115176676
Wall-crossing, Hitchin systems, and the WKB approximation
We consider BPS states in a large class of d = 4,N = 2 eld theories, obtained by reducing six-dimensional (2; 0) superconformal eld theories on Riemann surfaces, with defect operators inserted at points of the Riemann surface. Further dimensional reduction on S 1 yields sigma models, whose target spaces are moduli spaces of Higgs bundles on Riemann surfaces with ramication. In the case where the Higgs bundles have rank 2, we construct canonical Darboux coordinate systems on their moduli spaces. These coordinate systems are related to one another by Poisson transformations associated to BPS states, and have well-controlled asymptotic behavior, obtained from the WKB approximation. The existence of these coordinates implies the Kontsevich-Soibelman wall-crossing formula for the BPS spectrum. This construction provides a concrete realization of a general physical explanation of the wall-crossing formula which was proposed in (1). It also yields a new method for computing the spectrum using the combinatorics of triangulations of the Riemann surface.
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.
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
12818530
Electroweak bubble nucleation, nonperturbatively
We present a lattice method to compute bubble nucleation rates at radiatively induced first order phase transitions, in high temperature, weakly coupled field theories, nonperturbatively. A generalization of Langer's approach, it makes no recourse to saddle point expansions and includes completely the dynamical prefactor. We test the technique by applying it to the electroweak phase transition in the minimal standard model, at an unphysically small Higgs mass which gives a reasonably strong phase transition (lambda/g^2 =0.036, which corresponds to m(Higgs)/m(W) = 0.54 at tree level but does not correspond to a positive physical Higgs mass when radiative effects of the top quark are included), and compare the results to older perturbative and other estimates. While two loop perturbation theory slightly under-estimates the strength of the transition measured by the latent heat, it over-estimates the amount of supercooling by a factor of 2.
10799212
Classical field dynamics of the electroweak phase transition
We investigate the thermodynamics and dynamics of the electroweak phase transition by modeling the infrared physics with classical Yang-Mills Higgs theory. We discuss the accuracy of this approach and conclude that, for quantities whose determination is dominated by the infrared, the classical method should be correct up to parametrically suppressed [i.e., O({alpha})] corrections. For a Higgs self-coupling which at the tree level corresponds to m{sub H}{approx_equal}50 GeV, we determine the jump in the order parameter to be {delta}{phi}=1.5gT, the surface tension to be {sigma}=0.07g{sup 4}T{sup 3}, and the friction coefficient on the moving bubble wall due to infrared bosons to be {eta}{equivalent_to}P/v{sub w}=0.03{plus_minus}0.004g{sup 6}T{sup 4}. We also investigate the response of the Chern-Simons number to a spatially uniform chemical potential and find that it falls off a short distance inside the bubble wall, both in equilibrium and below the equilibrium temperature. {copyright} {ital 1997} {ital The American Physical Society}
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.
116215341
Chern-Simmons number diffusion in the symmetric electroweak phase
17084402
O(a) errors in 3D SU(N) Higgs theories
Abstract We compute the matching conditions between lattice and continuum 3D SU( N ) Higgs theories, with both adjoint and fundamental scalars, at O ( a ), except for additive corrections to masses and φ 2 insertions.