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D-Branes on the Conifold and N=1 Gauge/Gravity Dualities

Christopher P. Herzog, Igor R. Klebanov, Peter Ouyang

TL;DR

This work extends AdS/CFT to ${\cal N}=1$ gauge theories by placing D3-branes at a conifold apex, first realizing a conformal ${SU(N)\times SU(N)}$ theory dual to $AdS_5\times T^{1,1}$ with chiral primaries and dibaryons. It then introduces fractional D3-branes (wrapped D5-branes) to generate a logarithmic RG flow and an anomaly in the R-symmetry that is realized as a bulk Higgs mechanism, leading to the Klebanov-Tiseytlin cascade and, in the IR, the KS deformation of the conifold which yields confinement and chiral symmetry breaking. The paper provides detailed matching between gravity and field theory: beta-function structures, chiral anomalies, operator dimensions, and the spectrum of wrapped-brane states, and it derives IR phenomena such as the gluino condensate, domain walls, and the $q$-string tensions from the warped deformed conifold. Overall, it offers a concrete holographic framework for nonperturbative IR dynamics in ${\cal N}=1$ gauge theories, including RG cascades, confinement, and chiral symmetry phenomena, with quantitative connections between fluxes, geometry, and gauge-theory quantities.

Abstract

We review extensions of the AdS/CFT correspondence to gauge/ gravity dualities with N=1 supersymmetry. In particular, we describe the gauge/gravity dualities that emerge from placing D3-branes at the apex of the conifold. We consider first the conformal case, with discussions of chiral primary operators and wrapped D-branes. Next, we break the conformal symmetry by adding a stack of partially wrapped D5-branes to the system, changing the gauge group and introducing a logarithmic renormalization group flow. In the gravity dual, the effect of these wrapped D5-branes is to turn on the flux of 3-form field strengths. The associated RR 2-form potential breaks the U(1) R-symmetry to $Z_{2M}$ and we study this phenomenon in detail. This extra flux also leads to deformation of the cone near the apex, which describes the chiral symmetry breaking and confinement in the dual gauge theory.

D-Branes on the Conifold and N=1 Gauge/Gravity Dualities

TL;DR

This work extends AdS/CFT to gauge theories by placing D3-branes at a conifold apex, first realizing a conformal theory dual to with chiral primaries and dibaryons. It then introduces fractional D3-branes (wrapped D5-branes) to generate a logarithmic RG flow and an anomaly in the R-symmetry that is realized as a bulk Higgs mechanism, leading to the Klebanov-Tiseytlin cascade and, in the IR, the KS deformation of the conifold which yields confinement and chiral symmetry breaking. The paper provides detailed matching between gravity and field theory: beta-function structures, chiral anomalies, operator dimensions, and the spectrum of wrapped-brane states, and it derives IR phenomena such as the gluino condensate, domain walls, and the -string tensions from the warped deformed conifold. Overall, it offers a concrete holographic framework for nonperturbative IR dynamics in gauge theories, including RG cascades, confinement, and chiral symmetry phenomena, with quantitative connections between fluxes, geometry, and gauge-theory quantities.

Abstract

We review extensions of the AdS/CFT correspondence to gauge/ gravity dualities with N=1 supersymmetry. In particular, we describe the gauge/gravity dualities that emerge from placing D3-branes at the apex of the conifold. We consider first the conformal case, with discussions of chiral primary operators and wrapped D-branes. Next, we break the conformal symmetry by adding a stack of partially wrapped D5-branes to the system, changing the gauge group and introducing a logarithmic renormalization group flow. In the gravity dual, the effect of these wrapped D5-branes is to turn on the flux of 3-form field strengths. The associated RR 2-form potential breaks the U(1) R-symmetry to and we study this phenomenon in detail. This extra flux also leads to deformation of the cone near the apex, which describes the chiral symmetry breaking and confinement in the dual gauge theory.

Paper Structure

This paper contains 17 sections, 147 equations.

Table of Contents

  1. Introduction
  2. D3-branes on the Conifold
  3. Dimensions of Chiral Operators
  4. Wrapped D3-branes as "dibaryons"
  5. Other ways of wrapping D-branes over cycles of $T^{1,1}$
  6. The RG cascade
  7. Matching of the $\beta$-functions
  8. The Chiral Anomaly
  9. The Anomaly as a Classical Effect in Supergravity
  10. The Anomaly as Spontaneous Symmetry Breaking in $AdS_5$
  11. Deformation of the Conifold
  12. The First-Order Equations and Their Solution
  13. $SO(4)$ invariant expressions for the 3-forms
  14. Infrared Physics
  15. Dimensional Transmutation and Confinement
  16. ...and 2 more sections