Worldsheet Descriptions of Wrapped NS Five-Branes

TL;DR

This paper constructs a world-sheet conformal field theory description of wrapped NS5-branes, resolving supergravity singularities and connecting to low-energy gauge theories, including Seiberg-Witten theory and (2,2) super-Yang-Mills.

Contribution

It provides a novel world-sheet CFT framework for wrapped NS5-branes on complex projective spaces, linking string theory to gauge theory phenomena.

Findings

World-sheet CFT describes wrapped NS5-branes on CP^1 and CP^2.

Singularities in the CFT match Argyres-Douglas points and monopole points.

The approach resolves supergravity singularities and relates to gauge theory prepotentials.

Abstract

We provide a world-sheet description of Neveu-Schwarz five-branes wrapped on a complex projective space. It is an orbifold of the product of an N=2 minimal model and the IR fixed point of a certain linear sigma model. We show how the naked singularity in the supergravity description is resolved by the world-sheet CFT. Applying mirror symmetry, we show that the low-energy theory of NS5-branes wrapped on CP^1 in Eguchi-Hanson space is described by the Seiberg-Witten prepotential for N=2 super-Yang-Mills, with the gauge group given by the ADE-type of the five-brane. The world-sheet CFT is generically regular, but singularities develop precisely at the Argyres-Douglas points and massless monopole points of the space-time theory. We also study the low-energy theory of NS5-branes wrapped on CP^2 in a Calabi-Yau 3-fold and its relation to (2,2) super-Yang-Mills theory in two dimensions.