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Strings in gravity with torsion. (English) Zbl 0971.83062

The main idea of this paper is that the string naturally gives rise to torsion in a theory of gravitation. In the author’s approach the torsion is connected with an antisymmetric potential \(\psi_{\mu\nu}\) : \(S_{\mu\nu\sigma} = \psi_{[\mu\nu ,\sigma]}\). The field equations of gravity with torsion interacting with a matter are obtained. The conservation laws are obtained and as a result it is shown that there are additional forces due to torsion, and that geodesic motion should not be expected. The equation of motion of a small particle with structure (string) in an external field are found using the method of Papapetrou. As a consequence two forces acting on the string are represented: (1) due to the gradient of the field; (2) due to the torsion. The equation for angular momentum is obtained. The author supposes that the string couples with the torsion potential \(\psi_{\mu\nu}\) as \(I_s = \mu\int \sqrt{-\gamma d^2\zeta} + \eta\int \psi_{\mu\nu}d\sigma^{\mu\nu}\). For this action an intrinsic spin of a string is calculated and it is shown that, even in the limit of a static configuration, the string has spin.

MSC:

83E30 String and superstring theories in gravitational theory
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories

Keywords:

string; torsion; spin
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References:

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