arXiv subjects

I. L. Buchbinder

Publications and source records attributed to I. L. Buchbinder.

At least 73 records · Page 4Linked to original sources

arXiv2019

Twistorial and space-time descriptions of massless infinite spin (super)particles and fields

We develop a new twistorial field formulation of a massless infinite spin particle. Unlike our previous approach arXiv:1805.09706, the quantization of such a world-line infinite spin particle model is carried without any gauge fixing. As a result, we construct a twistorial infinite spin field and derive its helicity decomposition. Using the field twistor transform, we construct the space-time infinite (continuous) spin field, which depends on the coordinate four-vector and additional commuting Weyl spinor. The equations of motion for infinite spin fields in the cases of integer and half-integer helicities are derived. We show that the infinite integer-spin field and infinite half-integer-spin field form the $\mathcal{N}{=}\,1$ infinite spin supermultiplet. The corresponding supersymmetry transformations are formulated and their on-shell algebra is derived. As a result, we find the field realization of the infinite spin $\mathcal{N}{=}\,1$ supersymmetry.

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arXiv2019

Integer superspin supercurrents of matter supermultiplets

In recent papers we demonstrated that consistent and non-trivial \emph{linear} transformations of matter supermultiplets generate half-integer superspin supercurrents and the cubic interactions between matter and half-integer superspin supermultiplets. In this work we show that consistent and non-trivial \emph{antilinear} transformations of matter superfields lead to the construction of integer superspin supercurrents and the cubic interactions between mater and integer superspin supermultiplets. Applying Noether's method to these transformations, we find new integer superspin supercurrents for the case of a free massless chiral superfield. Furthermore, we use them to find new integer superspin supercurrent multiplets for a massive chiral superfield and a chiral superfield with a linear superpotential. Also various selection rules for such interactions are found.

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arXiv2019

Lagrangian formulation for the infinite spin N=1 supermultiplets in d=4

We provide an explicit Lagrangian construction for the massless infinite spin N=1 supermultiplet in four dimensional Minkowski space. Such a supermultiplet contains a pair of massless bosonic and a pair of massless fermionic infinite spin fields with properly adjusted dimensionful parameters. We begin with the gauge invariant Lagrangians for such massless infinite spin bosonic and fermionic fields and derive the supertransformations which leave the sum of their Lagrangians invariant. It is shown that the algebra of these supertransformations is closed on-shell.

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arXiv2019

Superfield continuous spin equations of motion

We propose a description of %manifestly supersymmetric continuous spin representations in $4D,\mathcal{N}=1$ Minkowski superspace at the level of equations of motions. The usual continuous spin wave function is promoted to a chiral or a complex linear superfield which includes both the single-valued (span integer helicities) and the double-valued (span half-integer helicities) representations thus making their connection under supersymmetry manifest. The set of proposed superspace constraints for both superfield generate the expected Wigner's conditions for both representations.

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arXiv2019

Lagrangian formulation of the massive higher spin N=1 supermultiplets in $AdS_4$ space

We give an explicit component Lagrangian construction of massive higher spin on-shell $N=1$ supermultiplets in four-dimensional Anti-de Sitter space $AdS_4$. We use a frame-like gauge invariant description of massive higher spin bosonic and fermionic fields. For the two types of the supermultiplets (with integer and half-integer superspins) each one containing two massive bosonic and two massive fermionic fields we derive the supertransformations leaving the sum of four their free Lagrangians invariant such that the algebra of these supertransformations is closed on-shell.

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arXiv2019

Low-energy effective action in 5D, N=2 supersymmetric gauge theory

We construct ${\cal N}=2$ supersymmetric low-energy effective action of $5D, {\cal N}=2$ supersymmetric Yang-Mills theory in $5D, {\cal N}=1$ harmonic superspace. It is obtained as a hypermultiplet completion of the leading $W \ln W$-term in the ${\cal N}=1$ SYM low-energy effective action by invoking the second implicit on-shell ${\cal N}=1$ supersymmetry. After passing to components, the ${\cal N}=2$ effective action constructed displays, along with other terms, the $SO(5)$-invariant $F^4/X^3$ term. Though we specialize to the case of $SU(2)$ gauge group spontaneously broken to $U(1)$, our consideration is applicable to any gauge symmetry broken to some abelian subgroup.

