6878265
Distinguishing off-shell supergravities with on-shell physics
We show that it is possible to distinguish between different off-shell completions of supergravity at the on-shell level. We focus on the comparison of the 'new-minimal' formulation of off-shell four-dimensional N=1 supergravity with the 'old-minimal' formulation. We show that there are three-manifolds which admit supersymmetric compactifications in the new-minimal formulation but which do not admit supersymmetric compactifications in other formulations. Moreover, on manifolds with boundary the new-minimal formulation admits 'singleton modes' which are absent in other formulations.
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.
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.
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.
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) $.
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.
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.
119104096
Limits on Lorentz violation from the highest energy cosmic rays
We place several new limits on Lorentz violating effects, which can modify particles' dispersion relations, by considering the highest energy cosmic rays observed. Since these are hadrons, this involves considering the partonic content of such cosmic rays. We get a number of bounds on differences in maximum propagation speeds, which are typically bounded at the 10{sup -21} level, and on momentum dependent dispersion corrections of the form v=1{+-}p{sup 2}/{lambda}{sup 2}, which typically bound {lambda}>10{sup 21} GeV, well above the Planck scale. For (CPT violating) dispersion correction of the form v=1+p/{lambda}, the bounds are up to 15 orders of magnitude beyond the Planck scale.
10728679
Improved Hamiltonian for Minkowski Yang-Mills theory
I develop an improved Hamiltonian for classical, Minkowski Yang-Mills theory, which evolves infrared fields with tree level corrections from lattice spacing a beginning at O(a4). I use it to investigate the response of Chern-Simons number to a chemical potential, and to compute the maximal Lyapunov exponent. The Lyapunov exponent has a small a limit, and the Chern-Simons number response appears to be approaching one at the finest lattices considered. In both cases the limit is within 10% of the limit found using the unimproved (Kogut-Susskind) Hamiltonian. For the maximal Lyapunov exponent the limits differ between Hamiltonians by about 5%, significant at about 5σ, indicating that while a small a limit exists, its value depends on the specifics of the lattice cutoff. For Chern-Simons number the difference between Hamiltonians is within statistical errors of about 10%, which constitutes an upper bound on the lattice regulation dependence.