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Equation for one-loop divergences in two dimensions and its application to higher-spin fields

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Abstract

We derive a simple formula for one-loop logarithmic divergences on the background of a two-dimensional curved space–time for theories in which the second variation of the action is a nonminimal second-order operator with small nonminimal terms. In particular, this formula allows calculating terms that are integrals of total derivatives. As an application of the result, we obtain one-loop divergences for higher-spin fields on a constant-curvature background in a nonminimal gauge that depends on two parameters. By an explicit calculation, we demonstrate that with the considered accuracy, the result is gauge independent and, moreover, spin independent for spins s ≥ 3.

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Correspondence to K. V. Stepanyantz.

Additional information

The research of K. V. Stepanyantz is supported by the Russian Foundation for Basic Research (Grant No. 14- 01-00695).

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 187, No. 3, pp. 505–518, June, 2016.

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Popova, H.P., Stepanyantz, K.V. Equation for one-loop divergences in two dimensions and its application to higher-spin fields. Theor Math Phys 187, 888–898 (2016). https://doi.org/10.1134/S0040577916060076

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  • DOI: https://doi.org/10.1134/S0040577916060076

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