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 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.Comment: v3, published version, 12 page

Lax pairs for deformed Minkowski spacetimes

“…A twisted boundary condition is also discussed. In section 4, we show that the anticipated Lax pair works for arbitrary classical r-matrices which are composed of Poincaré 1 For an approach based on a scaling limit of q-deformed AdS5×S 5 , see [41].…”

Supergravity backgrounds of the η-deformed AdS2 × S2 × T6 and AdS5 × S5 superstrings

“…The maximal deformation limit [28,29], given by equation (3.27) and taking κ → ∞, is finite, however, it does not match the mirror AdS 5 × S 5 supergravity background of [28,30]. It is also different to the maximal deformation limit of the generalised supergravity background of [9], which remains a generalised supergravity background.…”

“…We also rescale x i → κ −1 x i and then take κ → ∞. This limit corresponds to a contraction of the q-deformed symmetry algebra [29]. In this limit we find the following supergravity background…”

On circular strings in (AdS3 × S 3)ϰ

“…But recently it was reported that instead of the usual supergravity equations of motion, the background satisfies a particular deformed set of IIB equations [42,43]. For various issues concerning the integrable structure of this background, look at [44][45][46][47][48][49][50][51][52][53][54]. 1 Given the integrable and astounding nature of the deformed background, various rigidly rotating and pulsating strings have been investigated in detail.…”