Abstract
Lattice computations are the only first principle method capable of quantitatively assessing the topological properties of QCD at high temperature, however the numerical determination of the topological properties of QCD, especially in the high temperature phase, is a notoriously difficult problem. We will discuss the difficulties encountered in such a computation and some strategies that have been proposed to avoid (or at least to alleviate) them.
Highlights
Since the discovery of the instanton solution [1] and the introduction of the θ-vacuum [2, 3] there has been constant interest in the study of the intrinsically non-perturbative aspects of gauge theories related to the θ-dependence. Such an interest was motivated by phenomenological and theoretical reasons: from the theoretical point of view θ-dependence is a new knob that can be used to investigate the properties of strongly interacting gauge theories, from the phenomenological side it is connected with the anomalous UA(1) symmetry of massless QCD and the CP invariance of strong interactions
This approach was initiated by Peccei and Quinn [5, 6] and, soon after its proposal, this mechanism was shown to imply the existence of a new light pseudoscalar particle [7, 8], the axion, whose properties are strictly related to the behaviour of the effective potential for small θ values
In the high temperature phase the freezing problem is still present in this case there is a new source of trouble: since the topological susceptibility goes to zero at high temperature, by keeping the physical volume fixed and increasing the temperature we are reducing the typical amount of topological charge that is present in the lattice, which is given by χ(T )V (see Eq (6))
Summary
Since the discovery of the instanton solution [1] and the introduction of the θ-vacuum [2, 3] there has been constant interest in the study of the intrinsically non-perturbative aspects of gauge theories related to the θ-dependence Such an interest was motivated by phenomenological and theoretical reasons: from the theoretical point of view θ-dependence is a new knob that can be used to investigate the properties of strongly interacting gauge theories, from the phenomenological side it is connected with the anomalous UA(1) symmetry of massless QCD and the CP invariance of strong interactions. At T = 0 chiral perturbation theory can be used to compute the effective potential as a function of the θ value [9, 10], obtaining at leading order for the physical case of two light flavours the result.
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