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

By A. Tseytlin, L. Wulff. 2016

162 citations recorded by the source corpus.

A bstractWe 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 Xa and imply the one-loop scale invariance of the GS sigma model. In the special case when Xa 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 Xa and Ka subject to 1st order differential relations (with the equations in the NS-NS sector depending only on the combination Xa = Xa + Ka). In the special case of Ka = 0 one finds that Xa = ∂aϕ and thus obtains the standard type II supergravity equations. New generalized solutions are found if Ka 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 AdSn × Sn 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.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/cabe47a4238bf0efde45b2a0691d76cf7f0c121b

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The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. R. Borsato
2. S. J. Tongeren
3. David Osten
4. L. Wulff
5. Alessandro Sfondrini

In Nuclear and High Energy Physics

1. David Osten
2. S. J. Tongeren
3. R. Borsato
4. L. Wulff
5. Alessandro Sfondrini

In Statistical and Nonlinear Physics

1. David Osten
2. R. Borsato
3. S. J. Tongeren
4. L. Wulff
5. Alessandro Sfondrini

Citations in the corpus

• Abelian Yang–Baxter deformations and TsT transformations (2016, background): “All Yang-Baxter deformations of the string preserve κ symmetry however [11, 27], meaning that their backgrounds necessarily solve a set of modified supergravity equations [28, 29], guaranteeing scale but not Weyl invariance.”
• Target space supergeometry of η and λ-deformed strings (2016, methodology): “he local fermionic symmetries of both deformed models are of the standard Green-Schwarz form. In section 3 we derive the target space supergeometry for the λ-model, and by comparing to the results of [30] we extract the corresponding background fields. Section 4 achieves the same goal for the η-model”