Lattice implementation of Abelian gauge theories with Chern-Simons number and an axion field

Abstract

Real time evolution of classical gauge fields is relevant for a number of applications in particle physics and cosmology, ranging from the early Universe to dynamics of quark-gluon plasma. We present a lattice formulation of the interaction between a $shift$-symmetric field and some $U(1)$ gauge sector, $a(x){\tilde{F}}_{\mu \nu }{F}^{\mu \nu }$, reproducing the continuum limit to order $\mathcal{O}(d{x}_{\mu }^2)$ and obeying the following properties: (i) the system is gauge invariant and (ii) shift symmetry is exact on the lattice. For this end we construct a definition of the {\it topological number density} $Q={\tilde{F}}_{\mu \nu }{F}^{\mu \nu }$ that admits a lattice total derivative representation $Q={\Delta }_{\mu }^{+}{K}^{\mu }$, reproducing to order $\mathcal{O}(d{x}_{\mu }^2)$ the continuum expression $Q={\partial }_{\mu }{K}^{\mu }\propto \vec{E}\cdot \vec{B}$. If we consider a homogeneous field $a(x)=a(t)$, the system can be mapped into an Abelian gauge theory with Hamiltonian containing a Chern-Simons term for the gauge fields. This allow us to study in an accompanying paper the real time dynamics of fermion number non-conservation (or chirality breaking) in Abelian gauge theories at finite temperature. When $a(x)=a(\vec{x},t)$ is inhomogeneous, the set of lattice equations of motion do not admit however a simple explicit local solution (while preserving an $\mathcal{O}(d{x}_{\mu }^2)$ accuracy). We discuss an iterative scheme allowing to overcome this difficulty.

30 pages

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Cited by in corpus (24)

• The art of simulating the early Universe -- Part I
• Lattice formulation of axion inflation. Application to preheating
• Lattice Simulations of Axion-U(1) Inflation
• Anomalous non-conservation of fermion/chiral number in Abelian gauge theories at finite temperature
• Instability in axion inflation with strong backreaction from gauge modes
• Gravitational wave background from non-Abelian reheating after axion-like inflation
• Chiral instabilities & the onset of chiral turbulence in QED plasmas
• Axion inflation in the strong-backreaction regime: decay of the Anber-Sorbo solution
• Electromagnetic Bursts from Mergers of Oscillons in Axion-like Fields
• Lattice simulations of Abelian gauge fields coupled to axions during Inflation
• Dipole Radiation and Beyond from Axion Stars in Electromagnetic Fields
• Evolution of the Primordial Axial Charge across Cosmic Times
• Gravitational Waves from an Axion-Dark Photon System: A Lattice Study
• Chiral charge dynamics in Abelian gauge theories at finite temperature
• Dark photon dark matter from an oscillating dilaton
• Equilibration of the chiral asymmetry due to finite electron mass in electron-positron plasma
• The non-linear dynamics of axion inflation: a detailed lattice study
• Experimental targets for dark photon dark matter
• Chiral gravitational waves and primordial black holes in UV-protected Natural Inflation
• On the Schwinger effect during axion inflation
• Dynamical Axions in $U(1)$ Quantum Spin Liquids
• Gravitational waves from axion inflation in the gradient expansion formalism. Part I. Pure axion inflation
• Electrical conductivity of hot Abelian plasma with scalar charge carriers
• Axion Fragmentation on the Lattice