Lattice implementation of Abelian gauge theories with ChernSimons 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 quarkgluon plasma. We present an explicit noncompact lattice formulation of the interaction between a shiftsymmetric field and some U (1) gauge sector, a (x)F_{μν}F^{∼μν}, reproducing the continuum limit to order O (dx_{μ}^{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 topological number density K =F_{μν}F^{∼μν} that admits a lattice total derivative representation K = ∆_{μ}^{+} K^{μ}, reproducing to order O (dx_{μ}^{2}) the continuum expression K =∂_{μ}K^{μ} ∝ E → ⋅ 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 ChernSimons term for the gauge fields. This allow us to study in an accompanying paper the real time dynamics of fermion number nonconservation (or chirality breaking) in Abelian gauge theories at finite temperature. When a (x) = a (x → , t) is inhomogeneous, the set of lattice equations of motion do not admit however a simple explicit local solution (while preserving an O (dx_{μ}^{2}) accuracy). We discuss an iterative scheme allowing to overcome this difficulty.
 Publication:

Nuclear Physics B
 Pub Date:
 January 2018
 DOI:
 10.1016/j.nuclphysb.2017.12.001
 arXiv:
 arXiv:1705.09629
 Bibcode:
 2018NuPhB.926..544F
 Keywords:

 High Energy Physics  Lattice;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 High Energy Physics  Phenomenology
 EPrint:
 30 pages