Nonperturbative Condensates in the Electroweak Phase-Transition

We discuss the electroweak phase-transition in the early universe, using non-perturbative flow equations for a computation of the free energy. For a scalar mass above $\sim 70$ GeV, high-temperature perturbation theory cannot describe this transition reliably. This is due to the dominance of three-dimensional physics at high temperatures which implies that the effective gauge coupling grows strong in the symmetric phase. We give an order of magnitude-estimate of nonperturbative effects in reasonable agreement with recent results from electroweak lattice simulations. (Talk given by C. Wetterich at the 3rd Colloque Cosmologie, Paris, June 7-9, 1995, to appear in the proceedings)Comment: 20 pages, LaTeX, 4 figures, Talk given by C. Wetterich at the 3rd Colloque Cosmologie, Paris, June 7-9, 1995, to appear in the proceedings, *** Replaced figure 1 **

Can being behind get you ahead? Reference Dependence and Asymmetric Equilibria in an Unfair Tournament

Everyone remembers a plot where a disadvantaged individual facing the prospect of failure, spends more effort, turns around the game and wins unexpectedly. Most tournament theories, however, predict the opposite pattern and see the disadvantaged agent investing less effort. We show that ’turn arounds’, i.e. situations where the trailing player spends more effort and becomes the likely winner of the tournament, can be the outcome of a Nash equilibrium when the initial unevenness is known and players have reference-dependent preferences. Under certain conditions, they are the only pure strategy equilibrium. If the initial unevenness is large enough the advantaged player will always invest the most effort. We also show that equilibria in which the player behind catches up without becoming the likely winner do not exist

PHASE TRANSITION OF N-COMPONENT SUPERCONDUCTORS

We investigate the phase transition in the three-dimensional abelian Higgs model for N complex scalar fields, using the gauge-invariant average action \Gamma_{k}. The dependence of \Gamma_{k} on the effective infra-red cut-off k is described by a non-perturbative flow equation. The transition turns out to be first- or second-order, depending on the ratio between scalar and gauge coupling. We look at the fixed points of the theory for various N and compute the critical exponents of the model. Comparison with results from the \epsilon-expansion shows a rather poor convergence for \epsilon=1 even for large N. This is in contrast to the surprisingly good results of the \epsilon-expansion for pure scalar theories. Our results suggest the existence of a parameter range with a second-order transition for all N, including the case of the superconductor phase transition for N=1.Comment: 30p. with 9 uuencoded .eps-figures appended, LaTe

Comparison of Renormalization-Group and Lattice Studies of the Electroweak Phase Transition

We compare the results of renormalization-group and lattice studies for the properties of the electroweak phase transition. This comparison reveals the mechanisms that underlie the phenomenology of the phase transition.Comment: 13 pages, 3 figure

Wilsonian flows and background fields

We study exact renormalisation group flows for background field dependent regularisations. It is shown that proper-time flows are approximations to exact background field flows for a specific class of regulators. We clarify the role of the implicit scale dependence introduced by the background field. Its impact on the flow is evaluated numerically for scalar theories at criticality for different approximations and regularisations. Implications for gauge theories are discussed.Comment: 12 pages, v2: references added. to appear in PL

Critical exponents from optimised renormalisation group flows

Within the exact renormalisation group, the scaling solutions for O(N) symmetric scalar field theories are studied to leading order in the derivative expansion. The Gaussian fixed point is examined for d>2 dimensions and arbitrary infrared regularisation. The Wilson-Fisher fixed point in d=3 is studied using an optimised flow. We compute critical exponents and subleading corrections-to-scaling to high accuracy from the eigenvalues of the stability matrix at criticality for all N. We establish that the optimisation is responsible for the rapid convergence of the flow and polynomial truncations thereof. The scheme dependence of the leading critical exponent is analysed. For all N > 0, it is found that the leading exponent is bounded. The upper boundary is achieved for a Callan-Symanzik flow and corresponds, for all N, to the large-N limit. The lower boundary is achieved by the optimised flow and is closest to the physical value. We show the reliability of polynomial approximations, even to low orders, if they are accompanied by an appropriate choice for the regulator. Possible applications to other theories are outlined.Comment: 34 pages, 15 figures, revtex, to appear in NP