Gravitationally dresed RG flows and zig-zag invariant strings

TL;DR

This paper introduces a world-sheet model for zigzag-invariant strings using a perturbed WZNW model coupled to 2D gravity, revealing solutions primarily for the group SL(2) and constraining target-space dimensions.

Contribution

It provides a novel realization of zigzag-invariant strings through gravitationally dressed RG flows in a WZNW framework, especially identifying solutions for specific group manifolds.

Findings

Zigzag symmetry emerges from self-consistent RG equations at large negative level k.

The only simple group solution is G=SL(2).

In supersymmetric cases, the target-space dimension is limited to seven.

Abstract

We propose a world-sheet realization of the zigzag-invariant bosonic and fermionic strings as a perturbed Wess-Zumino-Novikov-Witten model at large negative level $k$ on a group manifold $G$ coupled to 2D gravity. In the large $k$ limit the zigzag symmetry can be obtained as a result of a self-consistent solution of the gravitationally dressed RG equation. The only solution found for simple group is $G=SL(2)$. More general target-space geometries can be obtained via tensoring of various cosets based on SL(2). In the supersymmetric case the zigzag symmetry fixes the maximal target-space dimension of the confining fermionic string to be seven.