On integrability of strings on symmetric spaces
File(s)
Published version
Author(s)
Wulff, L
Type
Journal Article
Abstract
In the absence of NSNS three-form flux the bosonic string on a symmetric space is described by a symmetric space coset sigma-model. Such models are known to be classically integrable. We show that the integrability extends also to cases with non-zero NSNS flux (respecting the isometries) provided that the flux satisfies a condition of the form HabcHcde ∼ Rabde. We then turn our attention to the type II Green-Schwarz superstring on a symmetric space. We prove that if the space preserves some supersymmetry there exists a truncation of the full superspace to a supercoset space and derive the general form of the superisometry algebra. In the case of vanishing NSNS flux the corresponding supercoset sigma-model for the string is known to be integrable. We prove that the integrability extends to the full string by augmenting the supercoset Lax connection with terms involving the fermions which are not captured by the supercoset model. The construction is carried out to quadratic order in these fermions. This proves the integrability of strings on symmetric spaces supported by RR flux which preserve any non-zero amount of supersymmetry. Finally we also construct Lax connections for some supercoset models with non-zero NSNS flux describing strings in AdS2,3 × S2,3 × S2,3 × T2,3,4 backgrounds preserving eight supersymmetries.
Date Issued
2015-09-17
Date Acceptance
2015-08-28
Citation
Journal of High Energy Physics, 2015, 2015 (9)
ISSN
1126-6708
Publisher
Springer Verlag
Journal / Book Title
Journal of High Energy Physics
Volume
2015
Issue
9
Copyright Statement
© The Author(s) 2015. JHEP is an open-access journal funded by SCOAP3 and licensed under CC BY 4.0.
License URL
Subjects
Science & Technology
Physical Sciences
Physics, Particles & Fields
Physics
Superstrings and Heterotic Strings
AdS-CFT Correspondence
Integrable Field Theories
Sigma Models
NONLINEAR SIGMA-MODELS
Nuclear & Particles Physics
01 Mathematical Sciences
02 Physical Sciences
Publication Status
Published
Article Number
115