Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Superconformal index for large N quiver Chern-Simons theories

Yosuke Imamura, Daisuke Yokoyama, Shuichi Yokoyama

TL;DR

We develop a practical framework to compute the $N=2$ superconformal index for large $N$ quiver Chern-Simons theories via localization, obtaining a factorized form $I^{(0)}I^{(+)}I^{(-)}$ and treating diagonal monopole sectors with a Gaussian integration over neutral holonomies. Applying the method to theories dual to homogeneous Sasaki-Einstein manifolds $V^{5,2}$, $Q^{1,1,1}$, $Q^{2,2,2}$, $M^{1,1,1}$, and $N^{0,1,0}$, the authors verify that the index respects the expected isometry Weyl groups and, in several cases, exhibits symmetry enhancements consistent with the gravity side. They extend the formalism to chiral theories and to theories with flavors, showing how flavor fields modify the letter index and zero-point contributions while preserving diagonal-monopole factorization. The results provide nonperturbative checks of AdS$_4$/CFT$_3$ dualities and motivate further analysis of non-diagonal monopoles and KK spectra on gravity backgrounds.

Abstract

We investigate the N=2 superconformal index for supersymmetric quiver Chern-Simons theories with large N gauge groups. After general arguments about the large N limit, we compute the first few terms in the series expansion of the index for theories proposed as dual theories to homogeneous spaces V^{5,2}, Q^{1,1,1}, Q^{2,2,2}, M^{1,1,1}, and N^{0,1,0}. We confirm that the indices have symmetries expected from the isometries of dual manifolds.

Superconformal index for large N quiver Chern-Simons theories

TL;DR

We develop a practical framework to compute the superconformal index for large quiver Chern-Simons theories via localization, obtaining a factorized form and treating diagonal monopole sectors with a Gaussian integration over neutral holonomies. Applying the method to theories dual to homogeneous Sasaki-Einstein manifolds , , , , and , the authors verify that the index respects the expected isometry Weyl groups and, in several cases, exhibits symmetry enhancements consistent with the gravity side. They extend the formalism to chiral theories and to theories with flavors, showing how flavor fields modify the letter index and zero-point contributions while preserving diagonal-monopole factorization. The results provide nonperturbative checks of AdS/CFT dualities and motivate further analysis of non-diagonal monopoles and KK spectra on gravity backgrounds.

Abstract

We investigate the N=2 superconformal index for supersymmetric quiver Chern-Simons theories with large N gauge groups. After general arguments about the large N limit, we compute the first few terms in the series expansion of the index for theories proposed as dual theories to homogeneous spaces V^{5,2}, Q^{1,1,1}, Q^{2,2,2}, M^{1,1,1}, and N^{0,1,0}. We confirm that the indices have symmetries expected from the isometries of dual manifolds.

Paper Structure

This paper contains 12 sections, 132 equations, 7 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Formula for the index
  3. Large $N$ limit and the factorization
  4. Factorization of the prefactor
  5. Example 1: $V^{5,2}$
  6. Factorization in chiral theories
  7. Example 2: $Q^{1,1,1}$
  8. Example 3: $Q^{2,2,2}$
  9. Example 4: $M^{1,1,1}$
  10. Adding flavors
  11. Example 5: $N^{0,1,0}$
  12. Conclusions

Figures (7)

  • Figure 1: The quiver diagram of a Chern-Simons theory dual to $V^{5,2}/{\bf Z}_k$.
  • Figure 2: The quiver diagram and the brane tiling for a theory dual to $Q^{1,1,1}/{\bf Z}_k$.
  • Figure 3: The quiver diagram and the brane tiling for a theory dual to $Q^{1,1,1}/{\bf Z}_k$. The Chern-Simons levels are different from Figure \ref{['q111quiv2.eps']}.
  • Figure 4: The quiver diagram and the brane tiling for a theory dual to $Q^{2,2,2}/{\bf Z}_k$.
  • Figure 5: The quiver diagram and the brane tiling for a dual theory to $Q^{2,2,2}/{\bf Z}_k$ are shown.
  • ...and 2 more figures