9927956
Les Houches Lectures on Strings and Arithmetic
These are lecture notes for two lectures delivered at the Les Houches workshop on Number Theory, Physics, and Geometry, March 2003. They review two examples of interesting interactions between number theory and string compactification, and raise some new questions and issues in the context of those examples. The first example concerns the role of the Rademacher expansion of coefficients of modular forms in the AdS/CFT correspondence. The second example concerns the role of the ``attractor mechanism'' of supergravity in selecting certain arithmetic Calabi-Yau's as distinguished compactifications.
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
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.
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.
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.
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.
119020278
Energy loss of leading partons in a thermal QCD medium
We consider bremsstrahlung energy loss for hard partons traversing a quark-gluon plasma (QCP). Accounting correctly for the probabilistic nature of the energy loss, and making a leading-order-accurate treatment of bremsstrahlung, we find that the suppression of the spectrum is nearly flat, with the most suppression at energies $E~30\phantom{\rule{0.3em}{0ex}}T$ (where T is the QGP temperature), without the need for initial state effects such as shadowing and the Cronin effect. This flat pattern should also be observed at the LHC (Large Hadron Collider) out to an energy of $~30\phantom{\rule{0.3em}{0ex}}\mathrm{GeV}$.
16198175
Electromagnetic emission and energy loss in the QGP
I discuss why photon production from the quark-gluon plasma (QGP) presents an interesting problem, both experimentally and theoretically. I show how the photon emission rate can be computed under the simplifying assumption that the QGP fully thermalizes. The theoretical issues are very similar to those for jet energy loss; so it should be possible to treat them in a common formalism and relate the predictions of one phenomenon to those of the other.
119266207
Radiative energy loss and v 2 spectra for viscous hydrodynamics
This work investigates the first correction to the equilibrium phase-space distribution and its effects on spectra and elliptic flow in heavy-ion collisions. We show that the departure from equilibrium on the freeze-out surface is the largest part of the viscous corrections to ${v}_{2}({p}_{T})$. However, the momentum dependence of the departure from equilibrium is not known a priori, and it is probably not proportional to ${p}_{T}^{2}$ as has been assumed in hydrodynamic simulations. At high momentum in weakly coupled plasmas, it is determined by the rate of radiative energy loss and is proportional to ${p}_{T}^{3/2}$. The weaker ${p}_{T}$ dependence leads to straighter ${v}_{2}({p}_{T})$ curves at the same value of viscosity. Furthermore, the departure from equilibrium is generally species dependent. A species-dependent equilibration rate, with baryons equilibrating faster than mesons, can explain ``constituent quark scaling'' without invoking coalescence models.