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D. V. Uvarov

Publications and source records attributed to D. V. Uvarov.

At least 19 recordsLinked to original sources
arXiv2023

Massless spinning particle and null-string on $AdS_d$: projective-space approach

Massless spinning particle and tensionless string models on $AdS_d$ background in the projective-space realization are proposed as constrained Hamiltonian systems. Various forms of particle and string Lagrangians are derived and classical mechanics is studied including the Lax-type representation of the equations of motion. After that transition to the quantum theory is discussed. Analysis of potential anomalies in the tensionless string model necessitates introduction of ghosts and BRST charge. It is shown that quantum BRST charge is nilpotent for any $d$ if coordinate-momentum ordering for the phase-space bosonic variables, Weyl ordering for the fermions and $cb$ ($γβ$) ordering for ghosts is chosen, while conformal reparametrizations and space-time dilatations turn out to be anomalous for the ordering in terms of positive and negative Fourier modes of the phase-space variables and ghosts.

hep-th↗
arXiv2020

Supertwistor formulation for massless superparticle in $AdS_5\times S^5$ superspace

Starting with the first-order formulation of the massless superparticle model on the $AdS_5\times S^5$ superbackground and presenting the momentum components tangent to $AdS_5$ and $S^5$ subspaces as bilinear combinations of the constrained $SU(2)$-Majorana spinors allows to bring the superparticle's Lagrangian to the form quadratic in supertwistors. The $SU(2,2|4)$ supertwistors are assembled into a pair of $SU(2)$ doublets, one of which has even $SU(2,2)$ and odd $SU(4)$ components, while the other has odd $SU(2,2)$ and even $SU(4)$ components. They are subject to the first-class constraints that generate the $psu(2|2)\oplus u(1)$ gauge algebra. This justifies previously proposed group-theoretic definition of the $AdS_5\times S^5$ supertwistors and allows to derive the incidence relations with the $(10|32)$ supercoordinates of the $AdS_5\times S^5$ superspace. Whenever superparticle moves within the $AdS_5$ subspace of the $AdS_5\times S^5$ space-time, twistor formulation of its Lagrangian involves just one $SU(2)$ doublet of $SU(2,2|4)$ supertwistors with even $SU(2,2)$ and odd $SU(4)$ components. If in addition particle's 5-momentum is null, four first-class constraints which are the $su(2)\oplus u(1)$ generators single out upon quantization the states of $D=5$ $N=8$ gauged supergravity multiplet in the superambitwistor formulation.

hep-th↗
arXiv2020

Multitwistor mechanics of massless superparticle on $AdS_5\times S^5$ superbackground

Supertwistors relevant to $AdS_5\times S^5$ superbackground of IIB supergravity are studied in the framework of the $D=10$ massless superparticle model in the first-order formulation. Product structure of the background suggests using $D=1+4$ Lorentz-harmonic variables to express momentum components tangent to $AdS_5$ and $D=5$ harmonics to express momentum components tangent to $S^5$ that yields eight-supertwistor formulation of the superparticle's Lagrangian. We find incidence relations of the supertwistors with the $AdS_5\times S^5$ superspace coordinates and the set of the quadratic constraints they satisfy. It is shown how using the constraints for the (Lorentz-)harmonic variables it is possible to reduce eight-supertwistor formulation to the four-supertwistor one. Respective supertwistors agree with those introduced previously in other models. Advantage of the four-supertwistor formulation is the presence only of the first-class constraints that facilitates analysis of the superparticle model.

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arXiv2016

Ambitwistors, oscillators and massless fields on $AdS_5$

Positive energy unitary irreducible representations of $SU(2,2)$ can be constructed with the aid of bosonic oscillators in (anti)fundamental representation of $SU(2)_L\times SU(2)_R$ that are closely related to Penrose twistors. Starting with the correspondence between the doubleton representations, homogeneous functions on projective twistor space and on-shell $SL(2,\mathbb C)$ generalized Weyl curvature spinors and their low-spin counterparts, we study in the similar way the correspondence between the massless representations, homogeneous functions on ambitwistor space and, via the Penrose transform, with the gauge fields on Minkowski boundary of $AdS_5$. The possibilities of reconstructing massless fields on $AdS_5$ and some applications are also discussed.

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arXiv2016

Spinor description of $D=5$ massless low-spin gauge fields

Spinor description for the curvatures of $D=5$ Yang-Mills, Rarita-Schwinger and gravitational fields is elaborated. Restrictions imposed on the curvature spinors by the dynamical equations and Bianchi identities are analyzed. In the absence of sources symmetric curvature spinors with $2s$ indices obey first-order equations that in the linearized limit reduce to Dirac-type equations for massless free fields. These equations allow for a higher-spin generalization similarly to $4d$ case. Their solution in the form of the integral over Lorentz-harmonic variables parametrizing coset manifold $SO(1,4)/(SO(1,1)\times ISO(3))$ isomorphic to the three-sphere is considered. Superparticle model that contains such Lorentz harmonics as dynamical variables, as well as harmonics parametrizing the two-sphere $SU(2)/U(1)$ is proposed. The states in its spectrum are given by the functions on $S^3$ that upon integrating over the Lorentz harmonics reproduce on-shell symmetric curvature spinors for various massless supermultiplets of $D=5$ space-time supersymmetry.

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arXiv2014

Conformal higher-spin symmetries in twistor string theory

It is shown that similarly to massless superparticle, classical global symmetry of the Berkovits twistor string action is infinite-dimensional. We identify its superalgebra, whose finite-dimensional subalgebra contains $psl(4|4,\mathbb R)$ superalgebra. In quantum theory this infinite-dimensional symmetry breaks down to $SL(4|4,\mathbb R)$ one.

