Orientifold ABJM Matrix Model: Chiral Projections and Worldsheet Instantons

TL;DR

This paper analyzes the partition function of orientifold ABJM theories, revealing a Fermi gas representation with chiral projections and providing a direct method to compute worldsheet instanton invariants.

Contribution

It introduces a Fermi gas formulation for orthosymplectic supergroup theories with chiral projections and proposes an identity for calculating Gopakumar-Vafa invariants.

Findings

Partition functions can be realized as Fermi gas systems with chiral projections.

An identity is proposed to compute Gopakumar-Vafa invariants directly.

The approach connects orthosymplectic and unitary supergroup theories.

Abstract

We study the partition function of the orientifold ABJM theory, which is a superconformal Chern-Simons theory associated with the orthosymplectic supergroup. We find that the partition function associated with any orthosymplectic supergroup can be realized as the partition function of a Fermi gas system whose density matrix is identical to that associated with the corresponding unitary supergroup with a projection to the even or odd chirality. Furthermore we propose an identity which gives directly all of the Gopakumar-Vafa invariants for the worldsheet instanton effects in the chirally projected theories.