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

Twist operators in higher dimensions

We study twist operators in higher dimensional CFT's. In particular, we express their conformal dimension in terms of the energy density for the CFT in a particular thermal ensemble. We construct an expansion of the conformal dimension in power series around n=1, with n being replica parameter. We show that the coefficients in this expansion are determined by higher point correlations of the energy-momentum tensor. In particular, the first and second terms, i.e. the first and second derivatives of the scaling dimension, have a simple universal form. We test these results using holography and free field theory computations, finding agreement in both cases. We also consider the `operator product expansion' of spherical twist operators and finally, we examine the behaviour of correlators of twist operators with other operators in the limit n ->1.Comment: 44 pages, 2 figure

PNJL model for adjoint fermions

Recent work on QCD-like theories has shown that the addition of adjoint fermions obeying periodic boundary conditions to gauge theories on R^3 X S^1 can lead to a restoration of center symmetry and confinement for sufficiently small circumference L of S^1. At small L, perturbation theory may be used reliably to compute the effective potential for the Polyakov loop P in the compact direction. Periodic adjoint fermions act in opposition to the gauge fields, which by themselves would lead to a deconfined phase at small L. In order for the fermionic effects to dominate gauge field effects in the effective potential, the fermion mass must be sufficiently small. This indicates that chiral symmetry breaking effects are potentially important. We develop a Polyakov-Nambu-Jona Lasinio (PNJL) model which combines the known perturbative behavior of adjoint QCD models at small L with chiral symmetry breaking effects to produce an effective potential for the Polyakov loop P and the chiral order parameter psi-bar psi. A rich phase structure emerges from the effective potential. Our results are consistent with the recent lattice simulations of Cossu and D'Elia, which found no evidence for a direct connection between the small-L and large-L confining regions. Nevertheless, the two confined regions are connected indirectly if an extended field theory model with an irrelevant four-fermion interaction is considered. Thus the small-L and large-L regions are part of a single confined phase.Comment: 6 pages, 4 figures; presented at INPC 201

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

Assessing An Economics Programme: Hansen Proficiencies, ePortfolio, and Undergraduate Research

Numerous sources calling for more accountability in higher education are putting increased pressure on many economics departments to develop assessment plans. This paper discusses a set of principles for programmatic assessment gleaned from the assessment literature, while highlighting one US economic department's journey to develop an assessment of student learning outcomes based on Hansen's proficiencies. We explain the curriculum reforms that culminate with independent undergraduate research as suggested by the highest level of Hansen's proficiencies. We describe ePortfolios which showcase student abilities and integrate evidence of student learning across the curriculum. For departments without direct guidance from accreditation boards or other agencies, we put forth a process of forming programmatic assessment in economics.