Non-Riemannian gravity actions 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: 99%

“…String Newton-Cartan geometry with the zero torsion was discussed in[4,17,18]. Generalizations to the torsional case were later introduced in[15,16,19].…”

mentioning

confidence: 99%

Torsional deformation of nonrelativistic string theory

Yan

2021

“…This builds on a recent revival of interest in non-relativistic versions of string theory, see e.g. [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. This has been inspired in part by holographic set-ups in which nonrelativistic geometries make an appearance, but also intrinsically motivated by the desire to explore new, and potentially simpler, corners of the space of possible quantum gravitational theories.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, the usual gauge fields such as the string two-form will propagate. The beta functionals, (bosonic) background field equations and target space action of these geometries have been studied in [18,19,21,23,26,27].…”

Section: Introductionmentioning

confidence: 99%

“…It was previously realised in [33][34][35] that this generalised metric admits 'non-Riemannian parametrisations' in which, instead of an invertible metric, a degenerate metric structure (for instance of Newton-Cartan type) appears along with the B-field. This was exploited in [26,36] to study the equations of motion and action of non-relativistic strings and other theories of non-Riemannian nature. Now, the initial investigations of stringy non-relativistic limits [6][7][8]37] were firmly embedded within the M-theoretic duality web, and provided a variety of non-relativistic limits involving different branes as well as the duality relationships between them.…”

Section: Introductionmentioning

confidence: 99%

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A non-relativistic limit of M-theory and 11-dimensional membrane Newton-Cartan geometry

Blair

Gallegos

Zinnato

2021

Self Cite

We consider a non-relativistic limit of the bosonic sector of eleven-dimensional supergravity, leading to a theory based on a covariant ‘membrane Newton-Cartan’ (MNC) geometry. The local tangent space is split into three ‘longitudinal’ and eight ‘transverse’ directions, related only by Galilean rather than Lorentzian symmetries. This generalises the ten-dimensional stringy Newton-Cartan (SNC) theory. In order to obtain a finite limit, the field strength of the eleven-dimensional four-form is required to obey a transverse self-duality constraint, ultimately due to the presence of the Chern-Simons term in eleven dimensions. The finite action then gives a set of equations that is invariant under longitudinal and transverse rotations, Galilean boosts and local dilatations. We supplement these equations with an extra Poisson equation, coming from the subleading action. Reduction along a longitudinal direction gives the known SNC theory with the addition of RR gauge fields, while reducing along a transverse direction yields a new non-relativistic theory associated to D2 branes. We further show that the MNC theory can be embedded in the U-duality symmetric formulation of exceptional field theory, demonstrating that it shares the same exceptional Lie algebraic symmetries as the relativistic supergravity, and providing an alternative derivation of the extra Poisson equation.

Torsional string Newton-Cartan geometry for non-relativistic strings

Bidussi

Harmark

Hartong

et al. 2022

We revisit the formulation of non-relativistic (NR) string theory and its target space geometry. We obtain a new formulation in which the geometry contains a two-form field that couples to the tension current and that transforms under string Galilei boosts. This parallels the Newton-Cartan one-form that couples to the mass current of a non-relativistic point particle. We show how this formulation of the NR string arises both from an infinite speed of light limit and a null reduction of the relativistic closed bosonic string. In both cases, the two-form originates from a combination of metric quantities and the Kalb-Ramond field. The target space geometry of the NR string is seen to arise from the gauging of a new algebra that is obtained by an İnönü-Wigner contraction of the Poincaré algebra extended by the symmetries of the Kalb-Ramond field. In this new formulation, there are no superfluous target space fields that can be removed by fixing a Stückelberg symmetry. Classically, there are no foliation/torsion constraints imposed on the target space geometry.