The semi-classical approximation at high temperature revisited

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 $2\cdot 10^{-4}$. In addition we also correct the over-all constant of the instanton size distribution in the MSbar scheme which was widely used incorrectly in the literature if non-trivial fermion content is present.

arXiv comment14 pages, 6 figures, references added

References in corpus (19)

• Five-Loop Running of the QCD coupling constant
• The five-loop beta function of Yang-Mills theory with fermions
• Axion Cosmology Revisited
• Precision SU(3) lattice thermodynamics for a large temperature range
• The topological susceptibility in finite temperature QCD and axion cosmology
• Lattice QCD input for axion cosmology
• Axion cosmology, lattice QCD and the dilute instanton gas
• Change of theta dependence in 4D SU(N) gauge theories across the deconfinement transition
• Chiral observables and topology in hot QCD with two families of quarks
• Topological susceptibility at high temperature on the lattice
• Instantons in Deep-Inelastic Scattering - The Simplest Process -
• Topology in full QCD at high temperature: a multicanonical approach
• Instanton-Induced Cross-Sections in Deep-Inelastic Scattering
• Axions, Instantons, and the Lattice
• Topological susceptibility of SU(N) gauge theories at finite temperature
• Precise Quark Mass Dependence of Instanton Determinant
• ${\chi }_{\text{top}}(T\gg T_{\text{c}})$ in pure-glue QCD through reweighting
• Massive field contributions to the QCD vacuum tunneling amplitude
• Temperature-dependence of the QCD topological susceptibility

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• Minimal warm inflation with complete medium response
• Topological susceptibility of $N_f=2+1$ QCD from staggered fermions spectral projectors at high temperatures
• The chiral phase transition and the axial anomaly
• Ideal topological gas in the high temperature phase of SU(3) gauge theory
• The Myriad Uses of Instantons
• CFTs with $U(m)\times U(n)$ Global Symmetry in 3D and the Chiral Phase Transition of QCD
• Anomalous interactions between mesons with nonzero spin and glueballs
• Fractional topological charge in $SU(N)$ gauge theories without dynamical quarks
• Topological observables and $\theta$ dependence in high temperature QCD from lattice simulations