Vertex corrections in gauge theories for two-dimensional condensed matter systems

TL;DR

This paper investigates how two-loop vertex corrections affect the fermionic self-energy in two-dimensional gauge theories relevant to condensed matter, revealing logarithmic modifications that suggest higher-order corrections increase the self-energy exponent.

Contribution

It provides a detailed calculation of two-loop vertex corrections and their impact on the fermionic self-energy in 2D gauge theories, extending prior one-loop analyses.

Findings

Vertex corrections introduce a negative logarithmic term in the self-energy.

Higher order corrections likely increase the self-energy exponent gamma.

The results support the scenario of non-trivial scaling behavior in 2D gauge systems.

Abstract

We calculate the self-energy of two-dimensional fermions that are coupled to transverse gauge fields, taking two-loop corrections into account. Given a bare gauge field propagator that diverges for small momentum transfers q as 1 / q^{eta}, 1 < eta < 2, the fermionic self-energy without vertex corrections vanishes for small frequencies omega as Sigma (omega) propto omega^{gamma with gamma = {frac{2}{1 + eta}} < 1. We show that inclusion of the leading radiative correction to the fermion - gauge field vertex leads to Sigma (omega) propto omega^{gamma} [ 1 - a_{eta} ln (omega_0 / omega) ], where a_{\eta} is a positive numerical constant and omega_0 is some finite energy scale. The negative logarithmic correction is consistent with the scenario that higher order vertex corrections push the exponent gamma to larger values.