Searcharxiv⌕ Search

arXiv subjects

Sergei M. Kuzenko

Publications and source records attributed to Sergei M. Kuzenko.

At least 109 records · Page 6Linked to original sources
arXiv2016

Maximally supersymmetric solutions of $R^2$ supergravity

There are five maximally supersymmetric backgrounds in four-dimensional off-shell N=1 supergravity, two of which are well known: Minkowski superspace M^{4|4} and anti-de Sitter superspace AdS^{4|4}. The three remaining supermanifolds support spacetimes of different topology, which are: R x S^3, AdS_3 x R, and a supersymmetric plane wave isometric to the Nappi-Witten group. As is well known, the Minkowski and anti-de Sitter superspaces are solutions of the Poincaré and anti-de Sitter supergravity theories, respectively. Here we demonstrate that the other three superspaces are solutions of no-scale $R^2$ supergravity. We also present a new (probably the simplest) derivation of the maximally supersymmetric backgrounds of off-shell N=1 supergravity.

hep-th↗
arXiv2016

Implications of N=5, 6 superconformal symmetry in three spacetime dimensions

For general N=5 and N=6 superconformal field theories in three dimensions, we compute the three-point correlation functions of the supercurrent multiplets. In each case, N=5 and N=6, the functional form of this correlator is uniquely fixed modulo an overall coefficient which is related, by superconformal Ward identities, to the parameter in the two-point function of the supercurrent. The structure of the correlation functions obtained is consistent with the property that every N=5 superconformal field theory, considered as a special N=4 theory, is invariant under the mirror map.

hep-th↗
arXiv2016

Nilpotent chiral superfield in N=2 supergravity and partial rigid supersymmetry breaking

In the framework of N=2 conformal supergravity in four dimensions, we introduce a nilpotent chiral superfield suitable for the description of partial supersymmetry breaking in maximally supersymmetric spacetimes. As an application, we construct Maxwell-Goldstone multiplet actions for partial N=2 --> N=1 supersymmetry breaking on R x S^3, AdS_3 x S^1 (or its covering AdS_3 x R), and a pp-wave spacetime. In each of these cases, the action coincides with a unique curved-superspace extension of the N=1 supersymmetric Born-Infeld action, which is singled out by the requirement of U(1) duality invariance.

hep-th↗
arXiv2016

The anomalous current multiplet in 6D minimal supersymmetry

For supersymmetric gauge theories with eight supercharges in four, five and six dimensions, a conserved current belongs to the linear multiplet. In the case of six-dimensional $\cal N=(1,0)$ Poincaré supersymmetry, we present a consistent deformation of the linear multiplet which describes chiral anomalies. This is achieved by developing a superform formulation for the deformed linear multiplet. In the abelian case, we compute a nonlocal effective action generating the gauge anomaly.

hep-th↗
arXiv2015

Higher derivative couplings and massive supergravity in three dimensions

We develop geometric superspace settings to construct arbitrary higher derivative couplings (including R^n terms) in three-dimensional supergravity theories with N=1,2,3 by realising them as conformal supergravity coupled to certain compensators. For all known off-shell supergravity formulations, we construct supersymmetric invariants with up to and including four derivatives. As a warming-up exercise, we first give a new and completely geometric derivation of such invariants in N=1 supergravity. Upon reduction to components, they agree with those given in arXiv:0907.4658 and arXiv:1005.3952. We then carry out a similar construction in the case of N=2 supergravity for which there exist two minimal formulations that differ by the choice of compensating multiplet: (i) a chiral scalar multipet; (ii) a vector multiplet. For these formulations all four derivative invariants are constructed in completely general and gauge independent form. For a general supergravity model (in the N=1 and minimal N=2 cases) with curvature-squared and lower order terms, we derive the superfield equations of motion, linearise them about maximally supersymmetric backgrounds and obtain restrictions on the parameters that lead to models for massive supergravity. We use the non-minimal formulation for N = 2 supergravity (which corresponds to a complex linear compensator) to construct a novel consistent theory of massive supergravity. In the case of N = 3 supergravity, we employ the off-shell formulation with a vector multiplet as compensator to construct for the first time various higher derivative invariants. These invariants may be used to derive models for N = 3 massive supergravity. As a bi-product of our analysis, we also present superfield equations for massive higher spin multiplets in (1,0), (1,1) and (2,0) anti-de Sitter superspaces.

hep-th↗
arXiv2015

Symmetries of curved superspace in five dimensions

We develop a formalism to construct supersymmetric backgrounds within the superspace formulation for five-dimensional (5D) conformal supergravity given in arXiv:0802.3953. Our approach is applicable to any off-shell formulation for 5D minimal Poincare and anti-de Sitter supergravity theories realized as the Weyl multiplet coupled with two compensators. For those superspace backgrounds which obey the equations of motion for (gauged) supergravity, we naturally reproduce the supersymmetric solutions constructed a decade ago by Gauntlett et al. For certain supersymmetric backgrounds with eight supercharges, we construct a large family of off-shell supersymmetric sigma models such that the superfield Lagrangian is given in terms of the Kahler potential of a real analytic Kahler manifold.

