Large N Quantum Time Evolution Beyond Leading Order

For quantum theories with a classical limit (which includes the large N limits of typical field theories), we derive a hierarchy of evolution equations for equal time correlators which systematically incorporate corrections to the limiting classical evolution. Explicit expressions are given for next-to-leading order, and next-to-next-to-leading order time evolution. The large N limit of N-component vector models, and the usual semiclassical limit of point particle quantum mechanics are used as concrete examples. Our formulation directly exploits the appropriate group structure which underlies the construction of suitable coherent states and generates the classical phase space. We discuss the growth of truncation error with time, and argue that truncations of the large-N evolution equations are generically expected to be useful only for times short compared to a ``decoherence'' time which scales like N^{1/2}.Comment: 36 pages, 2 eps figures, latex, uses revtex, epsfig, float

Center-stabilized Yang-Mills theory: confinement and large NN volume independence

We examine a double trace deformation of SU(N) Yang-Mills theory which, for large $N$ and large volume, is equivalent to unmodified Yang-Mills theory up to $O(1/N^2)$ corrections. In contrast to the unmodified theory, large $N$ volume independence is valid in the deformed theory down to arbitrarily small volumes. The double trace deformation prevents the spontaneous breaking of center symmetry which would otherwise disrupt large $N$ volume independence in small volumes. For small values of $N$, if the theory is formulated on $\R^3 \times S^1$ with a sufficiently small compactification size $L$, then an analytic treatment of the non-perturbative dynamics of the deformed theory is possible. In this regime, we show that the deformed Yang-Mills theory has a mass gap and exhibits linear confinement. Increasing the circumference $L$ or number of colors $N$ decreases the separation of scales on which the analytic treatment relies. However, there are no order parameters which distinguish the small and large radius regimes. Consequently, for small $N$ the deformed theory provides a novel example of a locally four-dimensional pure gauge theory in which one has analytic control over confinement, while for large $N$ it provides a simple fully reduced model for Yang-Mills theory. The construction is easily generalized to QCD and other QCD-like theories.Comment: 29 pages, expanded discussion of multiple compactified dimension

Effective Kinetic Theory for High Temperature Gauge Theories

Quasiparticle dynamics in relativistic plasmas associated with hot, weakly-coupled gauge theories (such as QCD at asymptotically high temperature $T$) can be described by an effective kinetic theory, valid on sufficiently large time and distance scales. The appropriate Boltzmann equations depend on effective scattering rates for various types of collisions that can occur in the plasma. The resulting effective kinetic theory may be used to evaluate observables which are dominantly sensitive to the dynamics of typical ultrarelativistic excitations. This includes transport coefficients (viscosities and diffusion constants) and energy loss rates. We show how to formulate effective Boltzmann equations which will be adequate to compute such observables to leading order in the running coupling $g(T)$ of high-temperature gauge theories [and all orders in $1/\log g(T)^{-1}$]. As previously proposed in the literature, a leading-order treatment requires including both $22$ particle scattering processes as well as effective ``$12$'' collinear splitting processes in the Boltzmann equations. The latter account for nearly collinear bremsstrahlung and pair production/annihilation processes which take place in the presence of fluctuations in the background gauge field. Our effective kinetic theory is applicable not only to near-equilibrium systems (relevant for the calculation of transport coefficients), but also to highly non-equilibrium situations, provided some simple conditions on distribution functions are satisfied.Comment: 40 pages, new subsection on soft gauge field instabilities adde

Necessary and sufficient conditions for non-perturbative equivalences of large N orbifold gauge theories

