14378311
D-branes and K-theory in 2D topological field theory
This expository paper describes sewing conditions in two-dimensional open/closed topological field theory. We include a description of the G-equivariant case, where G is a finite group. We determine the category of boundary conditions in the case that the closed string algebra is semisimple. In this case we find that sewing constraints – the most primitive form of worldsheet locality – already imply that D-branes are (G-twisted) vector bundles on spacetime. We comment on extensions to cochain-valued theories and various applications. Finally, we give uniform proofs of all relevant sewing theorems using Morse 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.
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.
124306496
The M theory three form and E(8) gauge theory
118805589
Second order hydrodynamic coefficients from kinetic theory
In a relativistic setting, hydrodynamic calculations which include shear viscosity (which is first order in an expansion in gradients of the flow velocity) are unstable and acausal unless they also include terms to second order in gradients. To date such terms have only been computed in supersymmetric N=4 super-Yang-Mills theory at infinite coupling. Here we compute these second-order hydrodynamic coefficients in weakly coupled QCD, perturbatively to leading order in the QCD coupling, using kinetic theory. We also compute them in QED and scalar {lambda}{phi}{sup 4} theory.
117910269
New algorithm for classical gauge theory simulations in an expanding box
We propose a new algorithm for classical statistical simulations in scalar and gauge theories undergoing a one dimensional expansion, which allows simulations to study boxes of larger transverse extent and to continue for longer times, without losing lattice resolution in the expanding direction.
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.
17348300
Heavy quark diffusion in QCD and = 4 SYM at next-to-leading order
We present the full details of a calculation at next-to-leading order of the momentum diffusion coefficient of a heavy quark in a hot, weakly coupled, QCD plasma. Corrections arise at (gs); physically they represent interference between overlapping scatterings, as well as soft, electric scale (p ~ gT) gauge field physics, which we treat using the hard thermal loop (HTL) effective theory. In 3-color, 3-flavor QCD, the momentum diffusion constant of a fundamental representation heavy quark at NLO is κ = (16π/3)αs2T3(ln (1/gs)+0.07428+1.9026gs). We extend the computation to a heavy fundamental representation ``probe'' quark in large Nc, = 4 Super Yang-Mills theory, where the result is κ(SYM) = (λ2T3/6π)(ln (1/√λ)+0.4304+0.8010√λ) (where λ = g2Nc is the t'Hooft coupling). In the absence of some resummation technique, the convergence of perturbation theory is poor.
15369975
Motion of Chern-Simons number at high temperatures under a chemical potential
I investigate the evolution of finite temperature, classical Yang-Mills field equations under the influence of a chemical potential for Chern-Simons number Ncs. The rate of Ncs diffusion,, Γd, and the linear response of Ncs to a chemical potential, Γμ, are both computed; the relation Γd = 2Γμ is satisfied numerically and the results agree with the recent measurement of Γd by Ambjorn and Krasnitz. The response of Ncs under chemical potential remains linear at least to μ = 6T, which is impossible if there is a free energy barrier to the motion of Ncs. The possibility that the result depends on lattice artefacts via hard thermal loops is investigated by changing the lattice action and by examining elongated rectangular lattices; provided that the lattice is fine enough, the result is weakly if at all dependent on the specifics of the cutoff. I also compare SU(2) with SU(3) and find ΓSU(3)∼ 7(αs/αw)4ΓSU(2).