Self-interactions in a topological BF-type model inD= 5

Abstract

All consistent interactions in five spacetime dimensions that can be added to a free BF-type model involving one scalar field, two types of one-forms, two sorts of two-forms, and one threeform are investigated by means of deforming the solution to the master equation with the help of specific cohomological techniques. The couplings are obtained on the grounds of smoothness, locality, (background) Lorentz invariance, Poincaré invariance, and the preservation of the number of derivatives on each field.Since a is a d-closed modulo γ p-form, the equations (148) and (163) yieldWith the help of the property (155), from (164) we arrive toTheorem A.1 then implies thatwith β J an invariant polynomial. Inserting α J of the form (166) in (153), we obtain thatDue to the fact that de J = γê J and γλ 4 I,J = 0, we consequently have thatIn a similar manner, with the help of the relation (276) inserted in (271), we arrive to b I−1 = s ± Now, if we simultaneously perform some trivial redefinitions of a I and of the 'current' b I−1 like a ′ I = a I − s ± J λ 5 I+1and, meanwhile, fixā I andb I−1 from (267) and respectively from (271) as a I = ± J λ 4 I,Jê J , (282) b I−1 = ± J λ 3 I−1,Jê J ,

Consistent interaction vertices in arbitrary topological BF theories

“…We start with a topological BF model with a maximal field spectrum in D = 5, solved in detail in [9]. The field spectrum in D = 5 contains the pairs of fields [0] A ≡ ϕ,…”

Note on the BRST mass generation of a vector field. The case of couplings to N = 4 real scalars

“…Once the deformation equations (15)- (18), etc., have been solved by means of specific cohomological techniques, from the consistent nontrivial deformed solution to the master equation one can identify the entire gauge structure of the resulting interacting theory. The procedure just succinctly addressed was employed in deriving some gravity-related interacting models [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] and also in deducing the consistent couplings in theories that involve various kinds of forms [42][43][44] or matter fields in the presence of gauge forms [45][46][47].…”

Massive spin-one fields from couplings with five massless real scalars

“…at hand, from the deformed solution to the master equation (12) one can identify the entire gauge structure of the resulting interacting theory. The procedure previously exposed was successfully employed in constructing some gravity-related interacting models [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] and also in deducing the consistent couplings in theories that involve various kinds of forms [43][44][45] or matter fields in the presence of gauge forms [46][47][48]. It is worth noticing that a BRST Hamiltonian counterpart to the antifield deformation method was conceived [49].…”

“…The fully deformed solution to the master equations depends on two kinds of real constants [the antisymmetric 5 × 5 real matrixT and the real quintuplen ∈ R 5 ] and also on a polynomial function [V] subject to conditions (30) and (34).…”

“…In view of identifying the Lagrangian structure of the interacting theory from (37), we have to determine the most general polynomial function V which verifies equations (30) and (34). So, we assume thatT is of maximum rank [which is found to be equal to 4] and in canonical form [this can always be done via an orthogonal transformation in the space of scalar fields]T…”