14579879
Exact Gravitational Threshold Correction in the FHSV Model
We consider the automorphic forms which govern the gravitational threshold correction F1 in models of heterotic/IIA duality with N = 2 supersymmetry in four dimensions. In particular we derive the full nonperturbative formula for F1 for the dual pair originally considered by Ferrara, Harvey, Strominger and Vafa (FHSV). The answer involves an interesting automorphic product constructed by Borcherds which is associated to the “fake Monster Lie superalgebra.” As an application of this result we rederive a result of Jorgenson & Todorov on determinants of ∂̄ operators on K3 surfaces.
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.
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.
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
14446171
Was the electroweak phase transition preceded by a color broken phase
It has been suggested, in connection with electroweak baryogenesis in the minimal supersymmetric standard model (MSSM), that the right-handed top squark has a negative mass squared parameter, such that its field could condense prior to the electroweak phase transition (EWPT). Thus color and electric charge could have been broken just before the EWPT. Here we investigate whether the tunneling rate from the color-broken vacuum can ever be large enough for the EWPT to occur in this case. We find that, even when all parameters are adjusted to their most favorable values, the nucleation rate is many orders of magnitude too small. We conclude that, without additional physics beyond the MSSM, the answer to our title question is ``no.'' This gives constraints in the plane of the light top squark mass versus parameters related to top squark mixing. However it may be possible to get color breaking in extended models, such as those with R-parity violation.
28821908
Measuring the broken phase sphaleron rate nonperturbatively
We present details for a method to compute the broken phase sphaleron rate (rate of hot baryon number violation below the electroweak phase transition) nonperturbatively, using a combination of multicanonical and real time lattice techniques. The calculation includes the ``dynamical prefactor,'' which accounts for prompt recrossings of the sphaleron barrier. The prefactor depends on the hard thermal loops, getting smaller with increasing Debye mass; but for realistic Debye masses the effect is not large. The baryon number erasure rate in the broken phase is slower than a perturbative estimate by about $\mathrm{exp}(\ensuremath{-}3.6).$ Assuming the electroweak phase transition has enough latent heat to reheat the universe to the equilibrium temperature, baryon number is preserved after the phase transition if the ratio of (``dimensionally reduced'' thermal) scalar to gauge couplings $\ensuremath{\lambda}{/g}^{2}$ is less than 0.037.
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.
119423995
Landau-Pomeranchuk-Migdal resummation for dilepton production
We consider the thermal emission rate of dileptons from a QCD plasma in the small invariant mass ($Q^2 \\sim \\gs^2 T^2$) but large energy ($q^0 \\gsim T$) range. We derive an integral equation which resums multiple scatterings to include the LPM effect; it is valid at leading order in the coupling. Then we recast it as a differential equation and show a simple algorithm for its solution. We present results for dilepton rates at phenomenologically interesting energies and invariant masses.
17543214
The Sphaleron Rate: Where We Stand
I review what we know about the ``sphaleron rate'', which is the efficiency of baryon number violation at high temperatures of order 100 GeV in the Standard Model. The leading behavior at weak coupling in the symmetric phase is known accurately; Gamma = (10.7 +- .7) (g^2 T^2 / m_D^2) log(m_D/g^2T)\alpha_w^5 T^4. At realistic values of the coupling our accuracy is worse. We also now have the tools to determine the rate nonperturbatively in the broken electroweak phase; the sphaleron rate there is slower than perturbative estimates.