Five-brane current algebras in type II string theories

Abstract

Abstract We study the current algebras of the NS5-branes, the Kaluza-Klein (KK) five-branes and the exotic $$ {5}_2^2 $$ 5 2 2 -branes in type IIA/IIB superstring theories. Their worldvolume theories are governed by the six-dimensional $$ \mathcal{N} $$ N = (2, 0) tensor and the $$ \mathcal{N} $$ N = (1, 1) vector multiplets. We show that the current algebras are determined through the S- and T-dualities. The algebras of the $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ 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.