Covariant Cubic Interacting Vertices for Massless and Massive Integer Higher Spin Fields

We develop the BRST approach to construct the general off-shell local Lorentz covariant cubic interaction vertices for irreducible 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 follow our result in [arXiv:2105.12030[hep-th]] for massless fields and use 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-closeness 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 $\lambda$ with massless scalar and massive vector fields; two massive fields of spins $s, 0$ and massless scalar are also considered.Comment: 46 pages; presentation improved, Introduction, Conclusion, Appendix D modified, explicit form of traceless (constrained) vertex, 11 references adde

Comments on the Background Field Method in Harmonic Superspace: Non-holomorphic Corrections in N=4 SYM

We analyse the one-loop effective action of N=4 SYM theory in the framework of the background field formalism in N=2 harmonic superspace. For the case of on-shell background N=2 vector multiplet we prove that the effective action is free of harmonic singularities. When the lowest N=1 superspace component of the N=2 vector multiplet is switched off, the effective action of N=4 SYM theory is shown to coincide with that obtained by Grisaru et al on the base of the N=1 background field method. We compute the leading non-holomorphic corrections to the N=4 SU(2) SYM effective action.Comment: 15 pages, latex, no figures, some comments adde

On the D = 4, N = 2 Non-Renormalization Theorem

Using the harmonic superspace background field formulation for general D=4, N=2 super Yang-Mills theories, with matter hypermultiplets in arbitrary representations of the gauge group, we present the first rigorous proof of the N=2 non-renormalization theorem; specifically, the absence of ultraviolet divergences beyond the one-loop level. Another simple consequence of the background field formulation is the absence of the leading non-holomorphic correction to the low-energy effective action at two loops.Comment: 16 pages, LATEX, uses FEYMAN macros, minor change

Construction of one-loop N=4{\cal N}=4 SYM effective action on the mixed branch in the harmonic superspace approach

We develop a systematic approach to construct the one-loop ${\cal N}=4$ SYM effective action depending on both ${\cal N}=2$ vector multiplet and hypermultiplet background fields. Beginning with the formulation of ${\cal N}=4$ SYM theory in terms of ${\cal N}=2$ harmonic superfields, we construct the one-loop effective action using the covariant ${\cal N}=2$ harmonic supergraphs and calculate it in ${\cal N}=2$ harmonic superfield form for constant Abelian strength $F_{mn}$ and corresponding constant hypermultiplet fields. The hypermultiplet-dependent effective action is derived and given by integral over the analytic subspace of harmonic superspace. We show that each term in the Schwinger-De Witt expansion of the low-energy effective action is written as integral over full ${\cal N}=2$ superspace.Comment: 35 pages, JHEP styl

Lagrangian Formulation of Free Arbitrary N-Extended Massless Higher Spin Supermultiplets in 4D AdS Space

We derived the component Lagrangian for the free N-extended on-shell massless higher spin supermultiplets in four-dimensional anti-de Sitter space. The construction was based on the frame-like description of massless integer and half-integer higher spin fields. The massless supermultiplets were formulated for N≤4k, where k is a maximal integer or half-integer spin in the multiplet. The supertransformations that leave the Lagrangian invariant were found in explicit form and it was shown that their algebra is closed on-shell

Leading low-energy effective action in the 6D hypermultiplet theory on a vector/tensor background

We consider a six-dimensional(1, 0)hypermultiplet model coupled to an external field of vector/tensor system and study the structure of the low-energy effective action of this model. Manifestly a (1, 0)supersymmetric procedure of computing the effective action is developed in the framework of the superfield proper-time technique. The leading low-energy contribution to the effective action is calculated

Off-shell cubic hypermultiplet couplings to N = 2 higher spin gauge superfields

We construct manifestly 4D, N = 2 supersymmetric and gauge invariant off-shell cubic couplings of matter hypermultiplets to the higher integer spin gauge Al = 2 multiplets introduced in arXiv:2109 .07639. The hypermultiplet is described by an ana- lytic harmonic 4D, Al = 2 superfield q+ with the physical component spins s = (1/2, 0) and an infinite number of auxiliary fields. The cubic coupling constructed has the schematic structure q(+)(H) over cap (++ )((s))q(+), where (H) over cap (++ )((s)) is a differential analytic operator of the highest degree (s - 1) accommodating the massless gauge N = 2 multiplet with the highest spin s. For odd s the gauge group generators and couplings are proportional to U(1)p G generator of the internal SU(2)p G symmetry of the hypermultiplet and so do not exist if SU(2)p G is unbroken. If this U(1)p G is identified with the central charge of 4D,N = 2 supersymmetry, a mass for the hypermultiplet is generated and the odd s couplings vanish in the proper massless limit. For even s the higher-spin gauge transformations and cubic superfield couplings can be defined for both massive and massless (central-charge neutral) hypermultiplets without including U(1)p G generator. All these features directly extend to the case of n hypermultiplets with the maximal internal symmetry USp(2n) x SU(2)

Supersymmetric Higher Spin Models in Three Dimensional Spaces

We review the component Lagrangian construction of the supersymmetric higher spin models in three-dimensional (3D) Minkowski and anti de Sitter ( A d S ) spaces. The approach is based on the frame-like gauge-invariant formulation, where massive higher spin fields are realized through a system of massless ones. We develop a supersymmetric generalization of this formulation to the Lagrangian construction of the on-shell N = 1 , 3D higher spin supermultiplets. In 3D Minkowski space, we show that the massive supermultiplets can be constructed from one extended massless supermultiplet by adding the mass terms to the Lagrangian and the corresponding corrections to the supertransformations of the fermionic fields. In 3D A d S space, we construct massive supermultiplets using a formulation of the massive fields in terms of the set of gauge-invariant objects (curvatures) in the process of their consistent supersymmetric deformation