Worldsheet Descriptions of Wrapped NS Five-Branes

TL;DR

The paper provides a tractable world-sheet CFT framework for NS5-branes wrapped on holomorphic cycles ${\mathbb{C}}P^n$, realized as orbifolds of an ${\mathcal{N}}=2$ minimal model times an infrared fixed point of a gauged linear sigma model. Through T-duality and mirror symmetry, it connects these constructions to Seiberg-Witten theory for ${\mathcal{N}}=2$ SYM with ADE gauge groups and identifies Argyres-Douglas points via singularities in the world-sheet description. It also analyzes compactification on ${\mathbb{C}}P^2$, revealing a 2d $(2,2)$-theory structure and the role of world-sheet instantons, with a detailed examination of decoupling limits and the interplay between LST and gauge theory dynamics. Overall, the work links concrete world-sheet constructions to non-perturbative 4d and 2d gauge theories, providing a holographic perspective on Coulomb branches and conformal points. The approach showcases how simple linear sigma models, when combined with minimal models and mirror symmetry, yield rich Seiberg-Witten data and insights into wrapped-brane physics and non-critical string frameworks.

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.