Torsional Newton Cartan gravity from non-relativistic strings
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Publication:1995184
DOI10.1007/JHEP09(2020)172zbMATH Open1454.83131arXiv1906.01607MaRDI QIDQ1995184
Author name not available (Why is that?)
Publication date: 18 February 2021
Published in: (Search for Journal in Brave)
Abstract: We study propagation of closed bosonic strings in torsional Newton-Cartan geometry based on a recently proposed Polyakov type action derived by dimensional reduction of the ordinary bosonic string along a null direction. We generalize the Polyakov action proposal to include matter, i.e. the 2-form and the 1-form that originates from the Kalb-Ramond field and the dilaton. We determine the conditions for Weyl invariance which we express as the beta-function equations on the worldsheet, in analogy with the usual case of strings propagating on a pseudo-Riemannian manifold. The critical dimension of the TNC space-time turns out to be 25. We find that Newton's law of gravitation follows from the requirement of quantum Weyl invariance in the absence of torsion. Presence of the 1-form requires torsion to be non vanishing. Torsion has interesting consequences, in particular it yields a mass term and an advection term in the generalized Newton's law. U(1) mass invariance of the theory is an important ingredient in deriving the beta functions.
Full work available at URL: https://arxiv.org/abs/1906.01607
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