Subcritical Superstrings

TL;DR

This paper introduces a Liouville mode into the Green-Schwarz superstring, analyzing its implications on supersymmetry, constraints, and anomaly cancellation in specific dimensions, expanding understanding of superstring consistency conditions.

Contribution

It presents a novel formulation of superstrings with Liouville mode, addressing anomaly cancellation and constraint solutions in D=4 and 6 dimensions, which was not previously explored.

Findings

Liouville mode can cancel anomalies in superstrings in D=4 and 6

Second-class constraints are solvable via twisted chiral superspace

Anomaly coefficient c < 1 allows for consistent physical dimensions

Abstract

We introduce the Liouville mode into the Green-Schwarz superstring. Like massive supersymmetry without central charges, there is no kappa symmetry. However, the second-class constraints (and corresponding Wess-Zumino term) remain, and can be solved by (twisted) chiral superspace in dimensions D=4 and 6. The matter conformal anomaly is c = 4-D < 1. It thus can be canceled for physical dimensions by the usual Liouville methods, unlike the bosonic string (for which the consistency condition is c = D <= 1).