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arXiv2012

Lagrangian mechanics of massless superparticle on AdS_4 x CP^3 superbackground

Massless superparticle model is considered on the OSp(4|6)/(SO(1,3) x U(3)) supercoset manifold and in the AdS_4 x CP^3 superspace. In the former case integrability of the equations of motion is rather obvious, while for the AdS_4 x CP^3 superparticle we prove integrability in the partial kappa-symmetry gauge for which 4 anticommuting coordinates related to the broken conformal supersymmetry are set to zero. This allows us to propose expression for the Lax pair that may encode complete equations of motion for the AdS_4 x CP^3 superparticle.

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arXiv2012

A note about fermionic equations of AdS_4 x CP^3 superstring

It is proved that when 8 fermions associated with the supersymmetries broken by the AdS_4 x CP^3 superbackground are gauged away by using the kappa-symmetry corresponding equations obtained by variation of the AdS_4 x CP^3 superstring action are contained in the set of fermionic equations of the OSp(4|6)/(SO(1,3) x U(3)) sigma-model.

hep-th↗
arXiv2012

Kaluza-Klein gauge and minimal integrable extension of OSp(4|6)/(SO(1,3) x U(3)) sigma-model

Basing upon experience from performing double-dimensional reduction of the D=11 supermembrane on AdS_4 x S^7 background to Type IIA superstring on AdS_4 x CP^3 we introduce Kaluza-Klein (partial) kappa-symmetry gauge as a vanishing condition of the contribution to the D=11 supervielbein components tangent to D=10 space-time proportional to the differential of the coordinate parametrizing compact 11-th space-time dimension, that is identified with the supermembrane world-volume compact dimension. For AdS_4 x S^7 supermembrane Kaluza-Klein gauge removes half Grassmann coordinates associated with 8 space-time supersymmetries, broken by the AdS_4 x CP^3 superbackground, by imposing D=3 (anti-)Majorana condition on them. The consideration relies on the realization of osp(4|8) isometry superalgebra of the AdS_4 x S^7 superbackground as D=3 N=8 superconformal algebra. Requiring further vanishing of the D=10 dilaton leaves in the sector of broken supersymmetries just two Grassmann coordinates organized into D=3 (anti-)Majorana spinor that defines minimal SL(2,R)-covariant extension of the OSp(4|6)/(SO(1,3)x U(3)) sigma-model. Among 4 possibilities of such a minimal extension we consider in detail one, that corresponds to picking out D=3 Majorana coordinate related to broken Poincare supersymmetry, and show that the AdS_4 x CP^3 superstring equations of motion in this partial kappa-symmetry gauge are integrable. Also the relation between the OSp(4|6)/(SO(1,3) x U(3)) sigma-model and the AdS_4 x CP^3 superstring is revisited.

hep-th↗
arXiv2012

AdS_4 x CP^3 superstring in the light-cone gauge

The Type IIA superstring action on the AdS_4 x CP^3 background, obtainable by the double dimensional reduction of the AdS_4 x S^7 supermembrane, is considered in the kappa-symmetry light-cone gauge, in which the light-like directions are chosen on the D=3 Minkowski boundary of AdS_4. Such choice of the gauge condition relies on representing the AdS_4 x S^7 background isometry superalgebra osp(4|8) (and correspondingly the osp(4|6) isometry superalgebra of the AdS_4 x CP^3 background) as D=3 extended superconformal algebra. The gauge-fixed action includes contributions up to the 4th power in the fermions.

hep-th↗
arXiv2012

Light-cone gauge Hamiltonian for AdS_4 x CP^3 superstring

It is developed the phase-space formulation for the Type IIA superstring on the AdS_4 x CP^3 background in the kappa-symmetry light-cone gauge for which the light-like directions are taken from the D=3 Minkowski boundary of AdS_4. After fixing bosonic light-cone gauge the superstring Hamiltonian is expressed as a function of the transverse physical variables and in the quadratic approximation corresponds to the light-cone gauge-fixed IIA superstring in flat space.

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arXiv2011

AdS_4 x CP^3 superstring and D=3 N=6 superconformal symmetry

Motivated by the isomorphism between osp(4|6) superalgebra and D=3 N=6 superconformal algebra we consider the superstring action on the AdS_4 x CP^3 background parametrized by D=3 N=6 super-Poincare and CP^3 coordinates supplemented by the coordinates corresponoding to dilatation and superconformal generators. It is also discussed the relation between the degeneracy of fermionic equations of motion and the action kappa-invariance in the framework of the supercoset approach.

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arXiv2011

D=3 N=6 superconformal symmetry of AdS_4 x CP^3 superstring

Invariance of the AdS_4 x CP^3 superstring under D=3 N=6 superconformal symmetry is discussed in the sector described by the OSp(4|6)/(SO(1,3) x U(3)) supercoset sigma-model action presented in the conformal basis for the osp(4|6)/(so(1,3) x u(3)) Cartan forms. Transformation rules under D=3 N=6 superconformal symmetry for the (10|24)-dimensional 'reduced' AdS_4 x CP^3 superspace coordinates are obtained and used to derive corresponding world-sheet currents.

hep-th↗
arXiv2009

Canonical description of D=10 superstring formulated in supertwistor space

Canonical description of the D=10 superstring action involving supertwistor variables generalizing Penrose-Ferber supertwistors is developed. Primary and secondary constraints are identified and arranged into the first- and second-class sets. Dirac brackets are introduced and the deformation of the Poisson bracket algebra of the first-class constraints is studied. The role of the deformation parameter is played by alpha'.

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