Universality, Lee-Yang Singularities, and Series Expansions.

We introduce a new way of reconstructing the equation of state of a thermodynamic system near a second-order critical point from a finite set of Taylor coefficients computed away from the critical point. We focus on the Ising universality class (Z_{2} symmetry) and show that, in the crossover region of the phase diagram, it is possible to efficiently extract the location of the nearest thermodynamic singularity, the Lee-Yang edge singularity, from which one can (i) determine the location of the critical point, (ii) constrain the nonuniversal parameters that maps the equation of state to that of the Ising model in the scaling regime, and (iii) numerically evaluate the equation of state in the vicinity of the critical point. This is done by using a combination of Padé resummation and conformal maps. We explicitly demonstrate these ideas in the celebrated Gross-Neveu model.

Evolution of Non-Gaussian Hydrodynamic Fluctuations.

In the context of the search for the QCD critical point using non-Gaussian fluctuations, we obtain the evolution equations for non-Gaussian cumulants to the leading order of the systematic expansion in the magnitude of thermal fluctuations. We develop a diagrammatic technique in which the leading order contributions are given by tree diagrams. We introduce a Wigner transform for multipoint correlators and derive the evolution equations for three- and four-point Wigner functions for the problem of nonlinear stochastic diffusion with multiplicative noise.

Monte Carlo Study of Real Time Dynamics on the Lattice.

Monte Carlo studies involving real time dynamics are severely restricted by the sign problem that emerges from a highly oscillatory phase of the path integral. In this Letter, we present a new method to compute real time quantities on the lattice using the Schwinger-Keldysh formalism via Monte Carlo simulations. The key idea is to deform the path integration domain to a complex manifold where the phase oscillations are mild and the sign problem is manageable. We use the previously introduced "contraction algorithm" to create a Markov chain on this alternative manifold. We substantiate our approach by analyzing the quantum mechanical anharmonic oscillator. Our results are in agreement with the exact ones obtained by diagonalization of the Hamiltonian. The method we introduce is generic and, in principle, applicable to quantum field theory albeit very slow. We discuss some possible improvements that should speed up the algorithm.

Casimir Energy of Confining Large N Gauge Theories.

Four-dimensional asymptotically free large N gauge theories compactified on S(R)(3)×R have a weakly coupled confining regime when R is small compared to the strong scale. We compute the vacuum energy of a variety of confining large N nonsupersymmetric gauge theories in this calculable regime, where the vacuum energy can be thought of as the S(3) Casimir energy. The N=∞ renormalized vacuum energy turns out to vanish in the class of theories we have examined. This matches an implication of a recently observed temperature-reflection symmetry of such systems.

Chiral and gravitational anomalies on Fermi surfaces.

A Fermi surface threaded by a Berry phase can be described by the Wess-Zumino-Witten term. After gauging, it produces a five-dimensional Chern-Simons term in the action. We show how this Chern-Simons term captures the essence of the Abelian, non-Abelian, and mixed gravitational anomalies in describing both in- and off-equilibrium phenomena. In particular, we derive a novel contribution to the chiral vortical effect that arises when a temperature gradient is present. We also discuss the issue of universality of the anomalous currents.

Volume independence in the large N limit and an emergent fermionic symmetry.

Large-N volume independence in circle-compactified QCD with adjoint Weyl fermions implies the absence of any phase transitions as the radius is dialed to arbitrarily small values. This class of theories is believed to possess a Hagedorn density of hadronic states. It turns out that these properties are in apparent tension with each other, because a Hagedorn density of states typically implies a phase transition at some finite radius. This tension is resolved if there are degeneracies between the spectra of bosonic and fermionic states, as happens in the N(f) = 1 supersymmetric case. Resolution of the tension for N(f) >1 then suggests the emergence of a fermionic symmetry at large N, where there is no supersymmetry. We can escape the Coleman-Mandula theorem since the N = ∞ theory is free, with a trivial S matrix. We show an example of such a spectral degeneracy in a nonsupersymmetric toy example which has a Hagedorn spectrum.

Conformal anomaly as a source of soft photons in heavy ion collisions.

We introduce a novel photon production mechanism stemming from the conformal anomaly of QCD×QED and the existence of strong (electro)magnetic fields in heavy ion collisions. Using the hydrodynamical description of the bulk modes of QCD plasma, we show that this mechanism leads to the photon production yield that is comparable to the yield from conventional sources. This mechanism also provides a significant positive contribution to the azimuthal anisotropy of photons, v(2), as well as to the radial "flow." We compare our results to the data from the PHENIX Collaboration.

Chiral magnetic spirals.

We argue that the presence of a very strong magnetic field in the chirally broken phase induces inhomogeneous expectation values, of a spiral nature along the magnetic field axis, for the currents of charge and chirality, when there is finite baryon density or an imbalance between left and right chiralities. This "chiral magnetic spiral" is a gapless excitation transporting the currents of (i) charge (at finite chirality), and (ii) chirality (at finite baryon density) along the direction of the magnetic field. In both cases it also induces in the transverse directions oscillating currents of charge and chirality. In heavy ion collisions, the chiral magnetic spiral possibly provides contributions both to the out-of-plane and the in-plane dynamical charge fluctuations recently observed at BNL RHIC.

Self-consistent crystalline condensate in chiral Gross-Neveu and Bogoliubov-de Gennes systems.

We derive a new exact self-consistent crystalline condensate in the (1+1)-dimensional chiral Gross-Neveu model. This also yields a new exact crystalline solution for the one dimensional Bogoliubov-de Gennes equations and the Eilenberger equation of semiclassical superconductivity. We show that the functional gap equation can be reduced to a solvable nonlinear equation and discuss implications for the temperature-chemical potential phase diagram.