Finite-Volume Effects in Quantum Chromodynamics and Functional Renormalization Group Methods

Abstract

Quantum Chromodynamics (QCD) at finite temperature and density is currently a subject of great interest, due to both advances in experimental heavy-ion collisions and theoretical improvement of our understanding in recent years. Simulations of the theory on finite space-time lattices provide important theoretical advances. But in particular for investigating QCD phase transitions, finite quark masses and finite volumes in the simulations need to be taken into account. The investigation of finite-volume effects in QCD has a long tradition in the framework of chiral perturbation theory and random matrix theory and can provide useful tools for the analysis. With regard to a description of the chiral phase transition in QCD, it is very important to correctly take into account the effects of long-range fluctuations such as pions as the Goldstone bosons of spontaneous chiral symmetry breaking. It is natural to employ Renormalization Group methods for this purpose. Together with Hans-Jurgen Pirner, we have initiated work in this direction, and there has been an increasing interest in the investigation of such finite-volume effects. I will give an overview over recent developments.