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Adding flavor to AdS/CFT

Andreas Karch, Emanuel Katz

TL;DR

Karch and Katz propose embedding fundamental quarks into AdS/CFT by adding spacetime-filling, probe D-branes, effectively introducing an open-string sector in the bulk. They show these branes can exist without backreaction (the probe limit) and can end in AdS space due to the Breitenlohner-Freedman bound, while tadpoles are avoided by wrapping trivial cycles, enabling two distinct flavor brane sets that realize SU(M) × SU(M) chiral symmetry. The authors analyze several supersymmetric examples (D3-D7, orbifolds, and the conifold/Klebanov-Strassler backgrounds), verify supersymmetry via κ-symmetry, and discuss how the chiral condensate and meson spectra arise from bulk fields on the flavor branes. The work lays a framework to study flavored holographic QCD-like theories in the quenched limit and to extend to more realistic, non-supersymmetric contexts.

Abstract

Coupling fundamental quarks to QCD in the dual string representation corresponds to adding the open string sector. Flavors therefore should be represented by space-time filling D-branes in the dual 5d closed string background. This requires several interesting properties of D-branes in AdS. D-branes have to be able to end in thin air in order to account for massive quarks, which only live in the UV region. They must come in distinct sets, representing the chiral global symmetry, with a bifundamental field playing the role of the chiral condensate. We show that these expectations are born out in several supersymmetric examples. To analyze most of these properties it is not necessary to go beyond the probe limit in which one neglects the backreaction of the flavor D-branes.

Adding flavor to AdS/CFT

TL;DR

Karch and Katz propose embedding fundamental quarks into AdS/CFT by adding spacetime-filling, probe D-branes, effectively introducing an open-string sector in the bulk. They show these branes can exist without backreaction (the probe limit) and can end in AdS space due to the Breitenlohner-Freedman bound, while tadpoles are avoided by wrapping trivial cycles, enabling two distinct flavor brane sets that realize SU(M) × SU(M) chiral symmetry. The authors analyze several supersymmetric examples (D3-D7, orbifolds, and the conifold/Klebanov-Strassler backgrounds), verify supersymmetry via κ-symmetry, and discuss how the chiral condensate and meson spectra arise from bulk fields on the flavor branes. The work lays a framework to study flavored holographic QCD-like theories in the quenched limit and to extend to more realistic, non-supersymmetric contexts.

Abstract

Coupling fundamental quarks to QCD in the dual string representation corresponds to adding the open string sector. Flavors therefore should be represented by space-time filling D-branes in the dual 5d closed string background. This requires several interesting properties of D-branes in AdS. D-branes have to be able to end in thin air in order to account for massive quarks, which only live in the UV region. They must come in distinct sets, representing the chiral global symmetry, with a bifundamental field playing the role of the chiral condensate. We show that these expectations are born out in several supersymmetric examples. To analyze most of these properties it is not necessary to go beyond the probe limit in which one neglects the backreaction of the flavor D-branes.

Paper Structure

This paper contains 14 sections, 34 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Spacetime filling branes and Tadpoles
  3. The probe limit
  4. Tadpoles
  5. Worldvolume Scalars: D-branes vanishing in thin air
  6. Interactions and the subleading term in AdS/CFT
  7. $SU(M_1) \times SU(M_2)$ global symmetry
  8. $\kappa$- Symmetry
  9. Chiral symmetry and the Conifold
  10. Chiral symmetry from NS5 branes
  11. Chiral multiplets from D7 branes on orbifolds
  12. The conifold
  13. Conclusions
  14. Image of a Holomorphic Curve on $S^5$

Figures (2)

  • Figure 1: D3 D5 system with mass term for defect scalars, in the corresponding 5d AdS spacetime, the D5 brane ends in the middle of nowhere.
  • Figure 2: ${\cal N}=2$ SYM with ${\cal N}=2$ flavors from D6 branes and ${\cal N}=1$ flavors from D6' branes.