10728679
Improved Hamiltonian for Minkowski Yang-Mills theory
I develop an improved Hamiltonian for classical, Minkowski Yang-Mills theory, which evolves infrared fields with tree level corrections from lattice spacing a beginning at O(a4). I use it to investigate the response of Chern-Simons number to a chemical potential, and to compute the maximal Lyapunov exponent. The Lyapunov exponent has a small a limit, and the Chern-Simons number response appears to be approaching one at the finest lattices considered. In both cases the limit is within 10% of the limit found using the unimproved (Kogut-Susskind) Hamiltonian. For the maximal Lyapunov exponent the limits differ between Hamiltonians by about 5%, significant at about 5σ, indicating that while a small a limit exists, its value depends on the specifics of the lattice cutoff. For Chern-Simons number the difference between Hamiltonians is within statistical errors of about 10%, which constitutes an upper bound on the lattice regulation dependence.
119279378
Bjorken flow, plasma instabilities, and thermalization
A bstractAt asymptotically high energies, thermalization in heavy ion collisions can be described via weak-coupling QCD. We present a complete treatment of how thermalization proceeds, at the parametric weak-coupling level. We show that plasma instabilities dominate the dynamics, from immediately after the collision until well after the plasma becomes nearly in equilibrium. Initially they drive the system close to isotropy, but Bjorken expansion and increasing diluteness makes the system again become more anisotropic. At time $ \tau \sim {\alpha^{{\frac{{ - 12}}{5}}}}Q_s^{{ - 1}} $ the dynamics become dominated by a nearly-thermal bath; and at time $ \tau \sim {\alpha^{{\frac{{ - 5}}{2}}}}Q_s^{{ - 1}} $ the bath comes to dominate the energy density, completing thermalization. After this time there is a nearly isotropic and thermal Quark-Gluon Plasma.
119023526
The phantom menaced: Constraints on low-energy effective ghosts
It has been suggested that a scalar field with negative kinetic energy, or ``ghost,'' could be the source of the observed late-time cosmological acceleration. Naively, such theories should be ruled out by the catastrophic quantum instability of the vacuum. We derive phenomenological bounds on the Lorentz-violating ultraviolet cutoff $\ensuremath{\Lambda}$ which must apply to low-energy effective theories of ghosts, in order to keep the instability at unobservable levels. Assuming only that ghosts interact at least gravitationally, we show that $\ensuremath{\Lambda}\ensuremath{\lesssim}3\mathrm{MeV}$ for consistency with the cosmic gamma ray background. We also show that theories of ghosts with a Lorentz-conserving cutoff are completely excluded.
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}
118416779
Next-to-leading order thermal photon production in a weakly coupled quark-gluon plasma
A bstractWe compute the next-to-leading order O(g) correction to the thermal photon production rate in a QCD plasma. The NLO contributions can be expressed in terms of gauge invariant condensates on the light cone, which are amenable to novel sum rules and Euclidean techniques. We expect these technologies to be generalizable to other NLO calculations. For the phenomenologically interesting value of αs = 0.3, the NLO correction represents a 20% increase and has a functional form similar to the LO result.
18843095
Classical sphaleron rate on fine lattices
We measure the sphaleron rate for hot, classical Yang-Mills theory on the lattice, in order to study its dependence on lattice spacing. By using a topological definition of Chern-Simons number and going to extremely fine lattices [up to $\ensuremath{\beta}=32,$ or lattice spacing ${a=1/(8g}^{2}T)]$ we demonstrate nontrivial scaling. The topological susceptibility, converted to physical units, falls with lattice spacing on fine lattices in a way which is consistent with linear dependence on a (the Arnold-Son-Yaffe scaling relation) and is difficult to reconcile with a nonzero continuum limit. We also explain some unusual behavior of the rate in small volumes, reported by Ambj\o{}rn and Krasnitz.
1143874
Integrating over Higgs Branches
Abstract:We develop some useful techniques for integrating over Higgs branches in supersymmetric theories with 4 and 8 supercharges. In particular, we define a regularized volume for hyperkähler quotients. We evaluate this volume for certain ALE and ALF spaces in terms of the hyperkähler periods. We also reduce these volumes for a large class of hyperkähler quotients to simpler integrals. These quotients include complex coadjoint orbits, instanton moduli spaces on ℝ4 and ALE manifolds, Hitchin spaces, and moduli spaces of (parabolic) Higgs bundles on Riemann surfaces. In the case of Hitchin spaces the evaluation of the volume reduces to a summation over solutions of Bethe Ansatz equations for the non-linear Schrödinger system. We discuss some applications of our results.
11520732
Chiral Lagrangians, anomalies, supersymmetry, and holomorphy
Abstract We investigate higher-dimensional analogues of the bc systems of 2D RCFT. When coupled to gauge fields and Beltrami differentials defining integrable holomorphic structures, the bc partition functions can be explicitly evaluated using anomalies and holomorphy. The resulting induced actions generalize the chiral algebras of 2D RCFT to 2 n dimensions. Moreover, bc systems in four and six dimensions are closely related to supersymmetric matter. In particular, we show that d = 4, N = 2 hypermultiplets induce a theory of self-dual Yang-Mills fields coupled to self-dual gravity. In this way the bc systems fermionize both the algebraic sector of the WZW 4 theory, as defined by Losev et al., and the classical open N WS = 2 string.
16606536
Classification of Abelian spin Chern-Simons theories
We derive a simple classification of quantum spin Chern-Simons theories with gauge group T=U(1)^N. While the classical Chern-Simons theories are classified by an integral lattice the quantum theories are classified differently. Two quantum theories are equivalent if they have the same invariants on 3-manifolds with spin structure, or equivalently if they lead to equivalent projective representations of the modular group. We prove the quantum theory is completely determined by three invariants which can be constructed from the data in the classical action. We comment on implications for the classification of fractional quantum Hall fluids.
210001570
A Modern Fareytail
We revisit the "fareytail expansions" of elliptic genera which have been used in discussions of the AdS_3/CFT_2 correspondence and the OSV conjecture. We show how to write such expansions without the use of the problematic "fareytail transform." In particular, we show how to write a general vector-valued modular form of non-positive weight as a convergent sum over cosets of SL(2,Z). This sum suggests a new regularization of the gravity path integral in AdS_3, resolves the puzzles associated with the "fareytail transform," and leads to several new insights. We discuss constraints on the polar coefficients of negative weight modular forms arising from modular invariance, showing how these are related to Fourier coefficients of positive weight cusp forms. In addition, we discuss the appearance of holomorphic anomalies in the context of the fareytail.
122558113
The Partition Function of 2D String Theory
We derive a compact and explicit expression for the generating functional of all correlation functions of tachyon operators in 2D string theory. This expression makes manifest relations of the c = 1 system to KP flow and W 1+∞ constraints. Moreover we derive a Kontsevich-Penner integral representation of this generating functional.