Topology and axions in QCD

Abstract

QCD axions are at the crossroads of QCD topology and Dark Matter searches. We present here the current status of topological studies on the lattice, and their implication on axion physics. We outline the specific challenges posed by lattice topology, the different proposals for handling them, the observable effects of topology on the QCD spectrum and its interrelation with chiral and axial symmetries. We review the transition to the quark–gluon plasma, the fate of topology at the transition, and the approach to the high temperature limit. We discuss the extrapolations needed to reach the regime of cosmological relevance, and the resulting constraints on the QCD axion.

More axions from strings

“…where, as suggested by the dilute instanton gas approximation [37] and supported by recent lattice simulations [38][39][40][41][42] (see also ref. [43] for a recent review), we assume that the axion potential at early times is described by a single cosine potential and the axion mass has a power dependence on the temperature m a ∝ T −α/2 ∝ t α/4 , with α 8 the preferred value. 11 Naively one might think that the axions produced by strings propagate freely like radiation until their momenta (which is typically of order a few H) become of the same order as the axion mass m a , after which they would start propagating as nonrelativistic matter.…”

“…As shown below, provided q 1 its precise value is not important for large ξ log , so this choice does not have any significant effect on the results obtained. 43…”

Higher topological charge and the QCD vacuum

“…In addition, assume that the instantons are dilute, i.e., the spacetime distance between each instanton is large against their effective size. It has been demonstrated by numerous studies of QCD and Yang-Mills theory on the lattice that these assumptions are justified at temperatures above about 2.5T c [30][31][32][33][34][35][36][37][38][39]. Note that, while the overall power of the topological susceptibility with respect to T measured on the lattice agrees very well with the predictions of the dilute instanton gas, the prefactor is off.…”

“…The temperature dependence of the anharmonicity coefficients is solely due to multi-instanton effects. Computations of b 2 on the lattice above T c show indications that, starting from the single-instanton value −1/12 at very high temperature, b 2 decreases slightly with decreasing temperature for T 2.5T c , before it starts rising towards small temperatures [35][36][37][38]. As demonstrated here, multi-instanton corrections can explain this behavior qualitatively.…”

“…Finite temperature is crucial for a self-consistent treatment, since it effectively cuts off large-scale instantons. This is clearly shown by numerous first-principles studies of QCD on the lattice, both with dynamical quarks [30][31][32][33][34][35], and in the quenched limit [36][37][38][39]. It has been demonstrated that the temperature dependence of the lowest topological susceptibility χ 2 , which measures the variance of the topological charge distribution, is in very good agreement with the corresponding prediction from a dilute gas of instantons for T 2.5T c , where T c is the pseudocritical temperature of the chiral phase transition.…”