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On the Superconformal Index of N=1 IR Fixed Points: A Holographic Check

Abhijit Gadde, Leonardo Rastelli, Shlomo S. Razamat, Wenbin Yan

TL;DR

The paper tests Romelsberger's prescription for computing the ${ m N}=1$ superconformal index along RG flows to IR fixed points, focusing on the ${ m Y}^{p,q}$ quivers and the conifold case. It develops a large-$N$ field-theory computation via matrix-model saddle points, yielding a closed-form index for the ${ m Y}^{p,q}$ family and handling decoupled ${U}(1)$ factors to enable gravity comparison. On the gravity side, it reproduces the conifold index from KK reductions on ${AdS}_5\times T^{1,1}$ and finds exact agreement with the large-$N$ field-theory result. Collectively, these results provide a stringent check of the IR index prescription and strengthen the bulk/boundary dictionary in AdS/CFT for toric quiver theories.

Abstract

We evaluate the superconformal index of the Y^{p,q} quiver gauge theories using Romeslberger's prescription. For the conifold quiver Y^{1,0} we find exact agreement at large N with a previous calculation in the dual AdS_5 X T^{1,1} supergravity.

On the Superconformal Index of N=1 IR Fixed Points: A Holographic Check

TL;DR

The paper tests Romelsberger's prescription for computing the superconformal index along RG flows to IR fixed points, focusing on the quivers and the conifold case. It develops a large- field-theory computation via matrix-model saddle points, yielding a closed-form index for the family and handling decoupled factors to enable gravity comparison. On the gravity side, it reproduces the conifold index from KK reductions on and finds exact agreement with the large- field-theory result. Collectively, these results provide a stringent check of the IR index prescription and strengthen the bulk/boundary dictionary in AdS/CFT for toric quiver theories.

Abstract

We evaluate the superconformal index of the Y^{p,q} quiver gauge theories using Romeslberger's prescription. For the conifold quiver Y^{1,0} we find exact agreement at large N with a previous calculation in the dual AdS_5 X T^{1,1} supergravity.

Paper Structure

This paper contains 10 sections, 55 equations, 7 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Review of the ${\cal N}=1$ index
  3. Romelsberger's prescription
  4. Computing the index
  5. A universal result about ${\cal N}=2 \to {\cal N}=1$ flows
  6. The $Y^{p,q}$ quiver gauge theories
  7. Toric Duality
  8. Large $N$ evaluation of the index
  9. $T^{1,1}$ Index from Supergravity
  10. $\mathcal{N}=1$ superconformal shortening conditions and the index

Figures (7)

  • Figure 1: Left: quiver diagram for $Y^{4,4}$. Right: quiver diagram for $Y^{4,0}$.
  • Figure 2: Quiver diagram for $Y^{1,0}$ (the conifold theory $T^{1,1}$). The solid (cyan) arrow represents the $U$ field, the dash-dot (blue) arrow represents the $Y$ field and the dashed (green) arrow represents the $Z$ field.
  • Figure 3: Quiver of $Y^{1,1}$ theory. Solid (cyan) arrow represents $U$ field, dash-dot-dot arrow (red) represents $V$ field and dash-dot arrow (blue) represents $Y$ field.
  • Figure 4: Quiver diagram for $Y^{4,2}$, obtained from $Y^{4,4}$ by using the procedure in Benvenuti:2004dy.
  • Figure 5: A different quiver diagram for $Y^{4,2}$, related to the diagram above by toric duality.
  • ...and 2 more figures