16588606
Nonabelions in the fractional quantum Hall effect
Abstract Applications of conformal field theory to the theory of fractional quantum Hall systems are discussed. In particular, Laughlin's wave function and its cousins are interpreted as conformal blocks in certain rational conformal field theories. Using this point of view a hamiltonian is constructed for electrons for which the ground state is known exactly and whose quasihole excitations have nonabelian statistics; we term these objects “nonabelions”. It is argued that universality classes of fractional quantum Hall systems can be characterized by the quantum numbers and statistics of their excitations. The relation between the order parameter in the fractional quantum Hall effect and the chiral algebra in rational conformal field theory is stressed, and new order parameters for several states are given.
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.
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.
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.
118445577
3D N = 1 SYM Chern-Simons theory on the Lattice
We present a method to implement 3-dimensional N = 1 SUSY Yang-Mills theory (a theory with two real supercharges containing gauge fields and an adjoint Majorana fermion) on the lattice, including a way to implement the Chern-Simons term present in this theory. At nonzero Chern-Simons number our implementation suffers from a sign problem which will make the numerical effort grow exponentially with volume. We also show that the theory with vanishing Chern-Simons number is anomalous; its partition function identically vanishes.
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.
14877410
Sphaleron rate in the symmetric electroweak phase
Recently Bo''deker presented an effective infrared theory for the dynamics of Yang-Mills theory, suitable for studying the rate of baryon number violation in the early universe. We extend his theory to include the Higgs boson fields, and study how much the Higgs boson affects the baryon number violation rate in the symmetric phase, at the phase coexistence temperature of a first order electroweak phase transition. The rate is about 20% smaller than in pure Yang-Mills theory. We also analyze the sphaleron rate in the analytic crossover regime. Our treatment relies on the ergodicity conjecture for 3D scalar {phi}{sup 4} theory.
5758194
Constraining the New Aether: gravitational Cherenkov radiation
We study the simplest concrete theory for spontaneous Lorentz violation, the ``New Aether theory'' of Jacobson and Mattingly, which is a vector-tensor gravitational theory with a fixed-modulus condition on the vector field. We show that the observation of ultra-high energy cosmic rays (which implies the absence of energy loss via various Cherenkov type processes) places constraints on the parameters of this theory, which are much stronger than those previously found in the literature and are also stronger than the constraints generically arising when gravity displays sub-luminal propagation.
2704518
Kubo formulas for second-order hydrodynamic coefficients.
At second order in gradients, conformal relativistic hydrodynamics depends on the viscosity η and on five additional "second-order" hydrodynamical coefficients τ(Π), κ, λ₁, λ₂, and λ₃. We derive Kubo relations for these coefficients, relating them to equilibrium, fully retarded three-point correlation functions of the stress tensor. We show that the coefficient λ₃ can be evaluated directly by Euclidean means and does not in general vanish.