Abstract
We promote the usual QCD θ-parameter to a field and interpret it as the phase of the quark condensate, which becomes nontrivial when topological defects, vortices in our formulation, are induced in the quark condensate by the QCD strings (chromoelectric flux tubes). The QCD topological term emerges naturally as a derivative coupling between the Chern-Simons current and a supercurrent in the quark condensate. This new formulation can address theUA(1) problem and leads to the chiral magnetic effects. It is possible that in this formulation the strong CP problem can be avoided without the axion particle.
Highlights
The UA(1) problem, i.e. the absence of a ninth light pseudoscalar meson or the reason why the η meson is much heavier than expected, was considered a solved problem long time ago
Kogut and Susskind noted the necessary ingredient for the solution should be a pole at q2 = 0 in the matrix elements of some gauge-invariant operators [1]; ’t Hooft noticed that instantons can lead to an explicit solution as a result of the axial anomaly [2], and Crewther studied the problem using anomalous Ward identities [3]; Witten explained this problem from the large Nc point of view [4]and more concretely, Veneziano introduced a ghost state and showed the possibility to calculate the mass of the η meson [5]
Our focus is the quantum chromodynamics (QCD) topological charge term and we demonstrate that, assuming quantum vorticity in the quark condensate, a topological term can naturally emerge as an effective action in the bulk space due to the anomaly-inflow mechanism discovered by Callan and Harvey [17]
Summary
The UA(1) problem, i.e. the absence of a ninth light pseudoscalar meson or the reason why the η meson is much heavier than expected, was considered a solved problem long time ago. Kogut and Susskind noted the necessary ingredient for the solution should be a pole at q2 = 0 in the matrix elements of some gauge-invariant operators [1]; ’t Hooft noticed that instantons can lead to an explicit solution as a result of the axial anomaly [2], and Crewther studied the problem using anomalous Ward identities [3]; Witten explained this problem from the large Nc point of view [4]and more concretely, Veneziano introduced a ghost state and showed the possibility to calculate the mass of the η meson [5] Since all these solutions involve a topological charge term (e.g. the usual θ-term) in quantum chromodynamics (QCD), which cause another problem of the CP violation in the strong interaction (the strong CP problem), it seems to be still interesting to consider other scenarios to address the UA(1) problem again. Other applications in topics such as chiral magnetic effect and the possibility of avoiding the strong CP problem are discussed as well
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