121599429
Semi-off-shell string amplitudes
We study n-string amplitudes with one or two strings off-shell using the Polyakov path integral. The residues of the poles of these amplitudes correspond to the correct S-matrix elements. The coupling of gravitons to off-shell amplitudes shows that objects invariant under all world-sheet symmetries are also invariant under spacetime gauge symmetries. We interpret our results in terms of a local operator expansion.
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
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.
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.
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.
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).
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.
119291599
The sphaleron rate in SU(N) gauge theory
The sphaleron rate is defined as the diffusion constant for topological number $ {N_{\text{CS}}} \equiv \int {\frac{{{g^2}F\tilde{F}}}{{32{\pi^2}}}} $. It establishes the rate of equilibration of axial light quark number in QCD and is of interest both in electroweak baryogenesis and possibly in heavy ion collisions. We calculate the weak-coupling behavior of the SU(3) sphaleron rate, as well as making the most sensible extrapolation towards intermediate coupling which we can. We also study the behavior of the sphaleron rate at weak coupling at large Nc.
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.