Large N coherent state methods are used to study the relation between U(N) gauge theories containing adjoint representation matter fields and their orbifold projections. The classical dynamical systems which reproduce the large N limits of the quantum dynamics in parent and daughter orbifold theories are compared. We demonstrate that the large N dynamics of the parent theory, restricted to the subspace invariant under the orbifold projection symmetry, and the large N dynamics of the daughter theory, restricted to the untwisted sector invariant under "theory space'' permutations, coincide. This implies equality, in the large N limit, between appropriately identified connected correlation functions in parent and daughter theories, provided the orbifold projection symmetry is not spontaneously broken in the parent theory and the theory space permutation symmetry is not spontaneously broken in the daughter. The necessity of these symmetry realization conditions for the validity of the large N equivalence is unsurprising, but demonstrating the sufficiency of these conditions is new. This work extends an earlier proof of non-perturbative large N equivalence which was only valid in the phase of the (lattice regularized) theories continuously connected to large mass and strong coupling.Comment: 21 page, JHEP styl

Quark-Gluon Plasma - New Frontiers

As implied by organizers, this talk is not a conference summary but rather an outline of progress/challenges/``frontiers'' of the theory. Some fundamental questions addressed are: Why is sQGP such a good liquid? Do we understand (de)confinement and what do we know about ``magnetic'' objects creating it? Can we understand the AdS/CFT predictions, from the gauge theory side? Can they be tested experimentally? Can AdS/CFT duality help us understand rapid equilibration/entropy production? Can we work out a complete dynamical ``gravity dual'' to heavy ion collisions?Comment: final talk at Quark Matter 2008, Jaipur, India, Feb.200

Electroweak bubbles and sphalerons

We consider non-perturbative solutions of the Weinberg-Salam model at finite temperature. We employ an effective temperature-dependent potential yielding a first order phase transition. In the region of the phase transition, there exist two kinds of static, spherically symmetric solutions: sphalerons and bubbles. We analyze these solutions as functions of temperature. We consider the most general spherically symmetric fluctuations about the two solutions and construct the discrete modes in the region of the phase transition. Sphalerons and bubbles both possess a single unstable mode. We present simple approximation formulae for these levels.Comment: 14 pages, plain tex, 9 figures appended as postscript files at the end of the paper. THU-93/0

Valley Bifurcation in an O(3)O(3) σ\sigma Model: Implications for High-Energy Baryon Number Violation

The valley method for computing the total high-energy anomalous cross section $S_{anom}$ is the extension of the optical theorem to the case of instanton-antiinstanton backgrounds. As a toy model for baryon number violation in Electroweak theory, we consider a version of the $O(3)$ $\sigma$ model in which the conformal invariance is broken perturbatively. We show that at a critical energy the saddle-point values of the instanton size and instanton-antiinstanton separation bifurcate into complex conjugate pairs. This nonanalytic behavior signals the breakdown of the valley method at an energy where $S_{anom}$ is still exponentially suppressed. (Figures replaced 5/3/93).Comment: (14 pages, Los Alamos Preprint LA-UR-93-811). 3 uuencoded figures include

Comments on large-N volume independence

We study aspects of the large-N volume independence on R**3 x L**G, where L**G is a G-site lattice for Yang-Mills theory with adjoint Wilson-fermions. We find the critical number of lattice sites above which the center-symmetry analysis on L**G agrees with the one on the continuum S**1. For Wilson parameter set to one and G>=2, the two analyses agree. One-loop radiative corrections to Wilson-line masses are finite, reminiscent of the UV-insensitivity of the Higgs mass in deconstruction/Little-Higgs theories. Even for theories with G=1, volume independence in QCD(adj) may be guaranteed to work by tuning one low-energy effective field theory parameter. Within the parameter space of the theory, at most three operators of the 3d effective field theory exhibit one-loop UV-sensitivity. This opens the analytical prospect to study 4d non-perturbative physics by using lower dimensional field theories (d=3, in our example).Comment: 12 pages; added small clarifications, published versio

Towards a Realistic Equation of State of Strongly Interacting Matter

We consider a relativistic strongly interacting Bose gas. The interaction is manifested in the off-shellness of the equilibrium distribution. The equation of state that we obtain for such a gas has the properties of a realistic equation of state of strongly interacting matter, i.e., at low temperature it agrees with the one suggested by Shuryak for hadronic matter, while at high temperature it represents the equation of state of an ideal ultrarelativistic Stefan-Boltzmann gas, implying a phase transition to an effectively weakly interacting phase.Comment: LaTeX, figures not include