Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations

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Title: Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations
Authors: Tseytlin, AA
Wulff, L
Item Type: Journal Article
Abstract: We determine the constraints imposed on the 10d target superspace geometry by the requirement of classical kappa-symmetry of the Green-Schwarz superstring. In the type I case we find that the background must satisfy a generalization of type I supergravity equations. These equations depend on an arbitrary vector X a and imply the one-loop scale invariance of the GS sigma model. In the special case when X a is the gradient of a scalar ϕ (dilaton) one recovers the standard type I equations equivalent to the 2d Weyl invariance conditions of the superstring sigma model. In the type II case we find a generalized version of the 10d supergravity equations the bosonic part of which was introduced in arXiv:1511.05795. These equations depend on two vectors X a and K a subject to 1st order differential relations (with the equations in the NS-NS sector depending only on the combination X a = X a + K a ). In the special case of K a = 0 one finds that X a = ∂ a ϕ and thus obtains the standard type II supergravity equations. New generalized solutions are found if K a is chosen to be a Killing vector (and thus they exist only if the metric admits an isometry). Non-trivial solutions of the generalized equations describe K-isometric backgrounds that can be mapped by T-duality to type II supergravity solutions with dilaton containing a linear isometry-breaking term. Examples of such backgrounds appeared recently in the context of integrable η-deformations of AdS n × S n sigma models. The classical kappa-symmetry thus does not, in general, imply the 2d Weyl invariance conditions for the GS sigma model (equivalent to type II supergravity equations) but only weaker scale invariance type conditions.
Issue Date: 29-Jun-2016
Date of Acceptance: 22-Jun-2016
ISSN: 1029-8479
Publisher: Springer Verlag (Germany)
Journal / Book Title: Journal of High Energy Physics
Volume: 2016
Issue: 6
Copyright Statement: © 2016 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0 -, which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Keywords: Science & Technology
Physical Sciences
Physics, Particles & Fields
Sigma Models
Supergravity Models
Superstrings and Heterotic Strings
01 Mathematical Sciences
02 Physical Sciences
Nuclear & Particles Physics
Publication Status: Published
Article Number: 174
Online Publication Date: 2016-06-29
Appears in Collections:Physics
Theoretical Physics
Faculty of Natural Sciences

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