Abstract
In our recent study of two-flavor lattice QCD using chiral fermions, we find strong suppression of axial U(1) anomaly above the critical temperature of chiral phase transition. Our simulation data also indicate suppression of topological susceptibility. In this talk, we present both of our theoretical and numerical evidence for disappearance of axial U(1) anomaly, emphasizing the importance of controlling lattice chiral symmetry violation, which is enhanced at high temperature.
Highlights
In our recent study of two-flavor lattice QCD using chiral fermions, we find strong suppression of axial U(1) anomaly above the critical temperature of chiral phase transition
“Can axial U(1) anomaly disappear at high temperature?” To this question the standard answer would be “No.” The reason is that unlike spontaneous breaking of symmetry, anomaly is a symmetry breaking at the cut-off scale where the theory is defined, and the anomalous Ward-Takahashi identity (WTI) with any operator O(x )
Note that we have started with the anomalous WTI for the U(1)A symmetry but ended up with the chiral condensate, a probe of spontaneous symmetry breaking (SSB) of S U(N f )L × S U(N f )R symmetry
Summary
“Can axial U(1) anomaly disappear at high temperature?” To this question the standard answer would be “No.” The reason is that unlike spontaneous breaking of symmetry, anomaly is a symmetry breaking at the cut-off scale where the theory is defined, and the anomalous Ward-Takahashi identity (WTI) with any operator O(x ),. Note that we have started with the anomalous WTI for the U(1)A symmetry but ended up with the chiral condensate, a probe of spontaneous symmetry breaking (SSB) of S U(N f )L × S U(N f )R symmetry These SSB of S U(N f )L × S U(N f )R and U(1)A anomaly are tied together for the quark bi-linear operators: there is no operator whose expectation value can break U(1)A without breaking S U(N f )L × S U(N f )R, and vice versa. The examples given above cover only a limited number of operators, and far from a proof of vanishing U(1)A anomaly They demonstrate that SSB of the S U(N f )L × S U(N f )R symmetry and the U(1)A anomaly are tightly connected with each other. We refer the readers to Refs.[21,22,23,24,25]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
