Five-brane Current Algebras in Type II String Theories

TL;DR

This paper investigates the current algebras of various five-branes in type II string theories, revealing their structure through dualities and exploring implications for extended supersymmetric spaces and supergravity gauge transformations.

Contribution

It characterizes the current algebras of NS5-branes, KK five-branes, and exotic $5^2_2$-branes, highlighting their determination via dualities and their role in extended superspace formulations.

Findings

Current algebras are determined by S- and T-dualities.

Algebras of (2,0) theories involve Dirac brackets from self-dual gauge fields.

Algebras of (1,1) theories are given by Poisson brackets.

Abstract

We study the current algebras of the NS5-branes, the Kaluza-Klein (KK) five-branes and the exotic $5^2_2$-branes in type IIA/IIB superstring theories. Their worldvolume theories are governed by the six-dimensional $\mathcal{N}= (2,0)$ tensor and the $\mathcal{N} = (1,1)$ vector multiplets. We show that the current algebras are determined through the S- and T-dualities. The algebras of the $\mathcal{N} = (2,0)$ theories are characterized by the Dirac bracket caused by the self-dual gauge field in the five-brane worldvolumes, while those of the $\mathcal{N} = (1,1)$ theories are given by the Poisson bracket. By the use of these algebras, we examine extended spaces in terms of tensor coordinates which are the representation of ten-dimensional supersymmetry. We also examine the transition rules of the currents in the type IIA/IIB supersymmetry algebras in ten dimensions. Based on the algebras, we write down the section conditions in the extended spaces and gauge transformations of the supergravity fields.