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

E. P. Popova^a, K. V. Stepanyantz<sup>b

a</sup> Lomonosov Moscow State University, Moscow, Russia, Skobeltsyn Institute of Nuclear Physics, Moscow, Russia
^b Lomonosov Moscow State University, Faculty of Physics, Moscow, Russia

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 $s\ge3$.

Keywords: one-loop divergence, higher-spin field.

Received: 16.10.2015
Revised: 25.10.2015

DOI: 10.4213/tmf9067

 English version: Theoretical and Mathematical Physics, 2016, 187:3, 888–898

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