The semi-classical approximation at high temperature revisited

• Main Authors: Alexander Boccaletti, Daniel Nogradi
• Format: Article
• Language: English
• Published: SpringerOpen 2020-03-01
• Series: Journal of High Energy Physics
• Subjects: Lattice Quantum Field Theory; Nonperturbative Effects; Solitons Monopoles and Instantons
• Online Access: http://link.springer.com/article/10.1007/JHEP03(2020)045

Abstract We revisit the semi-classical calculation of the size distribution of instantons at finite temperature in non-abelian gauge theories in four dimensions. The relevant functional determinants were first calculated in the seminal work of Gross, Pisarski and Yaffe and the results were used for a wide variety of applications including axions most recently. In this work we show that the uncertainty on the numerical evaluations and semi-analytical expressions are two orders of magnitude larger than claimed. As a result various quantities computed from the size distribution need to be reevaluated, for instance the resulting relative error on the topological susceptibility at arbitrarily high temperatures is about 5% for QCD and about 10% for SU(3) Yang-Mills theory. With higher rank gauge groups this discrepancy is even higher. We also provide a simple semi-analytical formula for the size distribution with absolute error 2 · 10 −4. In addition we also correct the over-all constant of the instanton size distribution in the MS ¯ $$ \overline{\mathrm{MS}} $$ scheme which was widely used incorrectly in the literature if non-trivial fermion content is present.