Fermion RG blocking transformations and IR structure

TL;DR

This paper develops a practical fermion RG blocking scheme on the lattice to study the IR fixed points of gauge theories, enabling quick estimates of conformal windows for different groups and fermion representations.

Contribution

It introduces an approximate RG recursion scheme for fermion and gauge field blocking, facilitating efficient analysis of IR fixed points in lattice gauge theories.

Findings

Successfully applied to locate conformal windows in SU(2) and SU(3) gauge theories.

Provides insights into the locality issues of fermion blocking schemes.

Discusses reasons for the effectiveness of the proposed decimation methods.

Abstract

We explore fermion RG block-spinning transformations on the lattice with the aim of studying the IR structure of gauge theories and, in particular, the existence of IR fixed points for varying fermion content. In the case of light fermions the main concern and difficulty is ensuring locality of any adopted blocking scheme. We discuss the problem of constructing a local blocked fermion action in the background of arbitrary gauge fields. We then discuss the carrying out of accompanying gauge field blocking. In the presence of the blocked fermions implementation of MCRG is not straightforward. By adopting judicious approximations we arrive at an easily implementable approximate RG recursion scheme that allows quick, inexpensive estimates of the location of conformal windows for various groups and fermion representations. We apply this scheme to locate the conformal windows in the case of SU(2) and SU(3) gauge groups. Some of the reasons for the apparent efficacy of this and similar decimation schemes are discussed.