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Does hot QCD have a conformal manifold in the chiral limit?

Shi Chen, Aleksey Cherman, Robert D. Pisarski

Abstract

Recent lattice evidence suggests the chiral phase transition in QCD is second-order for $N_f \ge 2$ massless flavors. We constrain CFT descriptions of a critical line in temperature $T$ and imaginary baryon chemical potential $θ_B = iμ_B/T$. An 't Hooft anomaly at general $θ_B$ constrains the transition even at $θ_B = 0$, leaving only three minimal scenarios. The best-motivated scenario for $N_f\ge3$, and perhaps also $N_f = 2$, is beyond Ginzburg-Landau, featuring a conformal manifold of $θ_B$-dependent universality classes with an exactly marginal operator related to baryon density.

Does hot QCD have a conformal manifold in the chiral limit?

Abstract

Recent lattice evidence suggests the chiral phase transition in QCD is second-order for massless flavors. We constrain CFT descriptions of a critical line in temperature and imaginary baryon chemical potential . An 't Hooft anomaly at general constrains the transition even at , leaving only three minimal scenarios. The best-motivated scenario for , and perhaps also , is beyond Ginzburg-Landau, featuring a conformal manifold of -dependent universality classes with an exactly marginal operator related to baryon density.
Paper Structure (4 sections, 38 equations, 1 figure, 4 tables)

This paper contains 4 sections, 38 equations, 1 figure, 4 tables.

Table of Contents

  1. Effective theory in the high-$T$ gapped phase
  2. Second-order phase transition at $\theta_B=\pi$ in the high-$T$ phase
  3. The fate of emergent $U(1)_A$ symmetry at the chiral transition
  4. Extrapolating from $(2+\epsilon)$D to $3$D

Figures (1)

  • Figure 1: Minimal phase diagrams of massless QCD consistent with a natural second-order line of chiral phase transitions. Left: Landau scenario. Middle: Landau-DQCP scenario. Right: Conformal-manifold scenario. The conformal manifold scenario appears plausible for all $N_f \ge 2$, while the Landau and Landau-DQCP scenarios are only plausible for $N_f=2$.