String solitons and T-duality

Abstract

We construct for arbitrary dimensions a universal T-duality covariant expression for the Wess-Zumino terms of supersymmetric String Solitons in toroidally compactified string theories with 32 supercharges. The worldvolume fields occurring in the effective action of these String Solitons form either a vector or a tensor multiplet with 16 supercharges. We determine the dimensions of the conjugacy classes under T-duality to which these String Solitons belong. We do this in two steps. First, we determine the T-duality representations of the p-forms of maximal supergravities that contain the potentials that couple to these String Solitons. We find that these are p-forms, with D − 4 ≤ p ≤ 6 if D ≥ 6 and with D − 4 ≤ p ≤ D if D < 6, transforming in the antisymmetric representation of rank m = p + 4 − D ≤ 4 of the T-duality symmetry SO(10 − D, 10 − D). All branes support vector multiplets except when m = 10 − D. In that case the T-duality representation splits, for D < 10, into a selfdual and anti-selfdual part, corresponding to 5-branes supporting either a vector or a tensor multiplet. In a second step we show that only certain well-defined lightlike directions in the anti-symmetric tensor representations of the T-duality group correspond to supersymmetric String Solitons. These lightlike directions define the conjugacy classes. As a by-product we show how by a straightforward procedure all solitonic fields of maximal supergravity are derived using the Kac-Moody algebra E 11 .

Five-brane actions in double field theory

“…The NSNS contribution is complicated as it must describe the T-duals of the electromagnetic dual B 6 of the B-field, which means the electromagnetic dual of the KaluzaKlein vector, and other more exotic objects, for which non-linear definitions are not known. However, a linearised description in DFT has been achieved in [53] while the representation theory structure for this part of the WZ term in O(d, d) is known thanks to [54][55][56][57][58]. Furthermore, the paper [54] constructs a general formula for T-duality covariant WZ terms of solitonic 5-branes for general d < 10 by introducing worldvolume field strengths for every O(d, d) covariant multiplet of gauge fields.…”

“…However, a linearised description in DFT has been achieved in [53] while the representation theory structure for this part of the WZ term in O(d, d) is known thanks to [54][55][56][57][58]. Furthermore, the paper [54] constructs a general formula for T-duality covariant WZ terms of solitonic 5-branes for general d < 10 by introducing worldvolume field strengths for every O(d, d) covariant multiplet of gauge fields. These results apply for actual reductions, while in DFT we want to keep the dependence on the doubled internal coordinates (subject to the section condition) and so have more complicated gauge transformations to consider.…”

“…These results apply for actual reductions, while in DFT we want to keep the dependence on the doubled internal coordinates (subject to the section condition) and so have more complicated gauge transformations to consider. Still, the results of [54] provide a useful guide to the structures that we expect to appear. We will thus provide worldvolume field strengths, which are actually invariant under the gauge symmetries of the DFT RR fields only on contraction with an auxiliary worldvolume O(d, d) spinor which we will explain below.…”

Dual double field theory

“…The construction of the non-linear theory would be necessary in order to describe, for instance, the world-volume dynamics of Kaluza-Klein monopoles (in a way that is compatible with T-duality), for which the dual graviton is expected to play the same role as the B 6 potential does for the NS5-brane [15]. More generally, one expects from T-duality the appearance of further mixed-Young tableaux fields as exotic duals [17,19] of the usual gauge potentials [21][22][23], as further clarified in [24,25], together with associated 'exotic' branes [26,27]. We find that all expected fields are indeed described by the dual DFT.…”

“…Upon dimensional reduction, this would give rise to space-filling branes with the same scaling of the tension, which have been classified (see the second ref. in [21][22][23]). In general these branes do not have any solution in supergravity, but their existence is crucial for instance in orientifold models.…”