Nonrelativistic strings and the limits of $$ \mathcal{N} $$ = 2 dualities

Abstract

Abstract We carry out the formulation of nonrelativistic (NR) F-string theory for $$ \mathcal{N} $$ N = 2 Gaiotto-Maldacena class of geometries in type IIA supergravity. Considering the NS-NS sector, we reduce the type IIA theory into the NR sigma models those are formulated over the nonrelativistic target space geometries known as the torsional String Newton-Cartan (TSNC) backgrounds. Using these TSNC data, we write down the sigma model action and explore several properties in the semiclassical limit. In particular, we carry out the canonical analysis of the T-duality transformation rules in TSNC background. Following the standard canonical prescription of obtaining T-duality transformations, we map these TSNC sigma models to relativistic sigma models propagating over general relativity backgrounds. Finally, we conclude with a detailed discussion on the effects of adding flavour branes and thereby taking the corresponding TSNC limit in the bulk description of $$ \mathcal{N} $$ N = 2 quivers. We compute various field theory observables in the nonrelativistic limit and outline the structure of the NR Lagrangian following the light cone reduction of $$ \mathcal{N} $$ N = 2 SYM theory.