Orthosymplectic Chern-Simons Matrix Model and Chirality Projection

TL;DR

This paper proves the equivalence of the density matrix in an orthosymplectic Chern-Simons theory with a chirally projected ABJM theory, extending to fractional branes, and identifies related Gopakumar-Vafa invariants.

Contribution

It generalizes the match between orthosymplectic Chern-Simons and chirally projected ABJM theories to include fractional branes and computes initial Gopakumar-Vafa invariants.

Findings

Density matrix equivalence proven for general cases with fractional branes.

Identification of initial Gopakumar-Vafa invariants for the grand potential.

Extension of previous results to broader classes of theories.

Abstract

Recently it was found that the density matrix for a certain orthosymplectic Chern-Simons theory matches with that for the ABJM theory with the odd chiral projection. We prove this fact for a general case with the inclusion of fractional branes. We also identify the first few diagonal Gopakumar-Vafa invariants for the grand potential constructed from the chirally projected density matrix.