Type II NS Five-Branes: Non Critical Strings and their Topological Sectors

TL;DR

This paper analyzes the exact superconformal field theory describing the near-horizon geometry of NS5-branes, revealing the spectrum of bulk and brane states and their algebraic structure using worldsheet techniques.

Contribution

It provides a detailed derivation of bulk and brane spectra in the superconformal framework, highlighting the necessity of both for a complete theory and elucidating the non-abelian structure of 5-brane fields.

Findings

Bulk states are massive and belong to long N=2 supermultiplets.

NS5-brane states are short N=2 supermultiplets.

Non-abelian gauge structures emerge from fusion coefficients.

Abstract

The near-horizon geometry of parallel NS5-branes is described by an exact superconformal 2d field theory based on K^10 = W(k)^4 x M^6, with M^6 a flat 5+1 space time and W(k)^4 =U(1) x SU(2)(k), a four dimensional background with non-trivial dilaton. The ten-dimensional ``BULK'' spectrum of excitations of K^10 can be derived combining unitary representations of the N=4 superconformal theory of W(k)^4 and M^6 in a modular-invariant way. All Bulk states are massive and belong to the long representations of the N=2 six dimensional space-time supersymmetry. The NS5-brane states, propagating on M^6, belong to the short representations of N=2. Both the bulk and the brane spectrum is derived using the powerful worldsheet technics of the N=4 superconformal theories. We claim that both bulk and brane states are necessary to well define the theory. The non abelian U(n) or SO(2n) structure of the 5-brane fields follows from the fusion coefficients appearing in the correlation functions involving SU(2)(k) conformal fields.