Searcharxiv⌕ Search

arXiv subjects

Sergei M. Kuzenko

Publications and source records attributed to Sergei M. Kuzenko.

At least 37 records · Page 2Linked to original sources
arXiv2024

Covariant quantisation of tensor multiplet models

The Batalin-Vilkovisky formalism is applied to quantise the ${\cal N}=1$ supersymmetric generalisation of the Freedman-Townsend (FT) model, which was proposed by Lindström and Roček in 1983 in Minkowski superspace and is lifted to a supergravity background in this paper. This super FT theory describes a non-Abelian tensor multiplet and is known to be classically equivalent to a supersymmetric nonlinear sigma model. Using path integral considerations, we demonstrate that this equivalence holds at the quantum level in the sense that the quantum supercurrents in the two theories coincide. A modified Faddeev-Popov procedure is employed to quantise models for the ${\cal N}=2$ tensor multiplet in harmonic superspace. The obtained results agree with those derived by applying the Batalin-Vilkovisky scheme within the harmonic superspace setting.

hep-th↗
arXiv2024

Higher-derivative deformations of the ModMax theory

We present higher-derivative deformations of the ModMax theory which preserve both $\mathsf{U}(1)$ duality symmetry and Weyl invariance. In particular, we single out a class of deformations expected to describe a low-energy effective action for the ModMax theory. We also elaborate on (higher-derivative) deformations of the $\mathcal{N}=1$ super ModMax theory.

hep-th↗
arXiv2024

Interacting Chiral Form Field Theories and $T\overline T$-like Flows in Six and Higher Dimensions

In this paper we initiate the study of six-dimensional non-linear chiral two-form gauge theories as deformations of free chiral two-form gauge theories driven by stress-tensor $T\overline T$-like flows. To lay the background for this study, we elaborate on the relationship between different Lagrangian formulations of duality-invariant p-form theories and corresponding $T\overline T$-like flows in various dimensions. To this end we propose a new formulation which (i) is a generalization of the four-dimensional construction by Ivanov, Nurmagambetov and Zupnik (INZ) and (ii) turns into the PST formulation upon integrating out an auxiliary self-dual field. We elucidate space-time covariant properties of the PST formulation by clarifying and making use of its relation to the INZ-type formulation and to a so-called ``clone" construction.

hep-th↗
arXiv2024

$\mathcal{N}=3$ conformal superspace in four dimensions

We develop a superspace formulation for ${\cal N}=3$ conformal supergravity in four spacetime dimensions as a gauge theory of the superconformal group $\mathsf{SU}(2,2|3)$. Upon imposing certain covariant constraints, the algebra of conformally covariant derivatives $\nabla_A = (\nabla_a,\nabla_α^i,\bar{\nabla}_i^{\dot α})$ is shown to be determined in terms of a single primary chiral spinor superfield, the super-Weyl spinor $W_α$ of dimension $+1/2$ and its conjugate. Associated with $W_α$ is its primary descendant $B^i{}_j$ of dimension $+2$, the super-Bach tensor, which determines the equation of motion for conformal supergravity. As an application of this construction, we present two different but equivalent action principles for ${\cal N}=3$ conformal supergravity. We describe the model for linearised $\mathcal{N}=3$ conformal supergravity in an arbitrary conformally flat background and demonstrate that it possesses $\mathsf{U}(1)$ duality invariance. Additionally, upon degauging certain local symmetries, our superspace geometry is shown to reduce to the $\mathsf{U}(3)$ superspace constructed by Howe more than four decades ago. Further degauging proves to lead to a new superspace formalism, called $\mathsf{SU}(3) $ superspace, which can also be used to describe ${\mathcal N}=3$ conformal supergravity. Our conformal superspace setting opens up the possibility to formulate the dynamics of the off-shell ${\mathcal N}=3$ super Yang-Mills theory coupled to conformal supergravity.

hep-th↗
arXiv2023

Correlation functions of spinor current multiplets in ${\mathcal N}=1$ superconformal theory

