Non-Abelian Ramond-Neveu-Schwarz String Theory

TL;DR

This paper develops a non-Abelian extension of the RNS string theory with matrix-valued coordinates, revealing a free string limit and a new dimension emerging at weak coupling, linking to matrix string theory and potential 11D interpretation.

Contribution

It introduces a locally supersymmetric worldsheet formulation of non-Abelian RNS string theory with matrix coordinates, connecting to orbifold CFT and matrix string theory.

Findings

In the free limit, it reduces to N copies of the usual RNS string.

A new dimension appears at weak coupling, interpreted as an 11D coordinate.

The theory relates to orbifold conformal field theory and matrix string models.

Abstract

We construct a locally supersymmetric worldsheet formulation of a non-Abelian Ramond-Neveu-Schwarz (NARNS) string theory where the string coordinates are noncommuting matrices in a group U(N). This is described by the two dimensional supergravity coupled to supersymmetric Yang-Mills fields and adjoint matters in the gauge group U(N). We show that our NARNS string theory has a free string limit where it becomes N-copies of usual RNS string which can be described by the orbifold conformal field theory corresponding to the covariant worldsheet version of the Matrix string theory of Dijkgraaf, Verlinde and Verlinde. In the weak coupling limit, i.e. $g_s \to 0$ where $g_s$ is the coupling constant of our theory related with the Yang-Mills coupling as $g_{YM}^{-2}=\alpha' g_s^2$, a new additional dimension appears in the string spectrum and it can be speculatively interpreted as the compactified eleven dimensional coordinate whose dynamics is given by an orbifold O(N) sigma model.