Enhanced Supersymmetry of Nonrelativistic ABJM Theory

TL;DR

This paper investigates how supersymmetry is enhanced in the nonrelativistic limit of ABJM theory at levels 1 and 2, revealing maximal supercharges and a super Schrödinger algebra similar to known cases.

Contribution

It demonstrates the supersymmetry enhancement in nonrelativistic ABJM theory, identifying additional supercharges and the structure of the super Schrödinger algebra, especially involving monopole operators.

Findings

Maximal 14 supercharges achieved in nonrelativistic limit.

Super Schrödinger algebra is isomorphic to the PPPP case.

Monopole operators play a key role in supersymmetry enhancement.

Abstract

We study the supersymmetry enhancement of nonrelativistic limits of the ABJM theory for Chern-Simons level $k=1,2$. The special attention is paid to the nonrelativistic limit (known as `PAAP' case) containing both particles and antiparticles. Using supersymmetry transformations generated by the monopole operators, we find additional 2 kinematical, 2 dynamical, and 2 conformal supercharges for this case. Combining with the original 8 kinematical supercharges, the total number of supercharges becomes maximal: 14 supercharges, like in the well-known PPPP limit. We obtain the corresponding super Schr\"odinger algebra which appears to be isomorphic to the one of the PPPP case. We also discuss the role of monopole operators in supersymmetry enhancement and partial breaking of supersymmetry in nonrelativistic limit of the ABJM theory.