Mass deformed ABJM and $\mathcal{PT}$ symmetry

TL;DR

This paper studies mass and FI deformations of ABJM theory that preserve supersymmetry, revealing a generalized $ ext{PT}$ symmetry in the spectral problem, which ensures real partition functions and aligns with holographic predictions.

Contribution

It demonstrates the existence of a generalized $ ext{PT}$ symmetry in deformed ABJM theory, enabling direct computation of the free energy from real deformations without analytic continuation.

Findings

Partition function remains real due to $ ext{PT}$ symmetry.

Results align with holographic predictions.

New approach avoids analytic continuation in deformations.

Abstract

We consider real mass and FI deformations of ABJM theory preserving supersymmetry in the large $N$ limit, and compare with holographic results. On the field theory side, the problems amounts to a spectral problem of a non-Hermitian Hamiltonian. For certain values of the deformation parameters this is invariant under an antiunitary operator (generalised $\mathcal{PT}$ symmetry), which ensures the partition function remains real and allows us to calculate the free energy using tools from statistical physics. The results obtained are compatible with previous work, the important new feature being that these are obtained directly from the real deformations, without analytic continuation.