Non-Relativistic Superstring Theories

TL;DR

This paper constructs a supersymmetric non-relativistic string theory with manifest symmetry, quantizes it, and explores its spectrum and generalizations, revealing similarities to Type IIB superstring theory with notable differences.

Contribution

It introduces a supersymmetric extension of non-relativistic string theory, quantizes it explicitly, and explores its spectrum and possible noncritical generalizations.

Findings

Spectrum similar to Type IIB superstring theory

Fermions are non-chiral

Infinite range of noncritical theories

Abstract

We construct a supersymmetric version of the ``critical'' non-relativistic bosonic string theory\cite{Kim:2007hb} with its manifest global symmetry. We introduce the anticommuting $bc$ CFT which is the super partner of the $\beta\gamma$ CFT. The conformal weights of the $b$ and $c$ fields are both 1/2. The action of the fermionic sector can be transformed into that of the relativistic superstring theory. We explicitly quantize the theory with manifest SO(8) symmetry and find that the spectrum is similar to that of Type IIB superstring theory. There is one notable difference: the fermions are non-chiral. We further consider ``noncritical'' generalizations of the supersymmetric theory using the superspace formulation. There is an infinite range of possible string theories similar to the supercritical string theories. We comment on the connection between the critical non-relativistic string theory and the lightlike Linear Dilaton theory.