Chiral anomaly, Schwinger effect, Euler-Heisenberg Lagrangian and application to axion inflation

Abstract

Particle production in strong electromagnetic fields is a recurring theme in solid state physics, heavy ion collisions, early universe cosmology and formal quantum field theory. In this paper we discuss the Dirac equation in a background of parallel electric and magnetic fields. We review the Schwinger particle production rate, clarify the emergence of the chiral anomaly equation and compute the induced current of charged fermions. We distinguish the contributions from nonperturbative particle production, from the running of the gauge coupling constant and from nonlinearities in the effective QED Lagrangian, and clarify how these contributions arise within a single framework. We apply these results to axion inflation. A Chern-Simons coupling between the pseudoscalar particle driving cosmic inflaton and an abelian gauge group induces a dual production of gauge fields and charged fermions. We show that the resulting scalar and gravitational wave power spectra strongly depend on the fermion mass.

Resonant backreaction in axion inflation

“…3. As |φ | drops, the gauge friction drops 5 As expected for the discussion in Sec. 3, the generic features of the results discussed here are not very sensitive to the precise form of the scalar potential.…”

“…These gauge fields backreact on the inflaton equation of motion. The physical electric and magnetic fields entering in (5) are obtained as…”

“…the case for the Standard Model hypercharge), these particles must be included in the analysis if they are sufficiently light, as they will be produced via Schwinger production from the vacuum, thereby significantly damping the gauge field production. On the contrary, the impact of heavier particles is exponentially suppressed and they can be safely integrated out [4,5].…”

Schwinger effect and false vacuum decay as quantum-mechanical tunneling of a relativistic particle

“…Setting the in-state to be the vacuum, the negative-frequency coefficient in the Bogolyubov transformation gives the number of the produced particles in the outstate. This method can also be used to study Schwinger effect in non-Abelian gauge theories [20,21].…”

Dynamic scale anomalous transport in QCD with electromagnetic background

“…Nowadays, the target field in which such chiral anomalous transports play some role has been extended with multiple aspects including not only QCD and condensed matter systems, but also applications to other cosmologically and theoretically important issues, such as production of the baryon number asymmetry of universe [5][6][7][8][9][10][11][12], inflationary scenarios with axion [13][14][15], and a solution for the gauge-hierarchy problem [16][17][18][19][20]. Thus, the anomalous transport physics has opened a vast ballpark in the theoretical particle physics.…”