120349392
Double scaled field theory at c = 1
Abstract We investigate the double-scaled free fermion theory of the c = 1 matrix model. We compute correlation functions of the eigenvalue density field and compare with the predictions of a relativistic boson theory. The c = 1 theory behaves as a relativistic theory at long distances, but has softer behavior at short distances. The soft short-distance behavior is closely related to the breakdown of the topological expansion at high energies. We also compute macroscopic loop amplitudes at c = 1, finding an integral representation for n -loop amplitudes to all orders of perturbation theory. We evaluate the integrals explicitly for two, three, and four macroscopic loops. The small loop length asymptotic expansion then gives correlation functions of local operators in the theory. The two-macroscopic-loop formula gives information on the spectrum and wave functions in the theory. The three- and four-loop amplitudes give scattering amplitudes for tachyon operators to all orders of perturbation theory. Again, the topological expansion breaks down at high energies. We compare our amplitudes with predictions from the Liouville 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.
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.
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
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) $.
12406747
Curing O(a) errors in 3D lattice SU(2) × U(1) Higgs theory
Abstract We show how to make O ( a ) corrections in the bare parameters of 3D lattice SU(2) × U(1) Higgs theory, which remove O ( a ) errors in the match between the infrared behavior and the infrared behavior of the continuum theory. The corrections substantially improve the convergence of lattice data to a small a limit.
15169655
Three dimensional N = 2 supersymmetry on the lattice
We show how 3-dimensional, N = 2 supersymmetric theories, including super QCD with matter fields, can be put on the lattice with existing techniques, in a way which will recover supersymmetry in the small lattice spacing limit. Residual supersymmetry breaking effects are suppressed in the small lattice spacing limit by at least one power of the lattice spacing a.
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.
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.