Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Preprint 2015-13

Anna Pachol and Stijn van Tongeren


Quantum deformations of the flat space superstring.


Abstract: We discuss a quantum deformation of the Green-Schwarz superstring on flat space, arising as a contraction limit of the corresponding deformation of AdS5 × S5. 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 AdS5 × S5 string by a double Wick rotation. Reversing this logic, the AdS5 × S5 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 κ- Poincar ́e type, and is T dual to dS5 ×H5, indicating interesting relations between symmetry algebras under T duality. Our results directly extend to AdS2 × S2 × T6 and AdS3 × S3 × T4, 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 κ-Poincar ́e symmetry. We also discuss possible null and spacelike deformations.

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2015-13


13 pp.