Finite size phase transitions in QCD with adjoint fermions

TL;DR

The paper investigates volume dependence in QCD with adjoint fermions by simulating $N_c=3$, $N_f=2$ adjoint Dirac fermions on a lattice with one compactified spatial dimension, and studies how the phase structure evolves with the compactification size $L_c$. Using adjoint staggered fermions and Hybrid Monte Carlo, the authors map four center-symmetry realizations (two confined, two center-broken) as functions of $eta$ and quark mass, via the Polyakov loop along the compact direction and chiral observables. They find that chiral symmetry remains spontaneously broken across the center-related transitions and only possibly restores at much shorter $L_c$, challenging the proposed volume-independence in the large-$N_c$ limit for adjoint QCD. The work highlights the need for continuum extrapolations and exploration at larger $N_c$ to determine robustness and universality of the phase structure in adjoint QCD on small volumes.

Abstract

We perform a lattice investigation of QCD with three colors and 2 flavors of Dirac (staggered) fermions in the adjoint representation, defined on a 4d space with one spatial dimension compactified, and study the phase structure of the theory as a function of the size Lc of the compactified dimension. We show that four different phases take place, corresponding to different realizations of center symmetry: two center symmetric phases, for large or small values of Lc, separated by two phases in which center symmetry is broken in two different ways; the dependence of these results on the quark mass is discussed. We study also chiral properties and how they are affected by the different realizations of center symmetry; chiral symmetry, in particular, stays spontaneously broken at the phase transitions and may be restored at much lower values of the compactification radius. Our results could be relevant to a recently proposed conjecture of volume indepedence of QCD with adjoint fermions in the large Nc limit.

Figures (12)

• Figure 1: Scatter plots of the distribution of the trace of the Polyakov line, $L_{(3)}$, in the complex plane, for various values of $\beta$ and at a fixed quark mass $a m = 0.10$ on a $16^3 \times 4$ lattice.
• Figure 2: Same as in Fig. \ref{['distr1']}, but for $a m = 0.02$.
• Figure 3: Average value of the Polyakov line modulus, on a $16^3\times 4$ lattice, as a function of $\beta$ and for different bare quark masses.
• Figure 4: Time histories (in units of Molecular Dynamics trajectories and including part of the thermalization) of the real and imaginary part of $L_{(3)}$, for $am = 0.01$ and two different $\beta$ values in the confined and deconfined phase respectively.
• Figure 5: Adjoint Polyakov loop compared to the modulus of the fundamental loop (divided by a factor ten to fit in the figure), as a function of $\beta$ for $a m = 0.05$ on a $16^3 \times 4$ lattice.