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arXiv2019

Harmonic superspace approach to the effective action in six-dimensional supersymmetric gauge theories

We review the recent progress in studying the quantum structure of $6D$, ${\cal N}=(1,0)$ and ${\cal N}=(1,1)$ supersymmetric gauge theories formulated through unconstrained harmonic superfields. The harmonic superfield approach allows one to carry out the quantization and calculations of the quantum corrections in a manifestly ${\cal N}=(1,0)$ supersymmetric way. The quantum effective action is constructed with the help of the background field method that secures the manifest gauge invariance of the results. Although the theories under consideration are not renormalizable, the extended supersymmetry essentially improves the ultraviolet behavior of the lowest-order loops. The ${\cal N}=(1,1)$ supersymmetric Yang--Mills theory turns out to be finite in the one-loop approximation in the minimal gauge. Also some two-loop divergences are shown to be absent in this theory. Analysis of the divergences is performed both in terms of harmonic supergraphs and by the manifestly gauge covariant superfield proper-time method. The finite one-loop leading low-energy effective action is calculated and analyzed. Also in the abelian case we discuss the gauge dependence of the quantum corrections and present its precise form for the one-loop divergent part of the effective action.

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arXiv2018

Gauge dependence of the one-loop divergences in $6D$, ${\cal N} = (1,0)$ abelian theory

We study the gauge dependence of the one-loop effective action for the abelian $6D$, ${\cal N}=(1,0)$ supersymmetric gauge theory formulated in harmonic superspace. We introduce the superfield $ξ$-gauge, construct the corresponding gauge superfield propagator, and calculate the one-loop two-and three-point Green functions with two external hypermultiplet legs. We demonstrate that in the general $ξ$-gauge the two-point Green function of the hypermultiplet is divergent, as opposed to the Feynman gauge $ξ=1$. The three-point Green function with two external hypermultiplet legs and one leg of the gauge superfield is also divergent. We verified that the Green functions considered satisfy the Ward identity formulated in ${\cal N}=(1,0)$ harmonic superspace and that their gauge dependence vanishes on shell. Using the result for the two- and three-point Green functions and arguments based on the gauge invariance, we present the complete divergent part of the one-loop effective action in the general $ξ$-gauge.

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arXiv2018

Conserved higher spin supercurrents for arbitrary spin massless supermultiplets and higher spin superfield cubic interactions

We give an explicit superspace construction of higher spin conserved supercurrents built out of $4D,\mathcal{N}=1$ massless supermultiplets of arbitrary spin. These supercurrents are gauge invariant and generate a large class of cubic interactions between a massless supermultiplet with superspin $Y_1=s_1+1/2$ and two massless supermultiplets of arbitrary superspin $Y_2$. These interactions are possible only for $s_1\geq 2Y_2$. At the equality, the supercurrent acquires its simplest form and defines the supersymmetric, higher spin extension of the linearized Bel-Robinson tensor.

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arXiv2018

Model of massless relativistic particle with continuous spin and its twistorial description

We propose a new world-line Lagrangian model of the D=4 massless relativistic particle with continuous spin and develop its twistorial formulation. The description uses two Penrose twistors subjected to four first class constraints. After the first quantization of the world-line twistorial model, the wave function is defined by an unconstrained function on the two-dimensional complex affine plane. We find the twistor transform that determines the space-time field of the continuous spin particle through the corresponding twistor one, which plays the role of a prepotential. It is shown that this space-time field is an exact solution of the space-time constraints defining the irreducible massless representation of the Poincare group with continuous spin.

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arXiv2018

Leading low-energy effective action in $6D$, ${\cal N}=(1,1)$ SYM theory

We elaborate on the low-energy effective action of $6D,\,{\cal N}=(1,1)$ supersymmetric Yang-Mills (SYM) theory in the ${\cal N}=(1,0)$ harmonic superspace formulation. The theory is described in terms of analytic ${\cal N}=(1,0)$ gauge superfield $V^{++}$ and analytic $ω$-hypermultiplet, both in the adjoint representation of gauge group. The effective action is defined in the framework of the background superfield method ensuring the manifest gauge invariance along with manifest ${\cal N}=(1,0)$ supersymmetry. We calculate leading contribution to the one-loop effective action using the on-shell background superfields corresponding to the option when gauge group $SU(N)$ is broken to $SU(N-1)\times U(1)\subset SU(N)$. In the bosonic sector the effective action involves the structure $\sim \frac{F^4}{X^2}$, where $F^4$ is a monomial of the fourth degree in an abelian field strength $F_{MN}$ and $X$ stands for the scalar fields from the $ω$-hypermultiplet. It is manifestly demonstrated that the expectation values of the hypermultiplet scalar fields play the role of a natural infrared cutoff.

