Phase diagrams of SU(N) gauge theories with fermions in various representations

We minimize the one-loop effective potential for SU(N) gauge theories including fermions with finite mass in the fundamental (F), adjoint (Adj), symmetric (S), and antisymmetric (AS) representations. We calculate the phase diagram on S^1 x R^3 as a function of the length of the compact dimension, beta, and the fermion mass, m. We consider the effect of periodic boundary conditions [PBC(+)] on fermions as well as antiperiodic boundary conditions [ABC(-)]. The use of PBC(+) produces a rich phase structure. These phases are distinguished by the eigenvalues of the Polyakov loop P. Minimization of the effective potential for QCD(AS/S,+) results in a phase where | Im Tr P | is maximized, resulting in charge conjugation (C) symmetry breaking for all N and all values of (m beta), however, the partition function is the same up to O(1/N) corrections as when ABC are applied. Therefore, regarding orientifold planar equivalence, we argue that in the one-loop approximation C-breaking in QCD(AS/S,+) resulting from the application of PBC to fermions does not invalidate the large N equivalence with QCD(Adj,-). Similarly, with respect to orbifold planar equivalence, breaking of Z(2) interchange symmetry resulting from application of PBC to bifundamental (BF) representation fermions does not invalidate equivalence with QCD(Adj,-) in the one-loop perturbative limit because the partition functions of QCD(BF,-) and QCD(BF,+) are the same. Of particular interest as well is the case of adjoint fermions where for Nf > 1 Majorana flavour confinement is obtained for sufficiently small (m beta), and deconfinement for sufficiently large (m beta). For N >= 3 these two phases are separated by one or more additional phases, some of which can be characterized as partially-confining phases.Comment: 39 pages, 26 figures, JHEP3; references added, small corrections mad

The QCD sign problem as a total derivative

We consider the distribution of the complex phase of the fermion determinant in QCD at nonzero chemical potential and examine the physical conditions under which the distribution takes a Gaussian form. We then calculate the baryon number as a function of the complex phase of the fermion determinant and show 1) that the exponential cancellations produced by the sign problem take the form of total derivatives 2) that the full baryon number is orthogonal to this noise. These insights allow us to define a self-consistency requirement for measurements of the baryon number in lattice simulations.Comment: 5 pages, reference added, version to appear in PRD rapid communication

The density in the density of states method

It has been suggested that for QCD at finite baryon density the distribution of the phase angle, i.e. the angle defined as the imaginary part of the logarithm of the fermion determinant, has a simple Gaussian form. This distribution provides the density in the density of states approach to the sign problem. We calculate this phase angle distribution using i) the hadron resonance gas model; and ii) a combined strong coupling and hopping parameter expansion in lattice gauge theory. While the former model leads only to a Gaussian distribution, in the latter expansion we discover terms which cause the phase angle distribution to deviate, by relative amounts proportional to powers of the inverse lattice volume, from a simple Gaussian form. We show that despite the tiny inverse-volume deviation of the phase angle distribution from a simple Gaussian form, such non-Gaussian terms can have a substantial impact on observables computed in the density of states/reweighting approach to the sign problem.Comment: 43 pages, 4 figure

Large N lattice QCD and its extended strong-weak connection to the hypersphere

We calculate an effective Polyakov line action of QCD at large Nc and large Nf from a combined lattice strong coupling and hopping expansion working to second order in both, where the order is defined by the number of windings in the Polyakov line. We compare with the action, truncated at the same order, of continuum QCD on S^1 x S^d at weak coupling from one loop perturbation theory, and find that a large Nc correspondence of equations of motion found in \cite{Hollowood:2012nr} at leading order, can be extended to the next order. Throughout the paper, we review the background necessary for computing higher order corrections to the lattice effective action, in order to make higher order comparisons more straightforward.Comment: 33 pages, 7 figure

New Phases of SU(3) and SU(4) at Finite Temperature

The addition of an adjoint Polyakov loop term to the action of a pure gauge theory at finite temperature leads to new phases of SU(N) gauge theories. For SU(3), a new phase is found which breaks Z(3) symmetry in a novel way; for SU(4), the new phase exhibits spontaneous symmetry breaking of Z(4) to Z(2), representing a partially confined phase in which quarks are confined, but diquarks are not. The overall phase structure and thermodynamics is consistent with a theoretical model of the effective potential for the Polyakov loop based on perturbation theory.Comment: 18 pages, 17 figures, RevTeX