arXiv subjects

Sergei M. Kuzenko

Publications and source records attributed to Sergei M. Kuzenko.

At least 55 records · Page 3Linked to original sources

arXiv2023

Weyl invariance, non-compact duality and conformal higher-derivative sigma models

We study a system of $n$ Abelian vector fields coupled to $\frac 12 n(n+1)$ complex scalars parametrising the Hermitian symmetric space $\mathsf{Sp}(2n, {\mathbb R})/ \mathsf{U}(n)$. This model is Weyl invariant and possesses the maximal non-compact duality group $\mathsf{Sp}(2n, {\mathbb R})$. Although both symmetries are anomalous in the quantum theory, they should be respected by the logarithmic divergent term (the ``induced action'') of the effective action obtained by integrating out the vector fields. We compute this induced action and demonstrate its Weyl and $\mathsf{Sp}(2n, {\mathbb R})$ invariance. The resulting conformal higher-derivative $σ$-model on $\mathsf{Sp}(2n, {\mathbb R})/ \mathsf{U}(n)$ is generalised to the cases where the fields take their values in (i) an arbitrary Kähler space; and (ii) an arbitrary Riemannian manifold. In both cases, the $σ$-model Lagrangian generates a Weyl anomaly satisfying the Wess-Zumino consistency condition.

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arXiv2022

Conformal $(p,q)$ supergeometries in two dimensions

We propose a superspace formulation for conformal $(p,q)$ supergravity in two dimensions as a gauge theory of the superconformal group $\mathsf{OSp}_0 (p|2; {\mathbb R} ) \times \mathsf{OSp}_0 (q|2; {\mathbb R} )$ with a flat connection. Upon degauging of certain local symmetries, this conformal superspace is shown to reduce to a conformally flat $\mathsf{SO}(p) \times \mathsf{SO}(q)$ superspace with the following properties: (i) its structure group is a direct product of the Lorentz group and $\mathsf{SO}(p) \times \mathsf{SO}(q)$; and (ii) the residual local scale symmetry is realised by super-Weyl transformations with an unconstrained real parameter. As an application of the formalism, we describe ${\cal N}$-extended AdS superspace as a maximally symmetric supergeometry in the $p=q \equiv \cal N$ case. If at least one of the parameters $p$ or $q$ is even, alternative superconformal groups and, thus, conformal superspaces exist. In particular, if $p = 2n$, a possible choice of the superconformal group is $\mathsf{SU}(1,1|n) \times \mathsf{OSp}_0 (q|2; {\mathbb R} )$, for $n \neq 2$, and $\mathsf{PSU}(1,1|2) \times \mathsf{OSp}_0 (q|2; {\mathbb R} )$, when $n=2$. In general, a conformal superspace formulation is associated with a supergroup $ G = G_L \times G_R$, where the simple supergroups $G_L$ and $G_R$ can be any of the extended superconformal groups, which were classified by Günaydin, Sierra and Townsend. Degauging the corresponding conformal superspace leads to a conformally flat $H_L \times H_R$ superspace, where $H_L $ ($H_R$) is the $R$-symmetry subgroup of $G_L$ ($G_R$). Additionally, for the $p,q \leq 2$ cases we propose composite primary multiplets which generate the Gauss-Bonnet invariant and supersymmetric extensions of the Fradkin-Tseytlin term.

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arXiv2022

Conformal interactions between matter and higher-spin (super)fields

In even spacetime dimensions, the interacting bosonic conformal higher-spin (CHS) theory can be realised as an induced action. The main ingredient in this definition is the model $\mathcal{S}[φ,h]$ describing a complex scalar field $φ$ coupled to an infinite set of background CHS fields $h$, with $\mathcal{S}[φ,h]$ possessing a non-abelian gauge symmetry. Two characteristic features of the perturbative constructions of $\mathcal{S}[φ, h]$ given in the literature are: (i) the background spacetime is flat; and (ii) conformal invariance is not manifest. In the present paper we provide a new derivation of this action in four dimensions such that (i) $\mathcal{S}[φ, h]$ is defined on an arbitrary conformally-flat background; and (ii) the background conformal symmetry is manifestly realised. Next, our results are extended to the $\mathcal{N}=1$ supersymmetric case. Specifically, we construct, for the first time, a model $\mathcal{S}[Φ, H]$ for a conformal scalar/chiral multiplet $Φ$ coupled to an infinite set of background higher-spin superfields $H$. Our action possesses a non-abelian gauge symmetry which naturally generalises the linearised gauge transformations of conformal half-integer superspin multiplets. The other fundamental features of this model are: (i) $\mathcal{S}[Φ, H]$ is defined on an arbitrary conformally-flat superspace background; and (ii) the background $\mathcal{N}=1$ superconformal symmetry is manifest. Making use of $\mathcal{S}[Φ, H]$, an interacting superconformal higher-spin theory can be defined as an induced action.

