BRST Cohomological Results on the Massless Tensor Field With the Mixed Symmetry of the Riemann Tensor

Abstract

The basic BRST cohomological properties of a free, massless tensor field with the mixed symmetry of the Riemann tensor are studied in detail. It is shown that any non-trivial co-cycle from the local BRST cohomology group can be taken to stop at antighost number three, its last component belonging to the cohomology of the exterior longitudinal derivative and containing non-trivial elements from the (invariant) characteristic cohomology.

Couplings of a collection of BF models to matter theories

“…This statement is also standard material and can be shown like in [14,15,16,17]. Its proof is mainly based on the formulas (48)-(50) and relies on the fact that we can successively eliminate all the pieces of antighost number strictly greater that four from the non-integrated density of the first-order deformation by adding only trivial terms.…”

“…This further leads to the conclusion that there is no non-trivial descent for H (γ|d) in strictly positive antighost number, or, to put it otherwise, that the equation (37) can always be replaced with (40) for J > 0. The proof to the last result can be done like in [15,16,17].…”

A novel mass generation scheme for an Abelian vector field

“…In consequence, a int reduces to the sum between its first two components only, a int = a int 0 + a int 1 . Inserting this decomposition of a int together with splitting (15) of s into the last equation from (35), we arrive at…”

“…Since the antifield number of both hand sides of this equation is strictly positive (equal to 1), it can be safely replaced by its homogeneous version without loss of nontrivial terms, namely, one can always take j µ int,1 = 0. The proof of this result is done in a standard manner (for instance, see [8,22,28,[34][35][36][37]). Equation (38) shows that a int 1 can be taken as a γ-closed object of pure ghost number one.…”

Yes-Go Cross-Couplings in Collections of Tensor Fields With Mixed Symmetries of the Type (3, 1) and (2, 2)

“…Special attention will be paid to the existence of cross-couplings among different spin-two fields (with the mixed symmetry of the Riemann tensor) intermediated by the presence of tensor fields with the mixed symmetry (3,1). Our analysis relies on the deformation of the solution to the master equation by means of cohomological techniques with the help of the local BRST cohomology, whose component in a single (3,1) sector has been reported in detail in [39] and in a single (2,2) sector has been investigated in [40,41]. The self-interactions in a collection of tensor fields with the mixed symmetry (3, 1) and respectively (2,2) has been approached in [42].…”