Background Effective Action with Nonlinear Massive Gauge Fixing
arXiv:2205.06707 · doi:10.1103/PhysRevD.106.116013
Abstract
We combine a recent construction of a BRST-invariant, nonlinear massive gauge fixing with the background field formalism. The resulting generating functional preserves background-field invariance as well as BRST invariance of the quantum field manifestly. The construction features BRST-invariant mass parameters for the quantum gauge and ghost fields. The formalism employs a background Nakanishi-Lautrup field which is part of the nonlinear gauge-fixing sector and thus should not affect observables. We verify this expectation by computing the one-loop effective action and the corresponding beta function of the gauge coupling as an example. The corresponding Schwinger functional generating connected correlation functions acquires additional one-particle reducible terms that vanish on shell. We also study off-shell one-loop contributions in order to explore the consequences of a nonlinear gauge fixing scheme involving a background Nakanishi-Lautrup field. As an application, we show that our formalism straightforwardly accommodates nonperturbative information about propagators in the Landau gauge in the form of the so-called decoupling solution. Using this nonperturbative input, we find evidence for the formation of a gluon condensate for sufficiently large coupling, whose scale is set by the BRST-invariant gluon mass parameter.
24 pages, 3 figures
References in corpus (21)
- Exact evolution equation for the effective potential
- A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
- Gluon and ghost propagators in the Landau gauge: Deriving lattice results from Schwinger-Dyson equations
- Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared
- Pinch Technique: Theory and Applications
- New features of the gluon and ghost propagator in the infrared region from the Gribov-Zwanziger approach
- Infrared propagators of Yang-Mills theory from perturbation theory
- Gluon mass generation in the PT-BFM scheme
- En route to Background Independence: Broken split-symmetry, and how to restore it with bi-metric average actions
- Power corrections to alpha_s(M_τ),|V_{us}| and m_s
- On the Nature of the Phase Transition in SU(N), Sp(2) and E(7) Yang-Mills theory
- Background independent exact renormalization group for conformally reduced gravity
- The background scale Ward identity in quantum gravity
- Manifestly Gauge Invariant QCD
- Gluon condensation and scaling exponents for the propagators in Yang-Mills theory
- Infrared finite ghost propagator in the Feynman gauge
- Yang-Mills propagators in linear covariant gauges from Nielsen identities
- Covariant and background independent functional RG flow for the effective average action
- Reducible contributions to quantum electrodynamics in external fields
- On the construction of QED using ERG
- Quantum Master Equation for QED in Exact Renormalization Group