We show in the SU(1, 1)-covariant formulation that IIB supergravity allows the introduction of a doublet and a quadruplet of ten-form potentials. The Ramond-Ramond ten-form potential which is associated with the SO(32) Type I superstring is in the quadruplet. Our results are consistent with a recently proposed E 11 symmetry underlying string theory. For the reader's convenience we present the full supersymmetry and gauge transformations of all fields both in the manifestly SU(1, 1) covariant Einstein frame and in the real U(1) gauge fixed string frame.
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 .
We give a universal SL(2, R)-invariant expression for all IIB p-brane actions with p = −1, 1, 3, 5, 7, 9. The Wess-Zumino terms in the brane actions are determined by requiring (i) target space gauge invariance and (ii) the presence of a single Born-Infeld vector. We find that for p = 7 (p = 9) brane actions with these properties only exist for orbits that contain the standard D7-brane (D9-brane). We comment about the actions for the other orbits.
We formulate all the five dimensional gauged maximal supergravity theories as non-linear realisations of the semi-direct product of E 11 and a set of generators which transform according to the first fundamental representation l of E 11 . The latter introduces a generalised space-time which plays a crucial role for these theories. We derive the E 11 and l transformations of all the form fields and their dynamics. We also formulate the five dimensional gauged supergravity theories using the closure of the supersymmetry algebra. We show that this closes on the bosonic field content predicted by E 11 and we derive the field transformations and the dynamics of this theory. The results are in precise agreement with those found from the E 11 formulation. This provides a very detailed check of E 11 and also the first substantial evidence for the generalised space-time. The results can be generalised to all gauged maximal supergravities, thus providing a unified framework of all these theories as part of E 11 . divergence reproduces the 3-form second-order field equations of 11-dimensional supergravity. The eleven-dimensional gravity field describes non-linearly SL(11, R), which is a subalgebra of this algebra. Indeed, gravity in D dimensions can be described as a non-linear realisation of the closure of the group SL(D, R) with the conformal group[10], as was shown in the four dimensional case in [11].• E 11 is the smallest Kac-Moody algebra which contains the algebra found in the nonlinear realisation above. This E 11 algebra is infinite-dimensional, and the E 11 nonlinear realisation contains an infinite number of fields with increasing number of indices. The first few fields are the graviton, a three form, a six form and a field which has the right spacetime indices to be interpreted as a dual graviton. This is the field content of eleven dimensional supergravity, and keeping only the first three of these fields one finds that the non-linear realisation of E 11 reduces to the construction discussed in the first point and so results in the dynamics of this theory [9].• Theories in D dimensions arise from the E 11 non-linear realisation by choosing a suitable SL(D, R) subalgebra, which is associated with D-dimensional gravity. The A D−1 Dynkin diagram of this subalgebra, called the gravity line, must include the node labelled 1 in the Dynkin diagram of Fig. 1. In ten dimensions there are two possible ways of constructing this subalgebra, and the corresponding non-linear realisations give rise to two theories that contain the fields of the IIA and IIB supergravity theories and their electromagnetic duals [9,12]. Below ten dimensions, there is a unique choice for this subalgebra, and this corresponds to the fact that maximal supergravity theories in dimensions below ten are unique. Again, the non-linear realisation in each case describes, among an infinite set of other fields, the fields of the corresponding supergravity and their electromagnetic duals. In each dimension, the part of the E 11 Dynkin diagram which is not c...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.