Local BRST cohomology in the antifield formalism: II. Application to Yang-Mills theory

Abstract

Yang-Mills models with compact gauge group coupled to matter fields are considered. The general tools developed in a companion paper are applied to compute the local cohomology of the BRST differential s modulo the exterior spacetime derivative d for all values of the ghost number, in the space of polynomials in the fields, the ghosts, the antifields (=sources for the BRST variations) and their derivatives. New solutions to the consistency conditions sa + db = 0 depending non trivially on the antifields are exhibited. For a semisimple gauge group, however, these new solutions arise only at ghost number two or higher. Thus at ghost number zero or one, the inclusion of the antifields does not bring in new solutions to the consistency condition sa + db = 0 besides the already known ones. The analysis does not use power counting and is purely cohomological. It can be easily extended to more general actions containing higher derivatives of the curvature, or Chern-Simons terms.

Higher-spin fermionic gauge fields and their electromagnetic coupling

“…The result is however more general and holds in fact also for higher order deformations, as it follows from the results of [34][35][36][37][38][39]. The significance of the various terms is worth recalling.…”

“…Now, if one makes an antighost-number expansion of the local form a, it stops at agh = 2 [9,[34][35][36][37][38],…”

“…Note that a 2 has been chosen to be Γ-closed, instead of Γ-closed modulo d, as is always possible [34][35][36][37]. We now analyze the conditions under which a 2 and a 1 are non-trivial.…”

“…We see that the cohomology of Γ modulo d plays an important role. The cubic vertex will deform the gauge algebra if and only if a 2 is a non-trivial element of the cohomology of Γ modulo d. Otherwise, can always choose a 2 = 0, and a 1 = Γ-closed [34][35][36][37]. Note that since a 2 is a cocycle of the cohomology of Γ modulo d, which can be chosen to be Γ-closed [34][35][36][37], one can investigate the general form of a 2 by studying the elements in the cohomology of Γ that are not d-exact.…”

Conformal (super)gravities with several gravitons

“…We first recall the results of [1,2], obtained by using the cohomological tools developed in [22,23,24,25,26] for dealing with the local cohomologies H(s|d) (s being the BRST differential and d the spacetime exterior derivative) relevant to the gauge-consistent deformations of a gauge-invariant theory (by gauge-consistent we mean that a M-graviton theory will have M times the number of gauge symmetries of the corresponding one-graviton theory). The various fields h a µν , a = 1, .…”