Existence and Construction of Exact FRG Flows of a UV-Interacting Scalar Field Theory

TL;DR

This paper proves the existence and provides a method to construct exact solutions of the Wetterich equation for a scalar  theory, capturing its behavior across all energy scales with explicit bounds.

Contribution

It introduces a novel iterative scheme for constructing momentum-dependent correlation functions of scalar  theories, ensuring boundedness and applicability to other systems.

Findings

Constructed exact Euclidean-invariant solutions to the Wetterich equation.

Derived explicit bounds for correlation functions in UV and IR limits.

Established a potential extension of the method to other physical systems.

Abstract

We prove the existence and give a construction procedure of Euclidean-invariant exact solutions to the Wetterich equation in $d > 2$ dimensions satisfying the naive boundary condition of a massive and interacting real scalar $\phi^4$ theory in the ultraviolet limit as well as a generalised free theory in the infrared limit. The construction produces the momentum-dependent correlation functions to all orders through an iterative scheme, based on a self-consistent ansatz for the four-point function. The resulting correlators are bounded at all regulator scales and we determine explicit bounds capturing the asymptotics in the UV and IR limits. Furthermore, the given construction principle may be extended to other systems and might become useful in the study of general properties of exact solutions.