hep-th↗
arXiv2015

Complex linear Goldstino superfield and de Sitter supergravity

The complex linear Goldstino superfield was proposed in arXiv:1102.3042 for the cases of global and local four-dimensional N=1 supersymmetry. Here we make use of this superfield to construct a supergravity action which is invariant under spontaneously broken local N=1 supersymmetry and has a positive cosmological constant for certain values of the parameters.

hep-th↗
arXiv2015

On superconformal Chern-Simons-matter theories in N=4 superspace

In three dimensions, every known N=4 supermultiplet has an off-shell completion. However, there is no off-shell N=4 formulation for the known extended superconformal Chern-Simons (CS) theories with eight and more supercharges. To achieve a better understanding of this issue, we provide N=4 superfield realisations for the equations of motion which correspond to various N=4 and N=6 superconformal CS theories, including the Gaiotto-Witten theory and the ABJM theory. These superfield realisations demonstrate that the superconformal CS theories with N>3 (except for the Gaiotto-Witten theory) require a reducible long N=4 vector multiplet, from which the standard left and right N=4 vector multiplets are obtained by constraining the field strength to be either self-dual or anti self-dual. Such a long multiplet naturally originates upon reduction of any off-shell N>4 vector multiplet to N=4 superspace. For the long N=4 vector multiplet we develop a prepotential formulation. It makes use of two prepotentials being subject to the constraint which defines the so-called hybrid projective multiplets introduced in the framework of N=4 supergravity-matter systems in arXiv:1101.4013. We also couple N=4 superconformal CS theories to N=4 conformal supergravity.

hep-th↗
arXiv2015

Superconformal field theory in three dimensions: Correlation functions of conserved currents

For N-extended superconformal field theories in three spacetime dimensions (3D), with N=1,2,3, we compute the two- and three-point correlation functions of the supercurrent and the flavour current multiplets. We demonstrate that supersymmetry imposes additional restrictions on the correlators of conserved currents as compared with the non-supersymmetric case studied by Osborn and Petkou in hep-th/9307010. It is shown that the three-point function of the supercurrent is determined by a single functional form consistent with the conservation equation and all the symmetry properties. Similarly, the three-point function of the flavour current multiplets is also determined by a single functional form in the N=1 and N=3 cases. The specific feature of the N=2 case is that two independent structures are allowed for the three-point function of flavour current multiplets, but only one of them contributes to the three-point function of the conserved currents contained in these multiplets. Since the supergravity and super-Yang-Mills Ward identities are expected to relate the coefficients of the two- and three-point functions under consideration, the results obtained for 3D superconformal field theory are analogous to those in 2D conformal field theory. In addition, we present a new supertwistor construction for compactified Minkowski superspace. It is suitable for developing superconformal field theory on 3D spacetimes other than Minkowski space, such as S^1 x S^2 and its universal covering space R x S^2.

hep-th↗
arXiv2015

Implications of N=4 superconformal symmetry in three spacetime dimensions

We study implications of N=4 superconformal symmetry in three dimensions, thus extending our earlier results in arXiv:1503.04961 devoted to the N=1,2,3 cases. We show that the three-point function of the supercurrent in N=4 superconformal field theories contains two linearly independent forms. However, only one of these structures contributes to the three-point function of the energy-momentum tensor and the other one is present in those N=4 superconformal theories which are not invariant under the mirror map. We point out that general N=4 superconformal field theories admit two inequivalent flavour current multiplets and show that the three-point function of each of them is determined by one tensor structure. As an example, we compute the two- and three-point functions of the conserved currents in N=4 superconformal models of free hypermultiplets. We also derive the universal relations between the coefficients appearing in the two- and three-point correlators of the supercurrent and flavour current multiplets in all superconformal theories with N=1,2,3,4 supersymmetry. Our derivation is based on the use of Ward identities in conjunction with superspace reduction techniques.

hep-th↗
arXiv2015

Supersymmetric Spacetimes from Curved Superspace

We review the superspace technique to determine supersymmetric spacetimes in the framework of off-shell formulations for supergravity in diverse dimensions using the case of 3D N=2 supergravity theories as an illustrative example. This geometric formalism has several advantages over other approaches advocated in the last four years. Firstly, the infinitesimal isometry transformations of a given curved superspace form, by construction, a finite-dimensional Lie superalgebra, with its odd part corresponding to the rigid supersymmetry transformations. Secondly, the generalised Killing spinor equation, which must be obeyed by the supersymmetry parameters, is a consequence of the more fundamental superfield Killing equation. Thirdly, general rigid supersymmetric theories on a curved spacetime are readily constructed in superspace by making use of the known off-shell supergravity-matter couplings and restricting them to the background chosen. It is the superspace techniques which make it possible to generate arbitrary off-shell supergravity-matter couplings. Fourthly, all maximally supersymmetric Lorentzian spaces correspond to those off-shell supergravity backgrounds for which the Grassmann-odd components of the superspace torsion and curvature tensors vanish, while the Grassmann-even components of these tensors are annihilated by the spinor derivatives.