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arXiv2022

Superconformal duality-invariant models and $\mathcal{N} = 4$ SYM effective action

We present $\mathcal{N}=2$ superconformal $\mathsf{U}(1)$ duality-invariant models for an Abelian vector multiplet coupled to conformal supergravity. In a Minkowski background, such a nonlinear theory is expected to describe (the planar part of) the low-energy effective action for the $\mathcal{N}=4$ $\mathsf{SU}(N)$ super-Yang-Mills (SYM) theory on its Coulomb branch where (i) the gauge group $\mathsf{SU}(N)$ is spontaneously broken to $\mathsf{SU}(N-1) \times \mathsf{U}(1)$; and (ii) the dynamics is captured by a single $\mathcal{N}=2$ vector multiplet associated with the $\mathsf{U}(1)$ factor of the unbroken group. Additionally, a local $\mathsf{U}(1)$ duality-invariant action generating the $\mathcal{N}=2$ super-Weyl anomaly is proposed. By providing a new derivation of the recently constructed $\mathsf{U}(1)$ duality-invariant $\mathcal{N}=1$ superconformal electrodynamics, we introduce its $\mathsf{SL}(2,{\mathbb R})$ duality-invariant coupling to the dilaton-axion multiplet.

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arXiv2021

Extended superconformal higher-spin gauge theories in four dimensions

Using the off-shell formulation for ${\cal N}=2$ conformal supergravity in four dimensions, we describe superconformal higher-spin multiplets of conserved currents in a curved background and present their associated unconstrained gauge prepotentials. The latter are used to construct locally superconformal chiral actions, which are demonstrated to be gauge invariant in arbitrary conformally flat backgrounds. The main ${\cal N}=2$ results are then generalised to the ${\cal N}$-extended case. We also present the gauge-invariant field strengths for on-shell massless higher-spin ${\cal N}=2$ supermultiplets in anti-de Sitter space. These field strengths prove to furnish representations of the ${\cal N}=2$ superconformal group.

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arXiv2021

Supertwistor realisations of AdS superspaces

We propose supertwistor realisations of $(p,q)$ anti-de Sitter (AdS) superspaces in three dimensions and $\cal N$-extended AdS superspaces in four dimensions. For each superspace, we identify a two-point function that is invariant under the corresponding isometry supergroup. This two-point function is a supersymmetric extension (of a function) of the geodesic distance. We also describe a bi-supertwistor formulation for $\cal N$-extended AdS superspace in four dimensions and harmonic/projective extensions of $(p,q)$ AdS superspaces in three dimensions.

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arXiv2021

AdS (super)projectors in three dimensions and partial masslessness

We derive the transverse projection operators for fields with arbitrary integer and half-integer spin on three-dimensional anti-de Sitter space, AdS$_3$. The projectors are constructed in terms of the quadratic Casimir operators of the isometry group $\mathsf{SO}(2,2)$ of AdS$_3$. Their poles are demonstrated to correspond to (partially) massless fields. As an application, we make use of the projectors to recast the conformal and topologically massive higher-spin actions in AdS$_3$ into a manifestly gauge-invariant and factorised form. We also propose operators which isolate the component of a field that is transverse and carries a definite helicity. Such fields correspond to an irreducible representation of $\mathsf{SO}(2,2)$. Our results are then extended to the case of $\mathcal{N}=1$ AdS$_3$ supersymmetry.

