16140939
Chaotic coupling constants
Abstract We examine some novel physical consequences of the general structure of moduli spaces of string vacua. These include (1) finiteness of the volume of the moduli space and (2) chaotic motion of the moduli in the early universe. To fix ideas we examine in detail the example of the (conjectural) dilaton-axion “S-duality” of four-dimensional string compactifications. The facts (1) and (2) together might help to solve some problems with the standard scenarios for supersymmetry breaking and vacuum selection in string theory.
118337669
Symmetries of the Bosonic String S-Matrix
The bracket operation on mutually local BRST classes may be combined with Lorentz invariance and analyticity to write an infinite set of finite difference relations on string scattering amplitudes. When combined with some simple physical criteria these relations uniquely determine the genus zero string $S$-matrix for $N\leq 26$-particle scattering in $\IR^{25,1}$ in terms of a single parameter, $\kappa$, the string coupling. We propose that the high-energy limit of the relations are the Ward identities for the high-energy symmetries of string theory.
124306496
The M theory three form and E(8) gauge theory
122595912
Anomalies in Nonlinear $\sigma$ Models
Certain nonlinear sigma models with fermions suffer from an anomaly similar to the one in non-Abelian gauge theory. We exhibit this anomaly using both perturbative and global methods. The affected theories are ill defined and hence unsuitable for describing low-energy dynamics. They include certain supersymmetric models in four space-time dimensions.
15868022
Donaldson Invariants for Non-Simply Connected Manifolds
Abstract:We study Coulomb branch (“u-plane”) integrals for supersymmetric SU(2),SO(3) Yang–Mills theory on 4-manifolds X of b1(X)>0, b2+(X)= 1. Using wall-crossing arguments we derive expressions for the Donaldson invariants for manifolds with b1(X)>0, b2+(X)>0. Explicit expressions for , where Fg is a Riemann surface of genus g are obtained using Kronecker's double series identity. The result might be useful in future studies of quantum cohomology.
14205277
Melvin Models and Diophantine Approximation
Melvin models with irrational twist parameter provide an interesting example of conformal field theories with non-compact target space, and localized states which are arbitrarily close to being delocalized. We study the torus partition sum of these models, focusing on the properties of the regularized dimension of the space of localized states. We show that its behavior is related to interesting arithmetic properties of the twist parameter γ, such as the Lyapunov exponent. Moreover, for γ in a set of measure one the regularized dimension is in fact not a well-defined number but must be considered as a random variable in a probability distribution.
14264323
A nonperturbative measurement of the broken phase sphaleron rate
Abstract We develop a method to compute the sphaleron rate in the electroweak broken phase nonperturbatively. The rate is somewhat slower than a perturbative estimate. In SU(2)×U(1) Higgs theory at the physical value of Θ W , and assuming that the latent heat of the phase transition reheats the universe to the equilibrium temperature, baryon number erasure after the phase transition is prevented only when ( λ / g 2 )≤0.036.
14877410
Sphaleron rate in the symmetric electroweak phase
Recently Bo''deker presented an effective infrared theory for the dynamics of Yang-Mills theory, suitable for studying the rate of baryon number violation in the early universe. We extend his theory to include the Higgs boson fields, and study how much the Higgs boson affects the baryon number violation rate in the symmetric phase, at the phase coexistence temperature of a first order electroweak phase transition. The rate is about 20% smaller than in pure Yang-Mills theory. We also analyze the sphaleron rate in the analytic crossover regime. Our treatment relies on the ergodicity conjecture for 3D scalar {phi}{sup 4} theory.
16153776
Computing the strong sphaleron rate
Abstract We measure the diffusion constant for Chern-Simons number for classical, lattice SU(3) Yang-Mills theory, using a generalization of the topological definition of Chern-Simons number developed recently by Moore and Turok. The diffusion constant is much larger than that for SU(2), even before the ratio of coupling constants has been accounted for, which implies that chiral quark number is efficiently destroyed by strong processes during the electroweak phase transition. For the physical value of αs we estimate the decay time for chiral quark number to be about 80 T , although various systematics make this number uncertain by about a factor of 2.
14338184
The Sphaleron Rate: Bodeker's Leading Log
Bodeker has recently shown that the high temperature sphaleron rate, which measures baryon number violation in the hot standard model, receives logarithmic corrections to its leading parametric behavior; Γ=κ′[log(mD/g2T)+O(1)](g2T2/mD2)αW5T4. After discussing the physical origin of these corrections, I compute the leading log coefficient numerically: κ′=10.8±0.7. The log is fairly small relative to the O(1) “correction;” so non-logarithmic contributions dominate at realistic values of the coupling.
12818530
Electroweak bubble nucleation, nonperturbatively
We present a lattice method to compute bubble nucleation rates at radiatively induced first order phase transitions, in high temperature, weakly coupled field theories, nonperturbatively. A generalization of Langer's approach, it makes no recourse to saddle point expansions and includes completely the dynamical prefactor. We test the technique by applying it to the electroweak phase transition in the minimal standard model, at an unphysically small Higgs mass which gives a reasonably strong phase transition (lambda/g^2 =0.036, which corresponds to m(Higgs)/m(W) = 0.54 at tree level but does not correspond to a positive physical Higgs mass when radiative effects of the top quark are included), and compare the results to older perturbative and other estimates. While two loop perturbation theory slightly under-estimates the strength of the transition measured by the latent heat, it over-estimates the amount of supercooling by a factor of 2.