Quantum deformations of the flat space superstring

TL;DR

This paper introduces a quantum deformation of the flat space superstring, connecting it to the mirror model via contraction limits and exploring its symmetry properties and T dualities, with implications for various superstring backgrounds.

Contribution

It presents a novel quantum deformation of the flat space superstring derived from AdS_5 x S^5, revealing new symmetry structures and dualities, and extending to other superstring models.

Findings

Quantum deformation of flat space superstring related to mirror model

Symmetries of timelike kappa-Poincare type realized in the deformed string

Connections between T duality and symmetry algebras in deformed models

Abstract

We discuss a quantum deformation of the Green-Schwarz superstring on flat space, arising as a contraction limit of the corresponding deformation of AdS_5 x S^5. This contraction limit turns out to be equivalent to a previously studied limit that yields the so-called mirror model - the model obtained from the light cone gauge fixed AdS_5 x S^5 string by a double Wick rotation. Reversing this logic, the AdS_5 x S^5 superstring is the double Wick rotation of a quantum deformation of the flat space superstring. This quantum deformed flat space string realizes symmetries of timelike kappa-Poincare type, and is T dual to dS_5 x H^5, indicating interesting relations between symmetry algebras under T duality. Our results directly extend to AdS_2 x S^2 x T^6 and AdS_3 x S^3 x T^4, and beyond string theory to many (semi)symmetric space coset sigma models, such as for example a deformation of the four dimensional Minkowski sigma model with timelike kappa-Poincare symmetry. We also discuss possible null and spacelike deformations.