Five-brane Current Algebras in Type II String Theories

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.

32 pages, 1 figure, version appeared in JHEP

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