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arXiv2021

Three-point functions of higher-spin spinor current multiplets in ${\mathcal N}=1$ superconformal theory

In this paper, we study the general form of three-point functions of conserved current multiplets $S_{α(k)}= S_{(α_1 \dots α_k)}$ of arbitrary rank in four-dimensional ${\mathcal N}=1$ superconformal theory. We find that the correlation function of three such operators $\langle \bar{S}_{\dotα(k)} (z_1) S_{β(k+l)} (z_2) \bar{S}_{\dotγ(l)} (z_3) \rangle$ is fixed by the superconformal symmetry up to a single complex coefficient though the precise form of the correlator depends on the values of $k$ and $l$. In addition, we present the general structure of mixed correlators of the form $\langle \bar{S}_{\dotα(k)} (z_1) S_{α(k)} (z_2) L(z_3) \rangle$ and $\langle \bar{S}_{\dotα(k)} (z_1) S_{α(k)} (z_2) J_{γ\dotγ} (z_3) \rangle$, where $L$ is the flavour current multiplet and $J_{γ\dotγ}$ is the supercurrent.

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arXiv2021

Higher-spin gauge models with (1,1) supersymmetry in AdS${}_3$: Reduction to (1,0) superspace

In three dimensions, there are two types of ${\cal N}=2$ anti-de Sitter (AdS) supersymmetry, which are denoted (1,1) and (2,0). They are characterised by different supercurrents and support different families of higher-spin gauge models (massless and massive) which were constructed in arXiv:1807.09098 and arXiv:1809.00802 for the (1,1) and (2,0) cases, respectively, using superspace techniques. It turns out that the precise difference between the (1,1) and (2,0) higher-spin supermultiplets can be pinned down by reducing these gauge theories to (1,0) AdS superspace. The present paper is devoted to the $(1,1) \to (1,0)$ AdS superspace reduction. In conjunction with the outcomes of the $(2,0) \to (1,0)$ AdS superspace reduction carried out in arXiv:1905.05050, we demonstrate that every known higher-spin theory with (1,1) or (2,0) AdS supersymmetry decomposes into a sum of two off-shell (1,0) supermultiplets which belong to four series of inequivalent higher-spin gauge models. The latter are reduced to components.

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arXiv2021

Higher-spin Cotton tensors and massive gauge-invariant actions in AdS$_3$

In a conformally flat three-dimensional spacetime, the linearised higher-spin Cotton tensor $\mathfrak{C}_{α(n)}(h)$ is the unique conserved conformal current which is a gauge-invariant descendant of the conformal gauge prepotential $h_{α(n)}$. The explicit form of $\mathfrak{C}_{α(n)}(h)$ is well known in Minkowski space. Here we solve the problem of extending the Minkowskian result to the case of anti-de Sitter (AdS) space and derive a closed-form expression for $\mathfrak{C}_{α(n)}(h)$ in terms of the AdS Lorentz covariant derivatives. It is shown that every conformal higher-spin action $S_{\text{CS}}^{(n)}[h]\propto \int\text{d}^3x\, e \, h^{α(n)}\mathfrak{C}_{α(n)}(h) $ factorises into a product of $(n-1)$ first-order operators that are associated with the spin-$n/2$ partially massless AdS values. Our findings greatly facilitate the on-shell analysis of massive higher-spin gauge-invariant actions in AdS$_3$. The main results are extended to the case of $\mathcal{N}=1$ AdS supersymmetry. In particular, we derive simple expressions for the higher-spin super-Cotton tensors in AdS$_3$.

