123115671
Physical solutions for unitary matrix models
Abstract We study the simplest double scaling limit of the integral over a unitary matrix, shown by Periwal and Shevitz to admit an exact solution in terms of the mKdV hierarchy. We show that there is a unique non-perturbative solution of the string equation corresponding to the true double scaling limit of the integral, which interpolates smoothly between weak and strong coupling regimes.
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.
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
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.
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.
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.
118445577
3D N = 1 SYM Chern-Simons theory on the Lattice
We present a method to implement 3-dimensional N = 1 SUSY Yang-Mills theory (a theory with two real supercharges containing gauge fields and an adjoint Majorana fermion) on the lattice, including a way to implement the Chern-Simons term present in this theory. At nonzero Chern-Simons number our implementation suffers from a sign problem which will make the numerical effort grow exponentially with volume. We also show that the theory with vanishing Chern-Simons number is anomalous; its partition function identically vanishes.
17729023
String-mediated electroweak baryogenesis: A critical analysis
We study the scenario of electroweak baryogenesis mediated by nonsuperconducting cosmic strings. This idea relies upon electroweak symmetry being restored in a region around the core of the topological defect so that, within this region, the rate of baryon number violation is enhanced. We compute numerically how effectively baryon number is violated along a cosmic string, at an epoch when the baryon number violation rate elsewhere is negligible. We show that $B$ violation along nonsuperconducting strings is quite inefficient. When proper accounting is taken of the velocity dependence of the baryon number production by strings, it proves too small to explain the observed abundance by at least ten orders of magnitude, whether the strings are in the friction dominated or the scaling regime.
116626711
UV cascade in classical Yang-Mills theory via kinetic theory
We show that classical Yang-Mills theory with statistically homogeneous and isotropic initial conditions has a kinetic description and approaches a scaling solution at late times. We find the scaling solution by explicitly solving the Boltzmann equations, including all dominant processes (elastic and number-changing). Above a scale ˜ pmax ∝ t 1 7 the occupancy falls exponentially in p. For asymptotically late times and sufficiently small momenta the occupancy scales as f(p) ∝ 1/p, but this behavior sets in only at very late time scales. We find quantitative agreement of our results with lattice simulations, for times and momenta within the range of validity of kinetic theory.
118530387
The stickiness of sound: An absolute lower limit on viscosity and the breakdown of second order relativistic hydrodynamics
Hydrodynamics predicts long-lived sound and shear waves. Thermal fluctuations in these waves can lead to the diffusion of momentum density, contributing to the shear viscosity and other transport coefficients. Within viscous hydrodynamics in 3+1dimensions, this leads to a positive contribution to the shear viscosity, which is finite but inversely proportional to the microscopic shear viscosity. Therefore the effective infrared viscosity is bounded from below. The contribution to the second-order transport coefficientτ� is divergent, which means that second-order relativistic viscous hydrodynamics is inconsistent below some frequency scale. We estimate the importance of each effect for the Quark-Gluon Plasma, finding them to be minor if η/s = 0.16 but important if η/s = 0.08.