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AdS Branes Corresponding to Superconformal Defects

Satoshi Yamaguchi

TL;DR

The work expands the AdS/dCFT dictionary by constructing supersymmetric $AdS_4\times L_2$ D5-brane and $AdS_3\times L_3$ M5-brane backgrounds in $AdS_5\times X_5$ (with $X_5$ Sasaki-Einstein and $X_7$ weak $G_2$), tying them to 3d ${\cal N}=1$ and 2d ${\cal N}=(1,0)$ superconformal defects respectively. It derives Killing spinors and kappa-symmetry projections, establishing precise conditions on bending and worldvolume flux that preserve the expected supersymmetry, such as $f=-M$ for D5-branes and $f=\frac{M}{1+\sqrt{1+M^2}}$ for M5-branes. A key explicit result is the $AdS_4\times T^2$ brane in $AdS_5\times S^5$, which exhibits an RG flow to $AdS_4\times S^2$ and illustrates defect fixed-point transitions in the brane picture. The paper further demonstrates the M-theory extension with associative submanifolds yielding 2d ${\cal N}=(1,0)$ SUSY, thereby broadening the class of holographic defect constructions and providing a framework to analyze defect CFTs and their flows.

Abstract

We investigate an AdS_4 x L_2 D5-brane in AdS_5 x X_5 space-time, in the context of AdS/dCFT correspondence. Here, X_5 is a Sasaki-Einstein manifold and L_2 is a submanifold of X_5. This brane has the same supersymmetry as the 3-dimensional N=1 superconformal symmetry if L_2 is a special Legendrian submanifold in X_5. In this case, this brane is supposed to correspond to a superconformal wall defect in 4-dimensional N=4 super Yang-Mills theory. We construct these new string backgrounds and show they have the correct supersymmetry, also in the case with non-trivial gauge flux on L_2. The simplest new example is AdS_4 x T^2 brane in AdS_5 x S^5. We construct the brane solution expressing the RG flow between two different defects. We also perform similar analysis for an AdS_3 x L_3 M5-brane in AdS_4 x X_7, for a weak G_2 manifold X_7 and its submanifold L_3. This system has the same supersymmetry as 2-dimensional N=(1,0) global superconformal symmetry, if L_3 is an associative submanifold.

AdS Branes Corresponding to Superconformal Defects

TL;DR

The work expands the AdS/dCFT dictionary by constructing supersymmetric D5-brane and M5-brane backgrounds in (with Sasaki-Einstein and weak ), tying them to 3d and 2d superconformal defects respectively. It derives Killing spinors and kappa-symmetry projections, establishing precise conditions on bending and worldvolume flux that preserve the expected supersymmetry, such as for D5-branes and for M5-branes. A key explicit result is the brane in , which exhibits an RG flow to and illustrates defect fixed-point transitions in the brane picture. The paper further demonstrates the M-theory extension with associative submanifolds yielding 2d SUSY, thereby broadening the class of holographic defect constructions and providing a framework to analyze defect CFTs and their flows.

Abstract

We investigate an AdS_4 x L_2 D5-brane in AdS_5 x X_5 space-time, in the context of AdS/dCFT correspondence. Here, X_5 is a Sasaki-Einstein manifold and L_2 is a submanifold of X_5. This brane has the same supersymmetry as the 3-dimensional N=1 superconformal symmetry if L_2 is a special Legendrian submanifold in X_5. In this case, this brane is supposed to correspond to a superconformal wall defect in 4-dimensional N=4 super Yang-Mills theory. We construct these new string backgrounds and show they have the correct supersymmetry, also in the case with non-trivial gauge flux on L_2. The simplest new example is AdS_4 x T^2 brane in AdS_5 x S^5. We construct the brane solution expressing the RG flow between two different defects. We also perform similar analysis for an AdS_3 x L_3 M5-brane in AdS_4 x X_7, for a weak G_2 manifold X_7 and its submanifold L_3. This system has the same supersymmetry as 2-dimensional N=(1,0) global superconformal symmetry, if L_3 is an associative submanifold.

Paper Structure

This paper contains 15 sections, 74 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. IIB $AdS_4\times L_2$ D5-brane in $AdS_5\times X_5$
  3. Supersymmetry of the closed string background
  4. Supersymmetry of D-brane background
  5. $AdS_4\times T^2$ brane and its flow to $AdS_4\times S^2$
  6. $AdS_3\times L_3$ M5-brane in $AdS_4\times X_7$
  7. Supersymmetry of the supergravity background
  8. Supersymmetry of the brane background
  9. Conclusion and Discussion
  10. Sasaki-Einstein manifolds and special Legendrian submanifolds
  11. Definitions and properties
  12. Proof of the formula (\ref{['IIB-key-formula']})
  13. Weak $G_2$ manifolds and associative submanifolds
  14. Definitions and properties
  15. Proof of the formula (\ref{['M-key-formula']})

Figures (1)

  • Figure 1: The image of the flow from $T^2$-brane to $S^2$-brane. (a) UV limit: The D3-branes are sitting at the tip of the $T^2$ cone. In the near horizon limit, the D5-brane becomes $AdS_4\times T^{2}$ and corresponds to $T^2$ defect. (b) Intermediate scale: The defect theory has the RG flow. (c) IR limit: The D3-branes are sitting on a flat D5-brane. In the near horizon limit, the D5-brane becomes $AdS_4\times S^{2}$ and corresponds to $S^2$ defect.