"Background Field Integration-by-Parts" and the Connection Between One-Loop and Two-Loop Heisenberg-Euler Effective Actions

We develop integration-by-parts rules for Feynman diagrams involving massive scalar propagators in a constant background electromagnetic field, and use these to show that there is a simple diagrammatic interpretation of mass renormalization in the two-loop scalar QED Heisenberg-Euler effective action for a general constant background field. This explains why the square of a one-loop term appears in the renormalized two-loop Heisenberg-Euler effective action. No integrals need be evaluated, and the explicit form of the background field propagators is not needed. This dramatically simplifies the computation of the renormalized two-loop effective action for scalar QED, and generalizes a previous result obtained for self-dual background fields.Comment: 13 pages; uses axodraw.st

Coordinate noncommutativity in strong non-uniform magnetic fields

Noncommuting spatial coordinates are studied in the context of a charged particle moving in a strong non-uniform magnetic field. We derive a relation involving the commutators of the coordinates, which generalizes the one realized in a strong constant magnetic field. As an application, we discuss the noncommutativity in the magnetic field present in a magnetic mirror.Comment: 4 page

Monopole decay in the external electric field

The possibility of the magnetic monopole decay in the constant electric field is investigated and the exponential factor in the probability is obtained. Corrections due to Coulomb interaction are calculated. The relation between masses of particles for the process to exist is obtained.Comment: 13 pages, 8 figure

Gravitational non-commutativity and G\"odel-like spacetimes

We derive general conditions under which geodesics of stationary spacetimes resemble trajectories of charged particles in an electromagnetic field. For large curvatures (analogous to strong magnetic fields), the quantum mechanicical states of these particles are confined to gravitational analogs of {\it lowest Landau levels}. Furthermore, there is an effective non-commutativity between their spatial coordinates. We point out that the Som-Raychaudhuri and G\"odel spacetime and its generalisations are precisely of the above type and compute the effective non-commutativities that they induce. We show that the non-commutativity for G\"odel spacetime is identical to that on the fuzzy sphere. Finally, we show how the star product naturally emerges in Som-Raychaudhuri spacetimes.Comment: Two sections added (Relation to the fuzzy sphere, Emergence of the star product). 10 pages, Revtex. To appear in General Relativity and Gravitatio

Supersymmetric Euler-Heisenberg effective action: Two-loop results

The two-loop Euler-Heisenberg-type effective action for N = 1 supersymmetric QED is computed within the background field approach. The background vector multiplet is chosen to obey the constraints D_\a W_\b = D_{(\a} W_{\b)} = const, but is otherwise completely arbitrary. Technically, this calculation proves to be much more laborious as compared with that carried out in hep-th/0308136 for N = 2 supersymmetric QED, due to a lesser amount of supersymmetry. Similarly to Ritus' analysis for spinor and scalar QED, the two-loop renormalisation is carried out using proper-time cut-off regularisation. A closed-form expression is obtained for the holomorphic sector of the two-loop effective action, which is singled out by imposing a relaxed super self-duality condition.Comment: 27 pages, 2 eps figures, LaTeX; V2: typos corrected, comments and reference adde

Chern-Simons Solitons, Chiral Model, and (affine) Toda Model on Noncommutative Space

We consider the Dunne-Jackiw-Pi-Trugenberger model of a U(N) Chern-Simons gauge theory coupled to a nonrelativistic complex adjoint matter on noncommutative space. Soliton configurations of this model are related the solutions of the chiral model on noncommutative plane. A generalized Uhlenbeck's uniton method for the chiral model on noncommutative space provides explicit Chern-Simons solitons. Fundamental solitons in the U(1) gauge theory are shaped as rings of charge `n' and spin `n' where the Chern-Simons level `n' should be an integer upon quantization. Toda and Liouville models are generalized to noncommutative plane and the solutions are provided by the uniton method. We also define affine Toda and sine-Gordon models on noncommutative plane. Finally the first order moduli space dynamics of Chern-Simons solitons is shown to be trivial.Comment: latex, JHEP style, 23 pages, no figur

Resurgence and the Nekrasov-Shatashvili limit: connecting weak and strong coupling in the Mathieu and Lamé systems

Abstract: The Nekrasov-Shatashvili limit for the low-energy behavior of N=2 and N=2* supersymmetric SU(2) gauge theories is encoded in the spectrum of the Mathieu and Lamé equations, respectively. This correspondence is usually expressed via an all-orders Bohr-Sommerfeld relation, but this neglects non-perturbative effects, the nature of which is very different in the electric, magnetic and dyonic regions. In the gauge theory dyonic region the spectral expansions are divergent, and indeed are not Borel-summable, so they are more properly described by resurgent trans-series in which perturbative and non-perturbative effects are deeply entwined. In the gauge theory electric region the spectral expansions are convergent, but nevertheless there are non-perturbative effects due to poles in the expansion coefficients, and which we associate with worldline instantons. This provides a concrete analog of a phenomenon found recently by Drukker, Mariño and Putrov in the large N expansion of the ABJM matrix model, in which non-perturbative effects are related to complex space-time instantons. In this paper we study how these very different regimes arise from an exact WKB analysis, and join smoothly through the magnetic region. This approach also leads to a simple proof of a resurgence relation found recently by Dunne and Ünsal, showing that for these spectral systems all non-perturbative effects are subtly encoded in perturbation theory, and identifies this with the Picard-Fuchs equation for the quantized elliptic curve

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

Twisted kink crystal in the chiral Gross-Neveu model

We present the detailed properties of a self-consistent crystalline chiral condensate in the massless chiral Gross-Neveu model. We show that a suitable ansatz for the Gorkov resolvent reduces the functional gap equation, for the inhomogeneous condensate, to a nonlinear Schrödinger equation, which is exactly soluble. The general crystalline solution includes as special cases all previously known real and complex condensate solutions to the gap equation. Furthermore, the associated Bogoliubov-de Gennes equation is also soluble with this inhomogeneous chiral condensate, and the exact spectral properties are derived. We find an all-orders expansion of the Ginzburg-Landau effective Lagrangian and show how the gap equation is solved order by order

Hydrodynamics, resurgence, and transasymptotics

The second order hydrodynamical description of a homogeneous conformal plasma that undergoes a boost-invariant expansion is given by a single nonlinear ordinary differential equation, whose resurgent asymptotic properties we study, developing further the recent work of Heller and Spalinski [Phys. Rev. Lett. 115, 072501 (2015)]. Resurgence clearly identifies the nonhydrodynamic modes that are exponentially suppressed at late times, analogous to the quasinormal modes in gravitational language, organizing these modes in terms of a trans-series expansion. These modes are analogs of instantons in semiclassical expansions, where the damping rate plays the role of the instanton action. We show that this system displays the generic features of resurgence, with explicit quantitative relations between the fluctuations about different orders of these nonhydrodynamic modes. The imaginary part of the trans-series parameter is identified with the Stokes constant, and the real part with the freedom associated with initial conditions