A note on local BRST cohomology of Yang-Mills type theories with free abelian factors

We extend previous work on antifield dependent local BRST cohomology for matter coupled gauge theories of Yang-Mills type to the case of gauge groups that involve free abelian factors. More precisely, we first investigate in a model independent way how the dynamics enters the computation of the cohomology for a general class of Lagrangians in general spacetime dimensions. We then discuss explicit solutions in the case of specific models. Our analysis has implications for the structure of characteristic cohomology and for consistent deformations of the classical models, as well as for divergences/counterterms and for gauge anomalies that may appear during perturbative quantization.Comment: 31 page

Uniqueness of N=2\mathcal{N}=2 and 33 pure supergravities in 4D

After proving the impossibility of consistent non-minimal coupling of a real Rarita-Schwinger gauge field to electromagnetism, we re-derive the necessity of introducing the graviton in order to couple a complex Rarita-Schwinger gauge field to electromagnetism, with or without a cosmological term, thereby obtaining ${\cal N}=2$ pure supergravity as the only possibility. These results are obtained with the BRST-BV deformation method around the flat and (A)dS backgrounds in 4 dimensions. The same method applied to $n_{v}$ vectors, ${\cal N}$ real spin-3/2 gauge fields and at most one real spinor field also requires gravity and yields ${\cal N}=3$ pure supergravity as well as ${\cal N}=1$ pure supergravity coupled to a vector supermultiplet, with or without cosmological terms. Independently from the matter content, we finally derive strong necessary quadratic constraints on the possible gaugings for an arbitrary number of spin-1 and spin-3/2 gauge fields, that are relevant for larger supergravities.Comment: LaTeX, 31 + 1 pages, no figure. v2: Extended discussion at the end of Section 3, corrected typos and references adde

Three-dimensional fractional-spin gravity

Using Wigner-deformed Heisenberg oscillators, we construct 3D Chern--Simons models consisting of fractional-spin fields coupled to higher-spin gravity and internal non-abelian gauge fields. The gauge algebras consist of Lorentz-tensorial Blencowe-Vasiliev higher-spin algebras and compact internal algebras intertwined by infinite-dimensional generators in lowest-weight representations of the Lorentz algebra with fractional spin. In integer or half-integer non-unitary cases, there exist truncations to gl(N,N +/- 1) or gl(N|N +/- 1) models. In all non-unitary cases, the internal gauge fields can be set to zero. At the semi-classical level, the fractional-spin fields are either Grassmann even or odd. The action requires the enveloping-algebra representation of the deformed oscillators, while their Fock-space representation suffices on-shell.Comment: 38 pages, 2 tables. References [7,13,61] added with comments in the second version. To appear in JHE

Gravitational and gauge couplings in Chern-Simons fractional spin gravity

We provide a necessary and sufficient condition for the consistency of the supertrace, through the existence of a certain ground state projector. We build this projector and check its properties to the first two orders in the number operator and to all orders in the deformation parameter. We then find the relation between the gravitational and internal gauge couplings in the resulting unified three-dimensional Chern--Simons theory for Blencowe--Vasiliev higher spin gravity coupled to fractional spin fields and internal gauge potentials. We also examine the model for integer or half-integer fractional spins, where infinite dimensional ideals arise and decouple, leaving finite dimensional gauge algebras $gl(2l+1)$ or $gl(l|l+1)$ and various real forms thereof.Comment: Published in JHEP. 32 pages, 3 figure