The Conformal Window from the Worldline Formalism

TL;DR

This paper employs the worldline formalism to derive a universal relation for the lower boundary of the conformal window in non-supersymmetric QCD-like theories, connecting different gauge groups and representations.

Contribution

It introduces a novel derivation of the conformal window boundary using the worldline formalism and compares estimates with other methods.

Findings

Derived a universal relation for the conformal window boundary.

Connected the boundary across different gauge groups and representations.

Estimated the boundary in QCD-like theories using SQCD and compared with existing approaches.

Abstract

We use the worldline formalism to derive a universal relation for the lower boundary of the conformal window in non-supersymmetric QCD-like theories. The derivation relies on the convergence of the expansion of the fermionic determinant in terms of Wilson loops. The expansion shares a similarity with the lattice strong coupling expansion and the genus expansion in string theory. Our result relates the lower boundary of the conformal window in theories with different representations and different gauge groups. Finally, we use SQCD to estimate the boundary of the conformal window in QCD-like theories and compare it with other approaches.