118480031
Framed BPS states
We consider a class of line operators in d = 4,N = 2 supersymmetric field theories which leave four supersymmetries unbroken. Such line operators support a new class of BPS states which we call “framed BPS states.” These include halo bound states similar to those of d = 4,N = 2 supergravity, where (ordinary) BPS particles are loosely bound to the line operator. Using this construction, we give a new proof of the KontsevichSoibelman wall-crossing formula for the ordinary BPS particles, by reducing it to the semiprimitive wall-crossing formula. After reducing on S1, the expansion of the vevs of the line operators in the IR provides a new physical interpretation of the “Darboux coordinates” on the moduli spaceM of the theory. Moreover, we introduce a “protected spin character” which keeps track of the spin degrees of freedom of the framed BPS states. We show that the generating functions of protected spin characters admit a multiplication which defines a deformation of the algebra of holomorphic functions on M. As an illustration of these ideas, we consider the six-dimensional (2, 0) field theory of A1 type compactified on a Riemann surface C. Here we show (extending previous results) that line operators are classified by certain laminations on a suitably decorated version of C, and we compute the spectrum of framed BPS states in several explicit examples. Finally we indicate some interesting connections to the theory of cluster algebras. ar X iv :1 00 6. 01 46 v2 [ he pth ] 6 O ct 2 01 2
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.
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
118805589
Second order hydrodynamic coefficients from kinetic theory
In a relativistic setting, hydrodynamic calculations which include shear viscosity (which is first order in an expansion in gradients of the flow velocity) are unstable and acausal unless they also include terms to second order in gradients. To date such terms have only been computed in supersymmetric N=4 super-Yang-Mills theory at infinite coupling. Here we compute these second-order hydrodynamic coefficients in weakly coupled QCD, perturbatively to leading order in the QCD coupling, using kinetic theory. We also compute them in QED and scalar {lambda}{phi}{sup 4} theory.
16445189
Chern-Simons number diffusion and hard thermal loops on the lattice
We develop a discrete lattice implementation of the hard thermal loop effective action by the method of added auxiliary fields. We use the resulting model to measure the sphaleron rate (topological susceptibility) of Yang-Mills theory at weak coupling. Our results give parametric behavior in accord with the arguments of Arnold, Son, and Yaffe, and are in quantitative agreement with the results of Moors, Hu, and Muller.
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.
41524496
SUPERSYMMETRIC ELECTROWEAK PHASE TRANSITION : BARYOGENESIS VERSUS EXPERIMENTAL CONSTRAINTS
We use the two loop effective potential to study the first order electroweak phase transition in the minimial supersymmetric standard model. A global search of the parameter space is made to identify parameters compatible with electroweak baryogenesis. We improve on previous such studies by fully incorporating squark and Higgs boson mixing, by using the latest experimental constraints, and by computing the latent heat and the sphaleron rate. We find the constraints tan beta > 2.1, top squark mass < 172 GeV, and Higgs mass < 107 GeV (becoming more or less restrictive if the heavy stop has mass less than or greater than 1 TeV). We also find that the change in tan beta in the bubble wall is rarely greater than 0.001, which severely constrains the mechanism of baryogenesis.
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.