Background Field Method for Nonlinear Sigma Models in Nonrelativistic String Theory

Abstract

We continue the study of nonrelativistic string theory in background fields. Nonrelativistic string theory is described by a nonlinear sigma model that maps a relativistic worldsheet to a non-Lorentzian and non-Riemannian target space geometry, which is known to be string Newton-Cartan geometry. We develop the covariant background field method in this non-Riemannian geometry. We apply this background field method to compute the beta-functions of the nonlinear sigma model that describes nonrelativistic string theory on a string Newton-Cartan geometry background, in presence of a Kalb-Ramond two-form and dilaton field.

arXiv comment38 pages, 1 figure; v2: references added; v3: minor corrections

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• Non-Relativistic Ten-Dimensional Minimal Supergravity
• Torsional Newton Cartan gravity from non-relativistic strings
• A non-relativistic limit of M-theory and 11-dimensional membrane Newton-Cartan geometry
• On the Non-Relativistic Expansion of Closed Bosonic Strings
• Torsional Deformation of Nonrelativistic String Theory
• Dual D-Brane Actions in Nonrelativistic String Theory
• Nonrelativistic Open String and Yang-Mills Theory
• Nonrelativistic Approximations of Closed Bosonic String Theory
• Spin Matrix Theory String Backgrounds and Penrose Limits of AdS/CFT
• Non-Riemannian isometries from double field theory
• Non-Riemannian gravity actions from double field theory
• Worldsheet Formalism for Decoupling Limits in String Theory
• The Supersymmetric Neveu-Schwarz Branes of Non-Relativistic String Theory
• Matrix Theory Reloaded: A BPS Road to Holography
• Nonrelativistic near-BPS corners of $\mathcal{N}=4$ super-Yang-Mills with $SU(1,1)$ symmetry
• Non-Lorentzian IIB Supergravity from a Polynomial Realization of SL(2,R)
• Lie Algebra Expansion and Integrability in Superstring Sigma-Models
• Generalized Newton-Cartan Geometries for Particles and Strings
• KLT Factorization of Nonrelativistic String Amplitudes
• The Panorama of Spin Matrix Theory
• Branched SL(2,Z) Duality
• Longitudinal Galilean and Carrollian limits of non-relativistic strings
• Spin Matrix Theory in near $\frac{1}{8}$-BPS corners of $\mathcal{N}=4$ super-Yang-Mills
• Dual Non-Lorentzian Backgrounds for Matrix Theories
• Non-relativistic quantum strings from gauged WZW models