A non-relativistic limit of NS-NS gravity

Abstract

We discuss a particular non-relativistic limit of NS-NS gravity that can be taken at the level of the action and equations of motion, without imposing any geometric constraints by hand. This relies on the fact that terms that diverge in the limit and that come from the Vielbein in the Einstein-Hilbert term and from the kinetic term of the Kalb-Ramond two-form field cancel against each other. This cancelling of divergences is the target space analogue of a similar cancellation that takes place at the level of the string sigma model between the Vielbein in the kinetic term and the Kalb-Ramond field in the Wess-Zumino term. The limit of the equations of motion leads to one equation more than the limit of the action, due to the emergence of a local target space scale invariance in the limit. Some of the equations of motion can be solved by scale invariant geometric constraints. These constraints define a so-called Dilatation invariant String Newton-Cartan geometry.

Torsional deformation of nonrelativistic string theory

“…Indeed, as we will detail in section 3.3, it is possible to consistently preserve only half of the Z A transformation in the symmetry algebra. We will show that imposing the symmetry generated by Z 0 + Z 1 on the sigma model leads to the torsional constraints that exactly match the ones found in [16] by requiring consistency with supersymmetry. We will provide a Feynman diagram argument to confirm that the halved Z A symmetry prohibits the λλ operator from being generated by quantum corrections at all loops.…”

“…It is recently suggested in [16] that the zero-torsion condition imposed by the Z A symmetry in the worldsheet QFT might be too strong for supersymmetrizations. Moreover, it is shown in [9,14,20] that a weaker version of the torsional constraints already…”

“…In section 3.1, we study the torsional deformation in string sigma models with arbitrary background fields. In section 3.2, we derive the beta-functionals that arise from fine-tuning the torsional deformation to zero in the relativistic beta-functionals, using the results given in [16]. Finally, in section 3.3, we discuss different spacetime gauge symmetries that act on worldsheet fields and apply them to define a renormalizable worldsheet QFT, using which nonrelativistic string theories can be studied from first principles.…”

“…• Nonrelativistic strings from a limit. The first perspective seeks a nonsingular limit of spacetime (super)gravity that exhibits nonrelativistic behaviors [12][13][14][15][16]. From the worldsheet point of view, this requires studying the renormalization group (RG) flow of the worldsheet QFT with all possible vertex operators.…”

Non-Riemannian gravity actions from double field theory

“…Close to the completion of this work we became aware of the work of Bergshoeff et al[85] where they obtained a similar action by taking a particular non-relativistic limit of NS-NS gravity.…”