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 $$ {5}_2^2 $$ 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.

Brane current algebras and generalised geometry from QP manifolds. Or, “when they go high, we go low”

“…The last fact has been empirically observed (through direct calculations of Poisson brackets) in a number of works that discuss brane current algebras in phase space, starting with a relatively early paper by Bonelli and Zabzine that relates a p-brane current algebra to an algebroid involving T M ⊕Λ p T M [11], and more recently for M2, M5 and D-branes by Hatsuda and collaborators [12][13][14] and also by Sakatani and Uehara [15]. Our construction explains why O(d, d)-and E d(d) -covariant structures and (exceptional) Dorfman, Courant, Vinogradov .…”

Perturbative F-theory 10-brane and M-theory 5-brane

“…In F-theory the 5-brane represents the SL(5) U-duality symmetry [46]. Recently it was shown that current algebras of 5-branes are preserved under the S and T-duality transformations with renaming the spacetime coordinates, where 5-branes include the NS5-brane, the D5-brane, KK5-branes and exotic 5-branes in 32-supersymmetric string theories [54]. 5-brane may give a clue of duality web including 16 supersymmetric string theories.…”

Currents, charges and algebras in exceptional generalised geometry

“…The aim of this paper is to close that gap and propose an E d(d) -covariant Hamiltonian formulation of world-volume theories, building on previous attempts [50,64,65] and most recently [66]. Besides the typical objects of E d(d) generalised geometry an additional object, the above mentioned charge, that specifies the type of world-volume, needs to be introduced to ensure E d(d) -covariance.…”