121922438
Modular Forms and Two Loop String Physics
Abstract The two-loop path integral for the closed bosonic string is given by a genus-two modular form: the product of the even theta functions. Thus the two-loop vacuum amplitude, scattering amplitudes, and the one-loop free energy may be expressed simply in terms of theta functions.
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.
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.
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
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.
119099410
Energy loss of leading hadrons and direct photon production in evolving quark-gluon plasma
We calculate the nuclear modification factor of neutral pions and the photon yield at high p{sub T} in central Au-Au collisions at the Relativistic Heavy-Ion Collider (RHIC) ({radical}(s)=200 GeV) and Pb-Pb collisions at the Large Hadron Collider (LHC) ({radical}(s)=5500 GeV). A leading-order accurate treatment of jet energy loss in the medium has been convolved with a physical description of the initial spatial distribution of jets and a one dimensional hydrodynamic expansion. We reproduce the nuclear modification factor for pions R{sub AA} at RHIC, assuming an initial temperature T{sub i}=370 MeV and a formation time {tau}{sub i}=0.26 fm/c, corresponding to dN/dy=1260. The resulting suppression depends on the particle rapidity density dN/dy but weakly on the initial temperature. The jet energy loss treatment is also included in the calculation of high p{sub T} photons. Photons coming from primordial hard N-N scattering are the dominant contribution at RHIC for p{sub T}>5 GeV, whereas at the LHC, the range 8
15735242
Hard Thermal Loops and the Sphaleron Rate on the Lattice
Abstract We measure the sphaleron rate (topological susceptibility) of hot SU(2) gauge theory, using a lattice implementation of the hard thermal loop (HTL) effective action. The HTL degrees of freedom are implemented by an expansion in spherical harmonics and truncation. Our results for the sphaleron rate agree with the parametric prediction of Arnold, Son and Yaffe: Γ ∝ α 5 T 4 .
119468202
The nonperturbative broken phase sphaleron rate
Abstract I present a technique for measuring the broken phase sphaleron rate nonperturbatively. There are three parts to the calculation: determination of the probability distribution of Chern-Simons number N CS ; measurement of 〈| dN CS / dt |〉 N CS = 1 2 , the mean rate of change of N CS at the barrier; and measurement of the “dynamical prefactor,” the fraction of barrier crossings which result in a permanent integer change in N CS .
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.
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.