LAUSR

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 N $$ \mathcal{N} $$ = (2 , 0) tensor and the N $$ \mathcal{N} $$ = (1 , 1) vector multiplets. We show that the current algebras are determined through the S- and T-dualities. The algebras of the N $$ \mathcal{N} $$ = (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 N $$ \mathcal{N} $$ = (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.