Four-dimensional couplings among BF and matter theories from BRST cohomology

Abstract

The local and manifestly covariant Lagrangian interactions in four spacetime dimensions that can be added to a "free" model that describes a generic matter theory and an abelian BF theory are constructed by means of deforming the solution to the master equation on behalf of specific cohomological techniques.

Gauge-invariant massive BF models

“…The massless real scalar fields are separately described by a linear theory with the Lagrangian action S L,scalar [φ] from (2) and without (nontrivial) gauge symmetries (see (5)), so its Cauchy order is equal to 1. On these grounds, the matter sector can be shown to be able to contribute nontrivially to the first-order deformation a int earliest in antifield number 1 (see [33] for a more detailed argument). Consequently, it is enough to expand a int and j µ int along the antifield number like…”

“…Next, we construct the BRST differential algebra for the free model under study in the context of the antifield-antibracket formalism [23,24,25,26,27,28,29,30,31,32]. Related to the BF sector, we use the notations and results exposed in [33]. We introduce the BRST generators as the original fields Φ α 0 from relation (1), the ghosts as dynamical variables respectively associated with both gauge and reducibility parameters displayed in (6), (8), and ( 11), together with their corresponding antifields (denoted by star variables)…”

“…We are interested only in (nontrivial) deformations that comply with the standard hypotheses of field theory: analyticity in the coupling constant, Lorentz covariance, spacetime locality, and Poincaré invariance. By analyticity in the coupling constant we mean that the deformed solution to the classical master equation, S as in (33), is an analytic function of g and reduces to the canonical BRST generator (32) of the starting model in the free limit (g = 0). The other requirements are translated at the level of its nonintegrated densities at all orders of perturbation theory to be expressed by (nontrivial) bosonic functions of ghost number 0 that are: (A) (background) Lorentz scalars; (B) smooth functions of the undifferentiated original fields Φ α 0 (see notation (1)); (C) polynomials in the derivatives of the original fields up to a finite order; (D) polynomials in the ghosts, antifields, and their spacetime derivatives up to a finite order (items (B), (C), and (D) ensure the spacetime locality); (E) without an explicit dependence of the spacetime coordinates (Poincaré invariance).…”

“…Equation ( 49) was addressed in [33] under some equivalent working hypotheses and in the framework of the same deformation approach. Employing all the results, notations, and conventions therein, it follows that a BF can be taken to decompose as a sum between pieces with the antifield number ranging from 0 to 4…”

Construction of consistent interactions in higher derivative Yang-Mills gauge theory with matter fields

“…Besides, the deformation procedure will alter the form of the gauge transformations of the matter fields and the deformation parameter can be regarded as the couplings constant among fields. Plenty of research has been made on the area of the deformations of the master action in various contexts of gauge theories through the analysis of BRST cohomology by Bizdadea et al [36][37][38][39] and the recent developments of BRST consistent deformations can be consulted in [40][41][42].…”