Diffeomorphism symmetry effect on the O(N ) universality class

TL;DR

This paper investigates whether diffeomorphism symmetry in curved spacetime affects the critical exponents of the O(N) scalar field theories, finding that they remain unchanged up to three-loop order.

Contribution

It introduces a momentum-coordinate-only renormalization approach and demonstrates that curved spacetime does not alter critical exponents at the examined loop levels.

Findings

Critical exponents in curved spacetime match flat spacetime values up to three loops.

The new renormalization method simplifies calculations in curved backgrounds.

Diffeomorphism symmetry does not influence the universality class at the studied order.

Abstract

We probe the effect of diffeomorphism symmetry on the critical exponents values for massive O($N$) $\lambda\phi^{4}$ scalar field theories in curved spacetime. We apply field-theoretic renormalization group tools, where we use only momentum coordinates as opposed to the earlier standard procedure with both space and momentum coordinates, for computing analytically the critical exponents up to three-loop order for one of them and up to two-loop level for the remaining ones. We found that the curved spacetime critical exponents are the same as their flat spacetime counterparts, at least up to the level considered. At the conclusions we present the physical interpretation for the results.