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.
Highlights
We study the current algebras of the NS5-branes, the Kaluza-Klein (KK) fivebranes and the exotic 522-branes in type IIA/IIB superstring theories
By the use of these algebras, we examine extended spaces in terms of tensor coordinates which are the representation of ten-dimensional supersymmetry
Since the T-duality transformation requires an isometry of geometries, one of the scalar fields in the brane worldvolume theories loses its meaning as the geometric fluctuation mode along xμ
Summary
We perform the direct dimensional reduction of the PST action to ten dimensions and obtain the effective action of the type IIA NS5-brane. Gμν, φ, Cμ[1] are the spacetime metric, the dilaton and the RR 1-form in ten-dimensional type IIA supergravity. The action (2.12) enables one to write down the current algebra This is obtained by the direct dimensional reduction of (2.9). We note that the algebra (2.15) is again characterized by the Dirac bracket This is obvious since the worldvolume supermultiplet, the N = (2, 0) tensor multiplet, is inherited from the M5-brane. The first and the second class constraints coming from the self-dual property of the 2-form A[2] are taken over to the type IIA NS5-brane
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