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arXiv2018

BRST approach to Lagrangian construction for bosonic continuous spin field

We formulate the conditions defining the irreducible continuous spin representation of the four-dimensional Poincaré group based on spin-tensor fields with dotted and undotted indices. Such a formulation simplifies analysis of the Bargmann-Wigner equations and reduces the number of equations from four to three. Using this formulation we develop the BRST approach and derive the covariant Lagrangian for the continuous spin fields.

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arXiv2018

Interaction of supersymmetric nonlinear sigma models with external higher spin superfields via higher spin supercurrents

We consider a four dimensional generalized Wess-Zumino model formulated in terms of an arbitrary Kähler potential $\mathcal{K}(Φ,\barΦ)$ and an arbitrary chiral superpotential $\mathcal{W}(Φ)$. A general analysis is given to describe the possible interactions of this theory with external higher spin gauge superfields of the ($s+1,s+1/2$) supermultiplet via higher spin supercurrents. It is shown that such interactions do not exist beyond supergravity $(s\geq2)$ for any $\mathcal{K}$ and $\mathcal{W}$. However, we find three exceptions, the theory of a free massless chiral, the theory of a free massive chiral and the theory of a free chiral with linear superpotential. For the first two, the higher spin supercurrents are known and for the third one we provide the explicit expressions. We also discuss the lower spin supercurrents. As expected, a coupling to (non-minimal) supergravity ($s=1$) can always be found and we give the generating supercurrent and supertrace for arbitrary $\mathcal{K}$ and $\mathcal{W}$. On the other hand, coupling to the vector supermultiplet ($s=0$) is possible only if $\mathcal{K}=\mathcal{K}(\barΦΦ)$ and $\mathcal{W}=0$.

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arXiv2018

BRST-BV quantization of gauge theories with global symmetries

We consider the general gauge theory with a closed irreducible gauge algebra possessing the non-anomalous global (super)symmetry in the case when the gauge fixing procedure violates the global invariance of classical action. The theory is quantized in the framework of BRST-BV approach in the form of functional integral over all fields of the configuration space. It is shown that the global symmetry transformations are deformed in the process of quantization and the full quantum action is invariant under such deformed global transformations in the configuration space. The deformed global transformations are calculated in an explicit form in the one-loop approximation.

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arXiv2017

Higher Spin Superfield interactions with the Chiral Supermultiplet: Conserved Supercurrents and Cubic Vertices

We investigate cubic interactions between a chiral superfield and higher spin superfield corresponding to irreducible representations of the $4D,\, \mathcal{N}=1$ super-Poincaré algebra. We do this by demanding an invariance under the most general transformation, linear in the chiral superfield. Following Noether's method we construct an infinite tower of higher spin supercurrent multiplets which are quadratic in the chiral superfield and include higher derivatives. The results are that a single, massless, chiral superfield can couple only to the half-integer spin supermultiplets $(s+1,s+1/2)$ and for every value of spin there is an appropriate improvement term that reduces the supercurrent multiplet to a minimal multiplet which matches that of superconformal higher spins. On the other hand a single, massive, chiral superfield can couple only to higher spin supermultiplets of type $(2l+2\hspace{0.3ex},\hspace{0.1ex}2l+3/2)$ and there is no minimal multiplet. Furthermore, for the massless case we discuss the component level higher spin currents and provide explicit expressions for the integer and half-integer spin conserved currents together with a R-symmetry current.

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arXiv2017

On the two-loop divergences of the 2-point hypermultiplet supergraphs for $6D$, ${\cal N} = (1,1)$ SYM theory

We consider $6D$, ${\cal N}=(1,1)$ supersymmetric Yang-Mills theory formulated in ${\cal N}=(1,0)$ harmonic superspace and analyze the structure of the two-loop divergences in the hypermultiplet sector. Using the ${\cal N}=(1,0)$ superfield background field method we study the two-point supergraphs with the hypermultiplet legs and prove that their total contribution to the divergent part of effective action vanishes off shell.

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arXiv2017

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 (AdS) 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 AdS 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.

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arXiv2017

Lagrangian description of massive higher spin supermultiplets in AdS_3 space

We construct the Lagrangian formulation of massive higher spin on-shell (1,0) supermultiplets in three dimensional anti-de Sitter space. The construction is based on description of the massive three dimensional fields in terms of frame-like gauge invariant formalism and technique of gauge invariant curvatures. For the two possible massive supermultiplets (s,s+1/2) and (s,s-1/2) we derive explicit form of the supertransformations leaving the sum of bosonic and fermionic Lagrangians invariant.

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