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

Effective Kinetic Theory for High Temperature Gauge Theories

Quasiparticle dynamics in relativistic plasmas associated with hot, weakly-coupled gauge theories (such as QCD at asymptotically high temperature $T$) can be described by an effective kinetic theory, valid on sufficiently large time and distance scales. The appropriate Boltzmann equations depend on effective scattering rates for various types of collisions that can occur in the plasma. The resulting effective kinetic theory may be used to evaluate observables which are dominantly sensitive to the dynamics of typical ultrarelativistic excitations. This includes transport coefficients (viscosities and diffusion constants) and energy loss rates. We show how to formulate effective Boltzmann equations which will be adequate to compute such observables to leading order in the running coupling $g(T)$ of high-temperature gauge theories [and all orders in $1/\log g(T)^{-1}$]. As previously proposed in the literature, a leading-order treatment requires including both $22$ particle scattering processes as well as effective ``$12$'' collinear splitting processes in the Boltzmann equations. The latter account for nearly collinear bremsstrahlung and pair production/annihilation processes which take place in the presence of fluctuations in the background gauge field. Our effective kinetic theory is applicable not only to near-equilibrium systems (relevant for the calculation of transport coefficients), but also to highly non-equilibrium situations, provided some simple conditions on distribution functions are satisfied.Comment: 40 pages, new subsection on soft gauge field instabilities adde

Necessary and sufficient conditions for non-perturbative equivalences of large N orbifold gauge theories

Large N coherent state methods are used to study the relation between U(N) gauge theories containing adjoint representation matter fields and their orbifold projections. The classical dynamical systems which reproduce the large N limits of the quantum dynamics in parent and daughter orbifold theories are compared. We demonstrate that the large N dynamics of the parent theory, restricted to the subspace invariant under the orbifold projection symmetry, and the large N dynamics of the daughter theory, restricted to the untwisted sector invariant under "theory space'' permutations, coincide. This implies equality, in the large N limit, between appropriately identified connected correlation functions in parent and daughter theories, provided the orbifold projection symmetry is not spontaneously broken in the parent theory and the theory space permutation symmetry is not spontaneously broken in the daughter. The necessity of these symmetry realization conditions for the validity of the large N equivalence is unsurprising, but demonstrating the sufficiency of these conditions is new. This work extends an earlier proof of non-perturbative large N equivalence which was only valid in the phase of the (lattice regularized) theories continuously connected to large mass and strong coupling.Comment: 21 page, JHEP styl

Center-stabilized Yang-Mills theory: confinement and large NN volume independence

We examine a double trace deformation of SU(N) Yang-Mills theory which, for large $N$ and large volume, is equivalent to unmodified Yang-Mills theory up to $O(1/N^2)$ corrections. In contrast to the unmodified theory, large $N$ volume independence is valid in the deformed theory down to arbitrarily small volumes. The double trace deformation prevents the spontaneous breaking of center symmetry which would otherwise disrupt large $N$ volume independence in small volumes. For small values of $N$, if the theory is formulated on $\R^3 \times S^1$ with a sufficiently small compactification size $L$, then an analytic treatment of the non-perturbative dynamics of the deformed theory is possible. In this regime, we show that the deformed Yang-Mills theory has a mass gap and exhibits linear confinement. Increasing the circumference $L$ or number of colors $N$ decreases the separation of scales on which the analytic treatment relies. However, there are no order parameters which distinguish the small and large radius regimes. Consequently, for small $N$ the deformed theory provides a novel example of a locally four-dimensional pure gauge theory in which one has analytic control over confinement, while for large $N$ it provides a simple fully reduced model for Yang-Mills theory. The construction is easily generalized to QCD and other QCD-like theories.Comment: 29 pages, expanded discussion of multiple compactified dimension

High temperature color conductivity at next-to-leading log order

The non-Abelian analog of electrical conductivity at high temperature has previously been known only at leading logarithmic order: that is, neglecting effects suppressed only by an inverse logarithm of the gauge coupling. We calculate the first sub-leading correction. This has immediate application to improving, to next-to-leading log order, both effective theories of non-perturbative color dynamics, and calculations of the hot electroweak baryon number violation rate.Comment: 47 pages, 6+2 figure

The Sphaleron Barrier in the Presence of Fermions

We calculate the minimal energy path over the sphaleron barrier in the pre\-sen\-ce of fermions, assuming that the fermions of a doublet are degenerate in mass. This allows for spherically symmetric ans\"atze for the fields, when the mixing angle dependence is neglected. While light fermions have little influence on the barrier, the presence of heavy fermions ($M_F \sim$ TeV) strongly deforms the barrier, giving rise to additional sphalerons for very heavy fermions ($M_F \sim$ 10 TeV). Heavy fermions form non-topological solitons in the vacuum sector.Comment: 19 pages, latex, 18 figures in 3 seperate uuencoded postscript files THU-93/1

Level Crossing Along Sphaleron Barriers

In the electroweak sector of the standard model topologically inequivalent vacua are separated by finite energy barriers, whose height is given by the sphale\-ron. For large values of the Higgs mass there exist several sphaleron solutions and the barriers are no longer symmetric. We construct paths of classical configurations from one vacuum to a neighbouring one and solve the fermion equations in the background field configurations along such paths, choosing the fermions of a doublet degenerate in mass. As in the case of light Higgs masses we observe the level crossing phenomenon also for large Higgs masses.Comment: 17 pages, latex, 10 figures in uuencoded postscript files. THU-94/0

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

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

Towards a Realistic Equation of State of Strongly Interacting Matter

We consider a relativistic strongly interacting Bose gas. The interaction is manifested in the off-shellness of the equilibrium distribution. The equation of state that we obtain for such a gas has the properties of a realistic equation of state of strongly interacting matter, i.e., at low temperature it agrees with the one suggested by Shuryak for hadronic matter, while at high temperature it represents the equation of state of an ideal ultrarelativistic Stefan-Boltzmann gas, implying a phase transition to an effectively weakly interacting phase.Comment: LaTeX, figures not include