Field theoretical approach to the study of theta dependence in Yang-Mills theories on the lattice

Abstract

We discuss the extension of the field theoretical approach, already used in the lattice determination of the topological susceptibility, to the computation of further terms in the expansion of the ground state energy $F(\theta )$ around $\theta =0$ in SU(N) Yang-Mills theories. In particular we determine the fourth order term in the expansion for SU(3) pure gauge theory and compare our results with previous cooling determinations. In the last part of the paper we make some considerations about the nature of the ultraviolet fluctuations responsible for the renormalization of the lattice topological charge correlation functions; in particular we propose and test an ansatz which leads to improved estimates of the fourth and higher order terms in the expansion of F(θ).

20 pages

References in corpus (1)

• Theta dependence of SU(N) gauge theories

Cited by in corpus (36)

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• $\theta$ dependence in $SU(3)$ Yang-Mills theory from analytic continuation
• Phase diagram of Yang-Mills theories in the presence of a theta term
• Theta-dependence of the spectrum of SU(N) gauge theories
• The 4D SU(3) gauge theory with an imaginary theta term
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• Cumulants of the QCD topological charge distribution
• Large-$N$ $SU(N)$ Yang-Mills theories with milder topological freezing
• $\theta$ dependence in trace deformed $SU(3)$ Yang-Mills theory: a lattice study
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• Topological properties of $C{P}^{N-1}$ models in the large-$N$ limit
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• Maximum-Likelihood Approach to Topological Charge Fluctuations in Lattice Gauge Theory
• Geometric Algorithm for Abelian-Gauge Models
• Topology via Spectral Projectors with Staggered Fermions
• Analyticity in theta on the lattice and the large volume limit of the topological susceptibility
• Topology and $\theta$ dependence in finite temperature $G_2$ lattice gauge theory
• Lattice determination of the topological susceptibility slope ${\chi }^{\prime }$ of $2d{\mathrm{CP}}^{N-1}$ models at large $N$
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• Topological features of the deconfinement transition
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• Analysis of systematic errors in the calculation of renormalization constants of the topological susceptibility on the lattice
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