18801563
Superpotentials and membrane instantons
We investigate nonperturbative effects in M-theory compactifications arising from wrapped membranes. In particular, we show that in $d=4, \CN=1$ compactifications along manifolds of $G_2$ holonomy, membranes wrapped on rigid supersymmetric 3-cycles induce nonzero corrections to the superpotential. Thus, membrane instantons destabilize many M-theory compactifications. Our computation shows that the low energy description of membrane physics is usefully described in terms of three-dimensional topological field theories, and the superpotential is expressed in terms of topological invariants of the 3-cycle. We discuss briefly some applications of these results. For example, using mirror symmetry we derive a counting formula for supersymmetric three-cycles in certain Calabi-Yau manifolds.
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.
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.
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
12239452
Lower bound on the propagation speed of gravity from gravitational Cherenkov radiation
Recently, interesting 4-D Lorentz violating models have been proposed, in which all particles have a common maximum velocity c, but gravity propagates (in the preferred frame) with a different maximum velocity cg≠c. We show that the case cg < c is very tightly constrained by the observation of the highest energy cosmic rays. Assuming a galactic origin for the cosmic rays gives a conservative bound of c−cg <2 × 10−15c; if the cosmic rays have an extragalactic origin the bound is orders of magnitude tighter, of order c−cg < 2 × 10−19c.
13918277
Real time simulations in lattice gauge theory
Abstract I review the study of real (Minkowski) time correlators in hot, weakly coupled Yang-Mills theory via lattice methods. I concentrate on the Minkowski time topological susceptibility, which is related to the efficiency of baryon number violation at high temperature. It can be computed by approximating the IR fields as classical and solving their dynamics nonperturbatively on the lattice. However it is essential to include the UV degrees of freedom. Their influence can be computed perturbatively and included in the lattice model by the addition of auxiliary fields.
15381941
Atomic Bose condensation and the lattice
Abstract I show how interaction corrections to the Bose condensation temperature of an atomic gas can be computed using a combination of perturbative effective field theory and lattice techniques.
118922289
Shear Viscosity in Weakly Coupled N=4 Super Yang-Mills Theory Compared to QCD
We compute the shear viscosity of weakly coupled N=4 supersymmetric Yang-Mills theory. Our result for {eta}/s, the viscosity to entropy-density ratio, is many times smaller than the corresponding weak-coupling result in QCD. This suggests that {eta}/s of QCD near the transition point is several times larger than the viscosity bound, {eta}/s{>=}1/4{pi}.
14194814
TRANSPORT COEFFICIENTS AT LEADING ORDER: KINETIC THEORY VERSUS DIAGRAMS
I review what is required to compute transport coefficients in ultra-relativistic, weakly coupled gauge theories, at leading order in $g$, using kinetic theory. Then I discuss how the calculation would look in alternative approaches: the 2PI method, and direct diagrammatic analysis. I argue that the 2PI method may be a good way to derive the kinetic theory, but is not very useful directly (in a gauge theory). The diagrammatic approach is almost hopeless.