak coupling is generically different. We comment on a class of correlators for which a non-renormalization theorem may still exist. Partial evidence for the conformality of the quantum theory is given, including a complete argument for the special case of a U(1) gauge group. Some weak coupling arguments which illuminate the duality are presented.

Paper Structure

This paper contains 17 sections, 138 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Description of the System
  3. Brane construction
  4. Near-horizon Limit
  5. Correlators in a defect CFT
  6. String theory side
  7. Correlators of dCFT from gravity
  8. D5-brane open-string modes
  9. D5-brane closed-string modes
  10. Field theory action
  11. The superspace boundary
  12. Action for field theory with defect
  13. Operator matching
  14. Perturbative Field Theory
  15. Quantum Conformal Invariance?
  16. ...and 2 more sections

Figures (2)

  • Figure 1: Feynman diagrams through one-loop order for the correlators $\langle \bar{q} M q(\vec{y}_1) \, \bar{q}(\vec{y}_2) \, q(\vec{y}_3) \rangle$ where $M$ is either $\sigma^A$ or $1$.
  • Figure 2: The generic contribution to the one point function $\langle {\rm Tr}\, (X_V)^k \rangle$ with all $k$$X_V$ lines pinned to the defect (vertical line), depicted here for $k=3$.