Lattice worldline representation of correlators in a background field

Thomas Epelbaum (1) , François Gelis (2) , Bin Wu (2)

1 McGill University = Université McGill [Montréal, Canada]
2 IPHT - Institut de Physique Théorique - UMR CNRS 3681

We use a discrete worldline representation in order to study the continuum limit of the one-loop expectation value of dimension two and four local operators in a background field. We illustrate this technique in the case of a scalar field coupled to a non-Abelian background gauge field. The first two coefficients of the expansion in powers of the lattice spacing can be expressed as sums over random walks on a d-dimensional cubic lattice. Using combinatorial identities for the distribution of the areas of closed random walks on a lattice, these coefficients can be turned into simple integrals. Our results are valid for an anisotropic lattice, with arbitrary lattice spacings in each direction.

Domaines: Physique des Hautes Energies - Phénoménologie [hep-ph]; Physique des Hautes Energies - Théorie [hep-th]; Physique Nucléaire Théorique [nucl-th]

Thomas Epelbaum, François Gelis, Bin Wu. Lattice worldline representation of correlators in a background field. 2016. ⟨cea-01280202⟩