120562912
A comment on sigma model anomalies
Abstract Some non-linear sigma models with fermions are known to be ill-defined because of a global obstruction to any consistent quantization. Sigma models relevant to phenomenological theories of dynamical symmetry breaking must satisfy the additional constraint of appropriately realizing the flavor symmetries of the underlying theory at the one-loop level. This is possible if and only if 't Hooft's anomaly condition is satisfied. In particular, we show that there always exists a Wess-Zumino term which correctly reproduces the flavor anomalies, and the global obstruction vanishes, whenever 't Hooft's condition is satisfied.
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.
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.
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.
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.
119023526
The phantom menaced: Constraints on low-energy effective ghosts
It has been suggested that a scalar field with negative kinetic energy, or ``ghost,'' could be the source of the observed late-time cosmological acceleration. Naively, such theories should be ruled out by the catastrophic quantum instability of the vacuum. We derive phenomenological bounds on the Lorentz-violating ultraviolet cutoff $\ensuremath{\Lambda}$ which must apply to low-energy effective theories of ghosts, in order to keep the instability at unobservable levels. Assuming only that ghosts interact at least gravitationally, we show that $\ensuremath{\Lambda}\ensuremath{\lesssim}3\mathrm{MeV}$ for consistency with the cosmic gamma ray background. We also show that theories of ghosts with a Lorentz-conserving cutoff are completely excluded.
18458269
TRANSPORT COEFFICIENTS IN HOT QCD
I give a physical explanation of what shear viscosity is, and what physics determines its value. Then I explain why determining the shear viscosity of the Quark-Gluon Plasma is interesting. I outline the leading-order calculation of the QGP shear viscosity (and baryon number diffusion constant), explaining why the quite complicated physics of parton splitting and Landau-Pomeranchuk-Migdal interference effects are required for its calculation. Then I briefly explore the range of applicability, emphasizing the importance of plasma instabilities.
116888742
Dileptons, spectral weights, and conductivity in the Quark-Gluon Plasma
We re-examine soft dilepton emission from a weakly coupled Quark-Gluon Plasma. We show that Braaten, Pisarski, and Yuan's result that the dilepton rate rises as E^-4 (and the spectral weight scales as 1/E) at small energy E<<gT is correct, but that the coefficient they found for this behavior is not correct, because their analysis was incomplete. At still smaller scales, the behavior moderates to ~1/E^2 for E <= g^4 T, consistent with a finite electrical conductivity. We evaluate the spectral weight in the E~g^4 T region by kinetic theory techniques and show that it satisfies a sum rule, which makes the determination of electrical conductivity from the Euclidean correlation function very challenging.
7244562
Electroweak bubble wall friction: analytic results
We present an entirely analytic, leading log order determination of the friction an electroweak bubble wall feels during a first order electroweak phase transition. The friction is dominated by W bosons, and gives a wall velocity parametrically ~ αw, and numerically small, ~ .01÷0.1 depending on the Higgs mass.
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.