Covariant and single-field effective action with the background-field formalism

Abstract

In the context of scalar quantum field theory we introduce a class of generically nonlinear quantum-background splits for which the splitting Ward identity, encoding the single field dependence in the effective action, can be solved exactly. We show that this can be used to construct an effective action which is both covariant and dependent on the background and fluctuation fields only through a single total field in a way independent from the dynamics. Moreover we discuss the criteria under which the ultraviolet symmetries are inherited by the quantum effective action. The approach is demonstrated through some examples, including the $O(N)$ effective field theory, which might be of interest for the Higgs sector of the Standard Model or its extensions.

32 pages, latex; v2: added refs, short example in sec.3, and some clarifications in the conclusions. To appear in PRD

References in corpus (3)

• Geometry of the Scalar Sector
• Geometrical effective action and Wilsonian flows
• Covariant and background independent functional RG flow for the effective average action

Cited by in corpus (10)

• The nonperturbative functional renormalization group and its applications
• Towards apparent convergence in asymptotically safe quantum gravity
• Form Factors in Asymptotic Safety: conceptual ideas and computational toolbox
• The background scale Ward identity in quantum gravity
• Infinite order quantum-gravitational correlations
• Split Weyl transformations in quantum gravity
• Lessons from conformally reduced quantum gravity
• BRST invariant RG flows
• Flows of multicomponent scalar models with U(1) gauge symmetry
• Background Effective Action with Nonlinear Massive Gauge Fixing