Complex Path Integrals and Saddles in Two-Dimensional Gauge Theory.

We study numerically the saddle point structure of two-dimensional lattice gauge theory, represented by the Gross-Witten-Wadia unitary matrix model. The saddle points are, in general, complex valued, even though the original integration variables and action are real. We confirm the trans-series and instanton gas structure in the weak-coupling phase, and we identify a new complex-saddle interpretation of nonperturbative effects in the strong-coupling phase.

Complexified Path Integrals, Exact Saddles, and Supersymmetry.

In the context of two illustrative examples from supersymmetric quantum mechanics we show that the semiclassical analysis of the path integral requires complexification of the configuration space and action, and the inclusion of complex saddle points, even when the parameters in the action are real. We find new exact complex saddles, and show that without their contribution the semiclassical expansion is in conflict with basic properties such as the positive semidefiniteness of the spectrum, as well as constraints of supersymmetry. Generic saddles are not only complex, but also possibly multivalued and even singular.

Infrared Renormalons versus Operator Product Expansions in Supersymmetric and Related Gauge Theories.

We use the connection between infrared (IR) renormalons and condensates in the operator product expansion for correlation functions to make predictions concerning the structure of singularities in the Borel plane for the perturbative series in quantum field theories with different levels of supersymmetry. The same conspiracy can be used for establishing the absence of condensates or IR renormalons in gauge theories with an IR conformal regime or gauge theories in the Higgs phase. The absence of the renormalon-induced factorial divergence implies that instanton contributions (where present) must be well defined.

Resurgence in quantum field theory: nonperturbative effects in the principal chiral model.

We explain the physical role of nonperturbative saddle points of path integrals in theories without instantons, using the example of the asymptotically free two-dimensional principal chiral model (PCM). Standard topological arguments based on homotopy considerations suggest no role for nonperturbative saddles in such theories. However, the resurgence theory, which unifies perturbative and nonperturbative physics, predicts the existence of several types of nonperturbative saddles associated with features of the large-order structure of the perturbation theory.

Time-dependent Hartree-Fock solution of Gross-Neveu models: twisted-kink constituents of baryons and breathers.

We find the general solution to the time-dependent Hartree-Fock problem for the Gross-Neveu models, with both discrete (GN(2)) and continuous [Nambu-Jona-Lasinio (NJL(2))] chiral symmetry. We find new multibaryon, multibreather, and twisted breather solutions, and show that all GN(2) baryons and breathers are composed of constituent twisted kinks of the NJL(2) model.

Spatial log-periodic oscillations of first-passage observables in fractals.

For transport processes in geometrically restricted domains, the mean first-passage time (MFPT) admits a general scaling dependence on space parameters for diffusion, anomalous diffusion, and diffusion in disordered or fractal media. For transport in self-similar fractal structures, we obtain an expression for the source-target distance dependence of the MFPT that exhibits both the leading power-law behavior, depending on the Hausdorff and spectral dimension of the fractal, as well as small log-periodic oscillations that are a clear and definitive signal of the underlying fractal structure. We also present refined numerical results for the Sierpinski gasket that confirm this oscillatory behavior.

Ramsey fringes and time-domain multiple-slit interference from vacuum.

Sequences of alternating-sign time-dependent electric field pulses lead to coherent interference effects in Schwinger vacuum pair production, producing a Ramsey interferometer, an all-optical time-domain realization of the multiple-slit interference effect, directly from the quantum vacuum. The interference, obeying fermionic quantum statistics, is manifest in the momentum dependence of the number of produced electrons and positrons along the linearly polarized electric field. The central value grows like N(2) for N pulses [i.

Thermodynamics of photons on fractals.

A thermodynamical treatment of a massless scalar field (a photon) confined to a fractal spatial manifold leads to an equation of state relating pressure to internal energy, PV(s) = U/d(s), where d(s) is the spectral dimension and V(s) defines the "spectral volume." For regular manifolds, V(s) coincides with the usual geometric spatial volume, but on a fractal this is not necessarily the case. This is further evidence that on a fractal, momentum space can have a different dimension than position space.

Stokes phenomenon and schwinger vacuum pair production in time-dependent laser pulses.

Particle production due to external fields (electric, chromoelectric, or gravitational) requires evolving an initial state through an interaction with a time-dependent background, with the rate being computed from a Bogoliubov transformation between the in and out vacua. When the background fields have temporal profiles with substructure, a semiclassical analysis of this problem confronts the full subtlety of the Stokes phenomenon: WKB solutions are only local, while the production rate requires global information. We give a simple quantitative explanation of the recently computed [Phys.

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.

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.

Precise quark-mass dependence of the instanton determinant.

The fermion determinant in an instanton background for a quark field of arbitrary mass is determined exactly using an efficient numerical method to evaluate the determinant of a partial-wave radial differential operator. The bare sum over partial waves is divergent but can be renormalized in the minimal subtraction scheme using the result of WKB analysis of the large partial-wave contribution. Previously, only a few leading terms in the extreme small and large mass limits were known for the corresponding effective action.

Particle number fractionalization of an atomic Fermi-Dirac gas in an optical lattice.

We show that a dilute two-species gas of Fermi-Dirac alkali-metal atoms in a periodic optical lattice may exhibit fractionalization of the particle number when the two components are coupled via a coherent electromagnetic field with a topologically nontrivial phase profile. This results in fractional eigenvalues of the spin operator with vanishing fluctuations. The fractional part can be accurately controlled by modifying the effective detuning of the electromagnetic field.