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.
121021214
Some global issues in string perturbation theory
Abstract Calculations of the type II string vacuum amplitude using the picture changing prescription have been shown to lead, in general, to a positive cosmological constant. We show that there is a global obstruction to the choices of gauge slice for super-Teichmuller space that lead to such measures. We discuss the general restrictions on gauge slices appropriate for use in explicit fermionic string calculations. We also discuss the relation of the functional determinant and conformal field theory versions of the path integral measure, and show that, at arbitrary genus and in arbitrary backgrounds preserving tree level N = 1 supersymmetry, the measure is an exact differential. We evaluate the boundary integrals of this total derivative at genus two in two ways for target space R 10 to show that the integrals are zero. Finally, we use the factorization hypothesis to show that in appropriate compactified spacetimes the boundary integrals continue to vanish.
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.
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
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.
119272325
3-loop 3PI effective action for 3D SU(3) QCD
A bstractThe 3PI method is a technique to resum an infinite class of diagrams, which may be useful in studying nonperturbative thermodynamics and dynamics in quantum field theory. But it has never been successfully applied to gauge theories, where there are serious questions about gauge invariance breaking. We show how to perform the 3PI resummation of QCD in 3 Euclidean spacetime dimensions, a warmup problem to the 4 or 3+1 dimensional case. We present the complete details of the technical problems and how they are overcome. We postpone a comparison of gauge invariant correlation functions with their lattice-determined counterparts to a future publication.
54009935
How much do heavy quarks thermalize in a heavy ion collision
We investigate the thermalization of charm quarks in high-energy heavy-ion collisions. To this end, we calculate the diffusion coefficient in the perturbative quark gluon plasma and relate it to collisional energy loss and momentum broadening. We then use these transport properties to formulate a Langevin model for the evolution of the heavy quark spectrum in the hot medium. The model is strictly valid in the nonrelativistic limit and for all velocities $\ensuremath{\gamma}vl\ensuremath{\alpha}{s}^{\ensuremath{-}1/2}$ to leading logarithm in $T/{m}_{D}$. The corresponding Fokker-Planck equation can be solved analytically for a Bjorken expansion and the solution gives a simple estimate for the medium modifications of the heavy quark spectrum as a function of the diffusion coefficient. Finally we solve the Langevin equations numerically in a hydrodynamic simulation of the heavy-ion reaction. The results of this simulation are the medium modifications of the charm spectrum ${R}_{\mathit{AA}}$ and the expected elliptic flow ${v}_{2}({p}_{T})$ as a function of the diffusion coefficient.
119207466
Can electroweak bubble walls run away
In extensions of the Standard Model with SU(2) singlet scalar fields, there can be regions of parameter space for which the electroweak phase transition is first order already at the mean-field level of analysis. We show that in this case the phase interface (bubble wall) can become ultra-relativistic, with the relativistic gamma factor {gamma} = (1-v{sub wall}{sup 2}){sup -1/2} growing linearly with the wall's propagation distance. We provide a simple criterion for determining whether the bubble wall ''runs away'' in this way or if {gamma} approaches a terminal value.
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.