Z(3)-symmetric effective theory for SU(3) Yang-Mills theory at high temperature

A three-dimensional effective theory for high temperature SU(3) gauge theory, which maintains the Z(3) center symmetry of the full theory, is constructed. Such a Z(3) invariant effective theory should be applicable to a wider temperature range than the usual effective theory, known as EQCD, which fails to respect the center symmetry. This center-symmetric effective theory can reproduce domain wall and phase transition properties that are not accessible in EQCD. After identifying a convenient class of Z(3) invariant effective theories, we constrain the coefficients of the various terms in the Lagrangian using leading-order matching to EQCD at high temperature, plus matching of domain wall properties in the full theory. We sketch the expected structure of the phase diagram of the effective theory and briefly discuss the prospects of numerical simulations and the addition of quarks.Comment: 30 pages, 5 figures, v2 with minor correction

From Instantons to Sphalerons: Time-Dependent Periodic Solutions of SU(2)-Higgs Theory

We solve numerically for periodic, spherically symmetric, classical solutions of SU(2)-Higgs theory in four-dimensional Euclidean space. In the limit of short periods the solutions approach tiny instanton-anti-instanton superpositions while, for longer periods, the solutions merge with the static sphaleron. A previously predicted bifurcation point, where two branches of periodic solutions meet, appears for Higgs boson masses larger than $3.091 M_W$.Comment: 14 pages, RevTeX with eps figure

Non-perturbative equivalences among large N gauge theories with adjoint and bifundamental matter fields

We prove an equivalence, in the large N limit, between certain U(N) gauge theories containing adjoint representation matter fields and their orbifold projections. Lattice regularization is used to provide a non-perturbative definition of these theories; our proof applies in the strong coupling, large mass phase of the theories. Equivalence is demonstrated by constructing and comparing the loop equations for a parent theory and its orbifold projections. Loop equations for both expectation values of single-trace observables, and for connected correlators of such observables, are considered; hence the demonstrated non-perturbative equivalence applies to the large N limits of both string tensions and particle spectra.Comment: 40 pages, JHEP styl

Domain Walls and Metastable Vacua in Hot Orientifold Field Theories

We consider "Orientifold field theories", namely SU(N) gauge theories with Dirac fermions in the two-index representation at high temperature. When N is even these theories exhibit a spontaneously broken Z2 centre symmetry. We study aspects of the domain wall that interpolates between the two vacua of the theory. In particular we calculate its tension to two-loop order. We compare its tension to the corresponding domain wall in a SU(N) gauge theory with adjoint fermions and find an agreement at large-N, as expected from planar equivalence between the two theories. Moreover, we provide a non-perturbative proof for the coincidence of the tensions at large-N. We also discuss the vacuum structure of the theory when the fermion is given a large mass and argue that there exist N-2 metastable vacua. We calculate the lifetime of those vacua in the thin wall approximation.Comment: 29 pages, 4 figures. v2: minor changes in the introduction section. to appear in JHE

Quantum limit of deterministic theories

We show that the quantum linear harmonic oscillator can be obtained in the large $N$ limit of a classical deterministic system with SU(1,1) dynamical symmetry. This is done in analogy with recent work by G.'t Hooft who investigated a deterministic system based on SU(2). Among the advantages of our model based on a non--compact group is the fact that the ground state energy is uniquely fixed by the choice of the representation.Comment: 4 pages, 2 figures, minor corrections added. To appear in the Proceedings of Waseda International Symposium on Fundamental Physics: "New Perspectives in Quantum Physics", 12-15 November 2002, Waseda University, Tokyo, Japa

One-Loop Quantum Energy Densities of Domain Wall Field Configurations

We discuss a simple procedure for computing one-loop quantum energies of any static field configuration that depends non-trivially on only a single spatial coordinate. We specifically focus on domain wall-type field configurations that connect two distinct minima of the effective potential, and may or may not be the solutions of classical field equations. We avoid the conventional summation of zero-point energies, and instead exploit the relation between functional determinants and solutions of associated differential equations. This approach allows ultraviolet divergences to be easily isolated and extracted using any convenient regularization scheme. Two examples are considered: two-dimensional $\phi^4$ theory, and three-dimensional scalar electrodynamics with spontaneous symmetry breaking at the one-loop level.Comment: RevTex, 29 pages, 1 figure, minor corrections, references adde

Center clusters in the Yang-Mills vacuum

Properties of local Polyakov loops for SU(2) and SU(3) lattice gauge theory at finite temperature are analyzed. We show that spatial clusters can be identified where the local Polyakov loops have values close to the same center element. For a suitable definition of these clusters the deconfinement transition can be characterized by the onset of percolation in one of the center sectors. The analysis is repeated for different resolution scales of the lattice and we argue that the center clusters have a continuum limit.Comment: Table added. Final version to appear in JHE

Critical Exponents from AdS/CFT with Flavor

We use the AdS/CFT correspondence to study the thermodynamics of massive N=2 supersymmetric hypermultiplet flavor fields coupled to N=4 supersymmetric SU(Nc) Yang-Mills theory, formulated on curved four-manifolds, in the limits of large Nc and large 't Hooft coupling. The gravitational duals are probe D-branes in global thermal AdS. These D-branes may undergo a topology-changing transition in the bulk. The D-brane embeddings near the point of the topology change exhibit a scaling symmetry. The associated scaling exponents can be either real- or complex-valued. Which regime applies depends on the dimensionality of a collapsing submanifold in the critical embedding. When the scaling exponents are complex-valued, a first-order transition associated with the flavor fields appears in the dual field theory. Real scaling exponents are expected to be associated with a continuous transition in the dual field theory. For one example with real exponents, the D7-brane, we study the transition in detail. We find two field theory observables that diverge at the critical point, and we compute the associated critical exponents. We also present analytic and numerical evidence that the transition expresses itself in the meson spectrum as a non-analyticity at the critical point. We argue that the transition we study is a true phase transition only when the 't Hooft coupling is strictly infinite.Comment: 31 pages, 21 eps files in 12 figures; v2 added one reference and one footnote, version published in JHE

Debye screening in strongly coupled N=4 supersymmetric Yang-Mills plasma

Using the AdS/CFT correspondence, we examine the behavior of correlators of Polyakov loops and other operators in N=4 supersymmetric Yang-Mills theory at non-zero temperature. The implications for Debye screening in this strongly coupled non-Abelian plasma, and comparisons with available results for thermal QCD, are discussed.Comment: 21 pages, 5 figures, significantly expanded discussion of Polyakov loop correlator and static quark-antiquark potentia