Chiral Ring Generating Functions & Branches of Moduli Space

TL;DR

This paper studies the counting of chiral primary operators in D3-brane worldvolume theories on Calabi-Yau spaces, revealing how multiple moduli space branches affect generating functions and operator counting.

Contribution

It uncovers the impact of multiple moduli space branches on chiral ring generating functions and connects operator counting to Fock space structures in the large N limit.

Findings

Additional branches lead to extra terms in generating functions.

Operator counting corresponds to a product of Fock spaces.

Large N limit reveals a bosonic Fock space structure.

Abstract

We consider the worldvolume theory of N D3-branes transverse to various non-compact Calabi-Yau spaces, and describe subtleties in the counting of chiral primary operators in such theories due to the presence of multiple branches of moduli space. Extra branches, beyond those directly related to the transverse geometry, result in additional terms in the generating functions for single- and multi-trace operators. Ideals in the N=1 chiral ring correspond to various branches and, in the large N limit, the operator counting reveals a product of Fock spaces, including the Fock space of bosons on the space transverse to the branes.