Counting BPS Baryonic Operators in CFTs with Sasaki-Einstein duals

TL;DR

This paper develops a method to count BPS baryonic operators in certain supersymmetric gauge theories using D3 brane configurations and extracts geometric data of the dual Sasaki-Einstein manifolds from these counts.

Contribution

It provides explicit partition functions for BPS operators and formulas to derive geometric information about the internal cycles of Sasaki-Einstein manifolds.

Findings

Partition functions for BPS operators are explicitly constructed.

Geometric volumes of three-cycles in H are computed from partition functions.

A general framework links gauge theory operators to geometric properties of the dual manifold.

Abstract

We study supersymmetric D3 brane configurations wrapping internal cycles of type II backgrounds AdS(5) x H for a generic Sasaki-Einstein manifold H. These configurations correspond to BPS baryonic operators in the dual quiver gauge theory. In each sector with given baryonic charge, we write explicit partition functions counting all the BPS operators according to their flavor and R-charge. We also show how to extract geometrical information about H from the partition functions; in particular, we give general formulae for computing volumes of three cycles in H.