hep-th↗
arXiv2015

Conformal supergravity in five dimensions: New approach and applications

We develop a new off-shell formulation for five-dimensional (5D) conformal supergravity obtained by gauging the 5D superconformal algebra in superspace. An important property of the conformal superspace introduced is that it reduces to the superconformal tensor calculus (formulated in the early 2000's) upon gauging away a number of superfluous fields. On the other hand, a different gauge fixing reduces our formulation to the SU(2) superspace of arXiv:0802.3953, which is suitable to describe the most general off-shell supergravity-matter couplings. Using the conformal superspace approach, we show how to reproduce practically all off-shell constructions derived so far, including the supersymmetric extensions of $R^2$ terms, thus demonstrating the power of our formulation. Furthermore, we construct for the first time a supersymmetric completion of the Ricci tensor squared term using the standard Weyl multiplet coupled to an off-shell vector multiplet. In addition, we present several procedures to generate higher-order off-shell invariants in supergravity, including higher-derivative ones. The covariant projective multiplets proposed in arXiv:0802.3953 are lifted to conformal superspace, and a manifestly superconformal action principle is given. We also introduce unconstrained prepotentials for the vector multiplet, the ${\cal{O}}(2)$ multiplet (i.e., the linear multiplet without central charge) and ${\cal{O}}(4+n)$ multiplets, with $n=0,1,\dots$ Superform formulations are given for the BF action and the non-abelian Chern-Simons action. Finally, we describe locally supersymmetric theories with gauged central charge in conformal superspace.

hep-th↗
arXiv2015

Superconformal structures on the three-sphere

With the motivation to develop superconformal field theory on S^3, we introduce a 2n-extended supersphere S^{3|4n}, with n=1,2,..., as a homogeneous space of the three-dimensional Euclidean superconformal group OSp(2n|2,2) such that its bosonic body is S^3. Supertwistor and bi-supertwistor realizations of S^{3|4n} are derived. We study in detail the n=1 case, which is unique in the sense that the R-symmetry subgroup SO^*(2n) of the superconformal group is compact only for n=1. In particular, we show that the OSp(2|2,2) transformations preserve the chiral subspace of S^{3|4}. Several supercoset realizations of S^{3|4n} are presented. Harmonic/projective extensions of the supersphere by auxiliary bosonic fibre directions are sketched.

hep-th↗
arXiv2014

Supergravity-matter actions in three dimensions and Chern-Simons terms

We study off-shell N-extended Yang-Mills multiplets coupled to conformal supergravity in three spacetime dimensions. Superform formulations are presented for the non-Abelian Chern-Simons actions in the cases N=1, 2, 3, and the corresponding component actions are explicitly worked out. Such a Chern-Simons action does not exist for N=4. In the latter case, a superform formulation is given for the BF term that describes the coupling of two Abelian vector multiplets with self-dual and anti-self-dual superfield strengths respectively. The superform results obtained are used to construct linear multiplet action principles in the cases N=2, 3, 4. The N=3 and N=4 actions are demonstrated to be universal in the sense that all known off-shell supergravity-matter systems (with the exception of pure conformal supergravity) may be described using such an action. Starting from the N=3 and N=4 Abelian vector multiplets, we also construct composite O(2) multiplets which are analogues of the four-dimensional construction of an N=2 reduced chiral scalar engineered from the improved tensor multiplet. Using these composites, we present the superfield equations of motion for N=3 and N=4 anti-de Sitter and topologically massive supergravity theories. We also sketch the construction of a large family of higher derivative couplings for N=3 and N=4 vector multiplets.

hep-th↗
arXiv2014

N=4 supersymmetric Yang-Mills theories in AdS_3

For all types of N=4 anti-de Sitter (AdS) supersymmetry in three dimensions, we construct manifestly supersymmetric actions for Abelian vector multiplets and explain how to extend the construction to the non-Abelian case. Manifestly N=4 supersymmetric Yang-Mills (SYM) actions are explicitly given in the cases of (2,2) and critical (4,0) AdS supersymmetries. The N=4 vector multiplets and the corresponding actions are then reduced to (2,0) AdS superspace, in which only N=2 supersymmetry is manifest. Using the off-shell structure of the N=4 vector multiplets, we provide complete N=4 SYM actions in (2,0) AdS superspace for all types of N=4 AdS supersymmetry. In the case of (4,0) AdS supersymmetry, which admits a Euclidean counterpart, the resulting N=2 action contains a Chern-Simons term proportional to q/r, where r is the radius of AdS_3 and q is the R-charge of a chiral scalar superfield. The R-charge is a linear inhomogeneous function of X, an expectation value of the N=4 Cotton superfield. Thus our results explain the mysterious structure of N=4 supersymmetric Yang-Mills theories on S^3 discovered in arXiv:1401.7952. In the case of (3,1) AdS supersymmetry, which has no Euclidean counterpart, the SYM action contains both a Chern-Simons term and a chiral mass-like term. In the case of (2,2) AdS supersymmetry, which admits a Euclidean counterpart, the SYM action has no Chern-Simons and chiral mass-like terms.

hep-th↗