121357398
Bosonization on higher genus Riemann surfaces
We prove the equivalence between certain fermionic and bosonic theories in two spacetime dimensions. The theories have fields of arbitrary spin on compact surfaces with any number of handles. Global considerations require that we add new topological terms to the bosonic action. The proof that our prescription is correct relies on methods of complex algebraic geometry.
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.
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.
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.
14276560
Lattice Chern-Simons number without ultraviolet problems
We develop a topological method of measuring Chern-Simons number change in the real time evolution of classical lattice SU(2) and SU(2) Higgs theory. We find that the Chern-Simons number diffusion rate per physical four-volume is very heavily suppressed in the broken phase, and that it decreases with lattice spacing in pure Yang-Mills theory, although not as quickly as predicted by Arnold, Son, and Yaffe. {copyright} {ital 1997} {ital The American Physical Society}
119266207
Radiative energy loss and v 2 spectra for viscous hydrodynamics
This work investigates the first correction to the equilibrium phase-space distribution and its effects on spectra and elliptic flow in heavy-ion collisions. We show that the departure from equilibrium on the freeze-out surface is the largest part of the viscous corrections to ${v}_{2}({p}_{T})$. However, the momentum dependence of the departure from equilibrium is not known a priori, and it is probably not proportional to ${p}_{T}^{2}$ as has been assumed in hydrodynamic simulations. At high momentum in weakly coupled plasmas, it is determined by the rate of radiative energy loss and is proportional to ${p}_{T}^{3/2}$. The weaker ${p}_{T}$ dependence leads to straighter ${v}_{2}({p}_{T})$ curves at the same value of viscosity. Furthermore, the departure from equilibrium is generally species dependent. A species-dependent equilibration rate, with baryons equilibrating faster than mesons, can explain ``constituent quark scaling'' without invoking coalescence models.
16615457
Classical Approach to Electroweak Dynamics
I discuss the applicability of classical techniques to the study of the dynamics of infrared, bosonic fields at the electroweak phase transition. I present the lattice as a natural means of cutting off hard, nonclassical modes, and discuss the problem of integrating out the excluded modes perturbatively. I then apply the classical lattice technique to study the dynamics of the phase interface (bubble wall) and the generation of Chern-Simons number in each phase and on the bubble wall.
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.
119279865
Lattice four-dimensional N=4 SYM is practical
We show that nonperturbative lattice studies of four-dimensional N=4 Super-Yang-Mills are within reach. We use Ginsparg-Wilson fermions to avoid gluino masses and an exact implementation of the (chiral) $R$-symmetry, which greatly limits the number of counterterms that must be fine-tuned. Only bosonic operators require fine tuning, so all tunings can be done ``offline'' by a Ferrenberg-Swendsen type reweighting. We show what measurables can be used to perform the tuning.