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arXiv2021

Effective actions for dual massive (super) p-forms

In $d$ dimensions, the model for a massless $p$-form in curved space is known to be a reducible gauge theory for $p>1$, and therefore its covariant quantisation cannot be carried out using the standard Faddeev-Popov scheme. However, adding a mass term and also introducing a Stueckelberg reformulation of the resulting $p$-form model, one ends up with an irreducible gauge theory which can be quantised à la Faddeev and Popov. We derive a compact expression for the massive $p$-form effective action, $Γ^{(m)}_p$, in terms of the functional determinants of Hodge-de Rham operators. We then show that the effective actions $Γ^{(m)}_p$ and $Γ^{(m)}_{d-p-1}$ differ by a topological invariant. This is a generalisation of the known result in the massless case that the effective actions $Γ_p$ and $Γ_{d-p-2}$ coincide modulo a topological term. Finally, our analysis is extended to the case of massive super $p$-forms coupled to background ${\cal N}=1$ supergravity in four dimensions. Specifically, we study the quantum dynamics of the following massive super $p$-forms: (i) vector multiplet; (ii) tensor multiplet; and (iii) three-form multiplet. It is demonstrated that the effective actions of the massive vector and tensor multiplets coincide. The effective action of the massive three-form is shown to be a sum of those corresponding to two massive scalar multiplets, modulo a topological term.

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arXiv2021

Massless particles in five and higher dimensions

We describe a five-dimensional analogue of Wigner's operator equation ${\mathbb W}_a = λP_a$, where ${\mathbb W}_a $ is the Pauli-Lubanski vector, $P_a$ the energy-momentum operator, and $λ$ the helicity of a massless particle. Higher dimensional generalisations are also given.

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arXiv2021

Generalised superconformal higher-spin multiplets

We propose generalised $\mathcal{N}=1$ superconformal higher-spin (SCHS) gauge multiplets of depth $t$, $Υ_{α(n)\dotα(m)}^{(t)}$, with $n\geq m \geq 1$. At the component level, for $t>2$ they contain generalised conformal higher-spin (CHS) gauge fields with depths $t-1$, $t$ and $t+1$. The supermultiplets with $t=1$ and $t=2$ include both ordinary and generalised CHS gauge fields. Super-Weyl and gauge invariant actions describing the dynamics of $Υ_{α(n)\dotα(m)}^{(t)}$ on conformally-flat superspace backgrounds are then derived. For the case $n=m=t=1$, corresponding to the maximal-depth conformal graviton supermultiplet, we extend this action to Bach-flat backgrounds. Models for superconformal non-gauge multiplets, which are expected to play an important role in the Bach-flat completions of the models for $Υ^{(t)}_{α(n)\dotα(m)}$, are also provided. Finally we show that, on Bach-flat backgrounds, requiring gauge and Weyl invariance does not always determine a model for a CHS field uniquely.

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arXiv2020

Symmetries of $\mathcal{N} = (1,0)$ supergravity backgrounds in six dimensions

General $\mathcal{N}=(1,0)$ supergravity-matter systems in six dimensions may be described using one of the two fully fledged superspace formulations for conformal supergravity: (i) $\mathsf{SU}(2)$ superspace; and (ii) conformal superspace. With motivation to develop rigid supersymmetric field theories in curved space, this paper is devoted to the study of the geometric symmetries of supergravity backgrounds. In particular, we introduce the notion of a conformal Killing spinor superfield $ε^α$, which proves to generate extended superconformal transformations. Among its cousins are the conformal Killing vector $ξ^a$ and tensor $ζ^{a(n)}$ superfields. The former parametrise conformal isometries of supergravity backgrounds, which in turn yield symmetries of every superconformal field theory. Meanwhile, the conformal Killing tensors of a given background are associated with higher symmetries of the hypermultiplet. By studying the higher symmetries of a non-conformal vector multiplet we introduce the concept of a Killing tensor superfield. We also analyse the problem of computing higher symmetries for the conformal d'Alembertian in curved space and demonstrate that, beyond the first-order case, these operators are defined only on conformally flat backgrounds.

