We develop the BRST approach to construct the general off-shell local Lorentz covariant cubic interaction vertices for irreducible massless and massive higher spin fields on $d$-dimensional Minkowski space. We consider two different cases for interacting higher spin fields: with one massive and two massless; with two massive both with coinciding and with different masses and one massless fields of spins $s_1, s_2, s_3$. Unlike the previous results on cubic vertices we extend our earlier result in [arXiv:2105.12030[hep-th]] for massless fields and employ the complete BRST operator, including the trace constraints that is used to formulate an irreducible representation with definite integer spin. We generalize the cubic vertices proposed for reducible higher spin fields in [arXiv:1205.3131 [hep-th]] in the form of multiplicative and non-multiplicative BRST-closed constituents and calculate the new contributions to the vertex, which contain additional terms with a smaller number space-time derivatives of the fields. We prove that without traceless conditions for the cubic vertices in [arXiv:1205.3131 [hep-th]] it is impossible to provide the noncontradictory Lagrangian dynamics and find explicit traceless solution for these vertices. As the examples, we explicitly construct the interacting Lagrangian for the massive of spin $s$ field and massless scalars both with and without auxiliary fields. The interacting models with different combinations of triples higher spin fields: massive of spin $s$ with massless scalar and vector fields and with two vector fields; massless of helicity $λ$ with massless scalar and massive vector fields; two massive fields of spins $s, 0$ and massless scalar are also considered.
Performing the Hamiltonian analysis we explicitly established the canonical equivalence of the deformed oscillator, constructed in arXiv:1607.03756[hep-th], with the ordinary one. As an immediate consequence, we proved that the SU(1,2) symmetry is the dynamical symmetry of the ordinary two-dimensional oscillator. The characteristic feature of this SU(1,2) symmetry is a non-polynomial structure of its generators written it terms of the oscillator variables.
A bstractFor nonlinear models of an Abelian vector supermultiplet coupled to $ \mathcal{N} = 2 $ supergravity in four dimensions, we formulate the self-duality equation which expresses invariance under U(1) duality rotations. In the flat space limit, this equation reduces to the $ \mathcal{N} = 2 $ self-duality equation proposed in hep-th/0001068. We also give an example of a self-dual locally supersymmetric model containing a higher-derivative extension of the Born-Infeld action at the component level.
We prove that the rank 3 analogue of the tensor model defined in [arXiv:1111.4997 [hep-th]] is renormalizable at all orders of perturbation. The proof is given in the momentum space. The one-loop $γ$- and $β$-functions of the model are also determined. We find that the model with a unique coupling constant for all interactions and a unique wave function renormalization is asymptotically free in the UV.
We consider three-dimensional maximally superconformal Bagger–Lambert–Gustavsson (BLG) theory and its topologically gauged version (constructed recently in Gran and Nilsson (2009 J. High Energy Phys. JHEP03(2009)074 (arXiv:0809.4478 [hep-th]))) in the light-cone gauge. After eliminating the entire Chern–Simons gauge field, the ungauged BLG light-cone theory looks more conventional and, apart from the order of the interaction terms, resembles super-Yang–Mills theory in four dimensions. The light-cone superspace version of the BLG theory is given at the quadratic order together with a suggested form for the quartic terms. Some problems with constructing the sixth-order interaction terms are also discussed. In the topologically gauged case, we analyze the field equations related to the three Chern–Simons-type terms of conformal supergravity and discuss some of the special features of this theory and its couplings to BLG.