Non-Riemannian isometries from double field theory

Nonrelativistic string theory is a self-contained corner of string theory, with its string spectrum enjoying a Galilean-invariant dispersion relation. This theory is unitary and ultraviolet complete, and can be studied from first principles. In these notes, we focus on the bosonic closed string sector. In curved spacetime, nonrelativistic string theory is defined by a renormalizable quantum nonlinear sigma model in background fields, following certain symmetry principles that disallow any deformation towards relativistic string theory. We review previous proposals of such symmetry principles and propose a modified version that might be useful for supersymmetrizations. The appropriate target-space geometry determined by these local spacetime symmetries is string Newton-Cartan geometry. This geometry is equipped with a two-dimensional foliation structure that is restricted by torsional constraints. Breaking the symmetries that give rise to such torsional constraints in the target space will in general generate quantum corrections to a marginal deformation in the worldsheet quantum field theory. Such a deformation induces a renormalization group flow towards sigma models that describe relativistic strings.

Section: Jhep09(2021)035mentioning

confidence: 54%

Torsional deformation of nonrelativistic string theory

Yan

2021

“…22 Note that one can also perform a direct dimensional reduction of the NR NS-NS gravity action along a transversal spatial direction leading to a sector of NR string theory that does not follow from a null reduction of the relativistic NS-NS gravity action. 23 For other recent work on the NR string theory in DFT, see [36,37].…”

Section: Jhep06(2021)021mentioning

confidence: 99%

A non-relativistic limit of NS-NS gravity

Bergshoeff

Lahnsteiner

Romanò

et al. 2021

194

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.

“…Our usage of the relation between DFT and the previously mentioned non-relativistic geometries will not go further than (2.5). A detailed analysis pertaining the symmetries and related aspects of non-Riemann geometry following from (2.5) has been done by Blair et al in [53].…”

Section: Jhep06(2021)173mentioning

confidence: 99%

Non-Riemannian gravity actions from double field theory

Gallegos

Gürsoy

Verma

et al. 2021

Non-Riemannian gravitational theories suggest alternative avenues to understand properties of quantum gravity and provide a concrete setting to study condensed matter systems with non-relativistic symmetry. Derivation of an action principle for these theories generally proved challenging for various reasons. In this technical note, we employ the formulation of double field theory to construct actions for a variety of such theories. This formulation helps removing ambiguities in the corresponding equations of motion. In particular, we embed Torsional Newton-Cartan gravity, Carrollian gravity and String Newton-Cartan gravity in double field theory, derive their actions and compare with the previously obtained results in literature.