%0 Journal Article %1 figueroa2017lattice %A Figueroa, Daniel G. %A Shaposhnikov, Mikhail %D 2017 %K axions gauge-th lattice %T Lattice implementation of Abelian gauge theories with Chern-Simons number and an axion field %U http://arxiv.org/abs/1705.09629 %X 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, $a(x)F_\mu\nuF^\mu\nu$, reproducing the continuum limit to order $O(dx_\mu^2)$ 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 topological number density $Q = F_\mu\nuF^\mu\nu$ that admits a lattice total derivative representation $Q = \Delta_\mu^+ K^\mu$, reproducing to order $O(dx_\mu^2)$ the continuum expression $Q = \partial_K^\mu E B$. If we consider a homogeneous field $a(x) = a(t)$, the system can be mapped into an Abelian gauge theory with Hamiltonian containing a 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 $a(x) = a(x,t)$ is inhomogeneous, the set of lattice equations of motion do not admit however a simple explicit local solution (while preserving an $O(dx_\mu^2)$ accuracy). We discuss an iterative scheme allowing to overcome this difficulty.

@article{figueroa2017lattice, 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 $\mathcal{O}(dx_\mu^2)$ 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 $\mathcal{O}(dx_\mu^2)$ 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 $\mathcal{O}(dx_\mu^2)$ accuracy). We discuss an iterative scheme allowing to overcome this difficulty.}, added-at = {2017-05-29T12:48:50.000+0200}, author = {Figueroa, Daniel G. and Shaposhnikov, Mikhail}, biburl = {https://www.bibsonomy.org/bibtex/204ed6989fb6c3af2bc3c90effd2ff7a1/vindex10}, description = {Lattice implementation of Abelian gauge theories with Chern-Simons number and an axion field}, interhash = {8f0c0c2e1a498afa3d09353508d0cd07}, intrahash = {04ed6989fb6c3af2bc3c90effd2ff7a1}, keywords = {axions gauge-th lattice}, note = {cite arxiv:1705.09629Comment: 30 pages}, timestamp = {2017-05-29T12:48:50.000+0200}, title = {Lattice implementation of Abelian gauge theories with Chern-Simons number and an axion field}, url = {http://arxiv.org/abs/1705.09629}, year = 2017 }