Exact infrared scaling behavior of Randers-Finsler scalar field theories

TL;DR

This paper analytically investigates the infrared scaling behavior of Randers-Finsler scalar field theories, calculating radiative corrections to critical exponents across all loop levels and exploring the influence of Finsler geometry on these exponents.

Contribution

It provides the first all-loop order analysis of the critical exponents in Randers-Finsler scalar field theories considering the space-time's Finsler properties.

Findings

Computed radiative corrections to anomalous dimensions up to all-loop levels.

Demonstrated the effect of Finsler space-time parameters on critical exponents.

Provided physical interpretation of the influence of Finsler geometry on scalar field theories.

Abstract

We study the scaling behavior of Randers-Finsler massless scalar field theories in the infrared regime. For that, we compute analytically the radiative corrections to the corresponding anomalous dimensions, related to the critical exponents of the theory, first up to next-to-leading loop order and later for all-loop levels. We consider the effect of the Randers-Finsler space-time properties on the critical exponents by considering the parameter characterizing those space-times in its exact form. We employ field-theoretic renormalization group and $\epsilon$-expansion techniques at dimensions $d = 4 - \epsilon$ through three distinct and independent methods. At the end, we furnish the physical interpretation of the obtained results.