Large volumes and spectroscopy of walking theories

TL;DR

This study investigates finite size effects in SU(2) gauge theory with two adjoint fermions, emphasizing the need for large lattices to accurately capture the spectrum and supporting the theory's conformal nature with an anomalous dimension around 0.37.

Contribution

It provides a comprehensive analysis of finite size effects and spectral signatures in a near-conformal gauge theory, highlighting the importance of large lattices and full spectrum understanding.

Findings

Infinite volume limit reached when L M_PS ≥ 15

Scalar isosinglet is the lightest particle in the spectrum

Supports conformal behavior with anomalous dimension ~0.37

Abstract

A detailed investigation of finite size effects is performed for SU(2) gauge theory with two fermions in the adjoint representation, which previous lattice studies have shown to be inside the conformal window. The system is investigated with different spatial and temporal boundary conditions on lattices of various spatial and temporal extensions, for two values of the bare fermion mass representing a {\em heavy} and {\em light} fermion regime. Our study shows that the infinite volume limit of masses and decay constants in the mesonic sector is reached only when the mass of the pseudoscalar particle $M_\mathrm{PS}$ and the spatial lattice size $L$ satisfy the relation $L M_\mathrm{PS} \ge 15$. This bound, which is at least a factor of three higher than what observed in QCD, is a likely consequence of the different spectral signatures of the two theories, with the scalar isosinglet ($0^{++}$ glueball) being the lightest particle in our model. In addition to stressing the importance of simulating large lattice sizes, our analysis emphasises the need to understand quantitatively the {\em full} spectrum of the theory rather than just the spectrum in the mesonic isotriplet sector. While for the lightest fermion measuring masses from gluonic operators proves to be still challenging, reliable results for glueball states are obtained at the largest fermion mass and, in the mesonic sector, for both fermion masses. As a byproduct of our investigation, we perform a finite size scaling of the pseudoscalar mass and decay constant. The data presented in this work support the conformal behaviour of this theory with an anomalous dimension $\gamma_* \simeq 0.37$.