Perturbative computation in a QED${}_3$-inspired conformal abelian gauge model on the lattice

Abstract

We perform perturbative computations in a lattice gauge theory with a conformal measure that is quadratic in a non-compact abelian gauge field and is nonlocal, as inspired by the induced gauge action in massless QED${}_3$. In a previous work, we showed that coupling fermion sources to the gauge model led to nontrivial conformal data in the correlation functions of fermion bilinears that are functions of charge $q$ of the fermion. In this paper, we compute such gauge invariant fermionic observables to order $q^2$ in lattice perturbation theory with the same conformal measure. We reproduce the expectations for scalar anomalous dimension from previous estimates in dimensional regularization. We address the issue of the lattice regulator dependence of the amplitudes of correlation functions.

arXiv comment13 pages, 6 figures, 2 tables

References in corpus (18)

• On the Viability of Lattice Perturbation Theory
• Deconfined quantum critical points: symmetries and dualities
• Level/rank Duality and Chern-Simons-Matter Theories
• Lattice Perturbation Theory
• Non-Compact QED_3 with N_f=1 and N_f=4
• Non-compact QED_3 with N_f >=2
• Self-dual Quantum Electrodynamics as Boundary State of the three dimensional Bosonic Topological Insulator
• Scale-invariance of parity-invariant three-dimensional QED
• Towards Bootstrapping QED${}_3$
• No evidence for bilinear condensate in parity-invariant three-dimensional QED with massless fermions
• On $C_J$ and $C_T$ in Conformal QED
• Anomalous dimensions of scalar operators in $QE{D}_3$
• Numerical determination of monopole scaling dimension in parity-invariant three-dimensional non-compact QED
• Flavor and topological current correlators in parity-invariant three-dimensional QED
• Magnetic monopole plasma phase in (2+1)d compact quantum electrodynamics with fermionic matter
• QED${}_3$-inspired three-dimensional conformal lattice gauge theory without fine-tuning
• Monopole scaling dimension using Monte Carlo
• Lattice perturbation theory in the overlap formulation for the Yukawa and gauge interactions