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arXiv2020

New locally (super)conformal gauge models in Bach-flat backgrounds

For every conformal gauge field $h_{α(n)\dot α(m)}$ in four dimensions, with $n\geq m >0$, a gauge-invariant action is known to exist in arbitrary conformally flat backgrounds. If the Weyl tensor is non-vanishing, however, gauge invariance holds for a pure conformal field in the following cases: (i) $n=m=1$ (Maxwell's field) on arbitrary gravitational backgrounds; and (ii) $n=m+1 =2 $ (conformal gravitino) and $n=m=2$ (conformal graviton) on Bach-flat backgrounds. It is believed that in other cases certain lower-spin fields must be introduced to ensure gauge invariance in Bach-flat backgrounds, although no closed-form model has yet been constructed (except for conformal maximal depth fields with spin $s=5/2$ and $s=3$). In this paper we derive such a gauge-invariant model describing the dynamics of a conformal gauge field $h_{α(3)\dotα}$ coupled to a self-dual two-form. Similar to other conformal higher-spin theories, it can be embedded in an off-shell superconformal gauge-invariant action. To this end, we introduce a new family of $\mathcal{N}=1$ superconformal gauge multiplets described by unconstrained prepotentials $Υ_{α(n)}$, with $n>0$, and propose the corresponding gauge-invariant actions on conformally-flat backgrounds. We demonstrate that the $n=2$ model, which contains $h_{α(3)\dotα}$ at the component level, can be lifted to a Bach-flat background provided $Υ_{α(2)}$ is coupled to a chiral spinor $Ω_α$. We also propose families of (super)conformal higher-derivative non-gauge actions and new superconformal operators in any curved space. Finally, through considerations based on supersymmetry, we argue that the conformal spin-3 field should always be accompanied by a conformal spin-2 field in order to ensure gauge invariance in a Bach-flat background.

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arXiv2020

Non-compact duality, super-Weyl invariance and effective actions

In both ${\cal N}=1$ and ${\cal N}=2$ supersymmetry, it is known that $\mathsf{Sp}(2n, {\mathbb R})$ is the maximal duality group of $n$ vector multiplets coupled to chiral scalar multiplets $τ(x,θ) $ that parametrise the Hermitian symmetric space $\mathsf{Sp}(2n, {\mathbb R})/ \mathsf{U}(n)$. If the coupling to $τ$ is introduced for $n$ superconformal gauge multiplets in a supergravity background, the action is also invariant under super-Weyl transformations. Computing the path integral over the gauge prepotentials in curved superspace leads to an effective action $Γ[τ, \bar τ]$ with the following properties: (i) its logarithmically divergent part is invariant under super-Weyl and rigid $\mathsf{Sp}(2n, {\mathbb R})$ transformations; (ii) the super-Weyl transformations are anomalous upon renormalisation. In this paper we describe the ${\cal N}=1$ and ${\cal N}=2$ locally supersymmetric "induced actions" which determine the logarithmically divergent parts of the corresponding effective actions. In the ${\cal N}=1$ case, superfield heat kernel techniques are used to compute the induced action of a single vector multiplet $(n=1)$ coupled to a chiral dilaton-axion multiplet. We also describe the general structure of ${\cal N}=1$ super-Weyl anomalies that contain weight-zero chiral scalar multiplets $Φ^I$ taking values in a Kähler manifold. Explicit anomaly calculations are carried out in the $n=1$ case.

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arXiv2020

Generalised conformal higher-spin fields in curved backgrounds

The problem of constructing gauge-invariant actions for conformal higher-spin fields in curved backgrounds is known to be notoriously difficult. In this paper we present gauge-invariant models for conformal maximal depth fields with spin $s=5/2$ and $s=3$ in four-dimensional Bach-flat backgrounds. We find that certain lower-spin fields must be introduced to ensure gauge invariance when $s>2$, which is analogous to a conjecture made earlier in the literature for conformal higher-spin fields of minimal depth.

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arXiv2020

Generalised Fayet-Iliopoulos terms in supergravity

The U(1) vector multiplet theory with the Fayet-Iliopoulos (FI) term is one of the oldest and simplest models for spontaneously broken rigid supersymmetry. Lifting the FI term to supergravity requires gauged $R$-symmetry, as was first demonstrated in 1977 by Freedman within ${\cal N}=1$ supergravity. There exists an alternative to the standard FI mechanism, which is reviewed in this conference paper. It is obtained by replacing the FI model with a manifestly gauge-invariant action such that its functional form is determined by two arbitrary real functions of a single complex variable. One of these functions generates a superconformal kinetic term for the vector multiplet, while the other yields a generalised FI term. Coupling such a vector multiplet model to supergravity does not require gauging of the $R$-symmetry. These generalised FI terms are consistently defined for any off-shell formulation for ${\cal N}=1$ supergravity, and are compatible with a supersymmetric cosmological term.

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