# NLO critical exponents of O($N$) lambda $\phi^{4}$ scalar field theories in curved spacetime

## TL;DR

This paper analyzes how conformal symmetry affects quantum corrections to critical exponents in massless O(N) scalar field theories in curved spacetime, finding that these exponents match those in flat spacetime at the considered loop order.

## Contribution

It provides an analytical investigation of quantum corrections to critical exponents in curved spacetime, confirming the universality hypothesis at next-to-leading order.

## Key findings

- Critical exponents are unchanged in curved spacetime at the considered loop order.
- The results support the universality hypothesis in curved backgrounds.
- The BPHZ renormalization method was successfully applied in this context.

## Abstract

In this paper we investigate analytically the conformal symmetry influence on the next-to-leading order radiative quantum corrections to critical exponents for massless O($N$) $\lambda\phi^{4}$ scalar field theories in curved spacetime. We renormalize the theory by applying the BPHZ method. We find that the critical exponents are the same as that of flat spacetime, at least at the loop order considered. We argue that this result agrees perfectly with the universality hypothesis.