14684976
Large N 2D Yang-Mills Theory and Topological String Theory

Abstract:
We describe a topological string theory which reproduces many aspects of the 1/N expansion of SU(N) Yang-Mills theory in two spacetime dimensions in the zero coupling (A= 0) limit. The string theory is a modified version of topological gravity coupled to a topological sigma model with spacetime as target. The derivation of the string theory relies on a new interpretation of Gross and Taylor's “Ω-1 points ”. We describe how inclusion of the area, coupling of chiral sectors, and Wilson loop expectation values can be incorporated in the topological string approach.

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.
124306496
The M theory three form and E(8) gauge theory
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.
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.
18843095
Classical sphaleron rate on fine lattices
We measure the sphaleron rate for hot, classical Yang-Mills theory on the lattice, in order to study its dependence on lattice spacing. By using a topological definition of Chern-Simons number and going to extremely fine lattices [up to $\ensuremath{\beta}=32,$ or lattice spacing ${a=1/(8g}^{2}T)]$ we demonstrate nontrivial scaling. The topological susceptibility, converted to physical units, falls with lattice spacing on fine lattices in a way which is consistent with linear dependence on a (the Arnold-Son-Yaffe scaling relation) and is difficult to reconcile with a nonzero continuum limit. We also explain some unusual behavior of the rate in small volumes, reported by Ambj\o{}rn and Krasnitz.
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.
118835309
Thermalization in weakly coupled nonabelian plasmas
A bstractWe investigate how relativistic, nonabelian plasmas approach equilibrium in a general context. Our treatment is entirely parametric and for small Yang-Mills coupling α. First we study isotropic systems with an initially nonequilibrium momentum distribution. We consider both the case of initially very high occupancy and initially very low occupancy. Then we consider systems which are anisotropic. We consider both weak anisotropy and large anisotropy, and allow the occupancy to be parametrically large or small. Writing the typical momentum of an initial excitation as Q and the final temperature as Tfinal, full equilibration occurs in a time $ {t_{\text{eq}}} \sim {\alpha^{{ - {2}}}}T_{\text{final}}^{{ - 1}} $ for Tfinal > Q, and $ {t_{\text{eq}}} \sim {\alpha^{{ - 2}}}{Q^{{\frac{1}{2}}}}T_{\text{final}}^{{\frac{{ - 3}}{2}}} $ for Tfinal < Q, unless the initial system is sufficiently anisotropic and $ {T_{\text{final}}} > {\alpha^{{\frac{2}{3}}}}Q $, in which 7 case equilibration occurs somewhat faster, $ {t_{\text{eq}}} \sim \max \left( {{a^{{ - 2}}}{T^{{ - 1}}},\;{\alpha^{{\frac{{ - 13}}{7}}}}{Q^{{\frac{5}{7}}}}T_{\text{final}}^{{\frac{{ - 12}}{7}}}} \right) $.
119291599
The sphaleron rate in SU(N) gauge theory
The sphaleron rate is defined as the diffusion constant for topological number $ {N_{\text{CS}}} \equiv \int {\frac{{{g^2}F\tilde{F}}}{{32{\pi^2}}}} $. It establishes the rate of equilibration of axial light quark number in QCD and is of interest both in electroweak baryogenesis and possibly in heavy ion collisions. We calculate the weak-coupling behavior of the SU(3) sphaleron rate, as well as making the most sensible extrapolation towards intermediate coupling which we can. We also study the behavior of the sphaleron rate at weak coupling at large Nc.
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.