We consider ${\mathcal N}=1$ superconformal field theories in four dimensions possessing an additional conserved spinor current multiplet $S_α$ and study three-point functions involving such an operator. A conserved spinor current multiplet naturally exists in superconformal theories with ${\mathcal N}=2$ supersymmetry and contains the current of the second supersymmetry. However, we do not assume ${\mathcal N}=2$ supersymmetry. We show that the three-point function of two spinor current multiplets and the ${\mathcal N}=1$ supercurrent depends on three independent tensor structures and, in general, is not contained in the three-point function of the ${\mathcal N}=2$ supercurrent. It then follows, based on symmetry considerations only, that the existence of one more Grassmann odd current multiplet in ${\mathcal N}=1$ superconformal field theory does not necessarily imply ${\mathcal N}=2$ superconformal symmetry.

hep-th↗
arXiv2023

Duality-Invariant Non-linear Electrodynamics and Stress Tensor Flows

Given a model for self-dual non-linear electrodynamics in four spacetime dimensions, any deformation of this theory which is constructed from the duality-invariant energy-momentum tensor preserves duality invariance. In this work we present new proofs of this known result, and also establish a previously unknown converse: any parameterized family of duality-invariant Lagrangians, all constructed from an Abelian field strength $F_{μν}$ but not its derivatives, is related by a generalized stress tensor flow, in a sense which we make precise. We establish this and other properties of stress tensor deformations of theories of non-linear electrodynamics using both a conventional Lagrangian representation and using two auxiliary field formulations. We analyze these flows in several examples of duality-invariant models including the Born-Infeld and ModMax theories, and we derive a new auxiliary field representation for the two-parameter family of ModMax-Born-Infeld theories. These results suggest that the space of duality-invariant theories may be characterized as a subspace of theories of electrodynamics with the property that all tangent vectors to this subspace are operators constructed from the stress tensor.

hep-th↗
arXiv2023

Correlation Functions of Conserved Currents in N = 2 Superconformal Theory

Using a manifestly supersymmetric formalism, we determine the general structure of two- and three- point functions of the supercurrent and the flavour current of N = 2 superconformal field theories. We also express them in terms of N = 1 superfields and compare to the generic N = 1 correlation functions. A general discussion of the N = 2 supercurrent superfield and the multiplet of anomalies and their definition as derivatives with respect to the supergravity prepotentials is also included.

hep-th↗
arXiv2023

New duality-invariant models for nonlinear supersymmetric electrodynamics

We propose a new family of $\mathsf{U}(1)$ duality-invariant models for nonlinear ${\cal N}=1$ supersymmetric electrodynamics coupled to supergravity. It includes the Cribiori-Farakos-Tournoy-van Proeyen supergravity-matter theory for spontaneously broken local supersymmetry with a novel Fayet-Iliopoulos term without gauged $R$-symmetry. We present superconformal duality-invariant models, as well as new $\mathsf{U}(1)$ duality-invariant models for spontaneously broken local supersymmetry.

hep-th↗
arXiv2023

Self-duality for $\cal N$-extended superconformal gauge multiplets

We develop a general formalism of duality rotations for $\cal N$-extended superconformal gauge multiplets in conformally flat backgrounds as an extension of the approach given in arXiv:2107.02001. Additionally, we construct $\mathsf{U}(1)$ duality-invariant models for the ${\mathcal N}=2$ superconformal gravitino multiplet recently described in arXiv:2305.16029. Each of them is automatically self-dual with respect to a superfield Legendre transformation. A method is proposed to generate such self-dual models, including a family of superconformal theories.

hep-th↗
arXiv2023

Quantisation of the gauge-invariant models for massive higher-spin bosonic fields

In 2001, Zinoviev proposed a gauge-invariant formulation for a massive bosonic field with spin $s \geq 2$ in a spacetime of constant curvature. In this paper we carry out the Faddeev-Popov quantisation of this theory in $d$-dimensional Minkowski space. We also make use of the Zinoviev theory to derive a generalisation of the Singh-Hagen model for a massive integer-spin field in $d>4 $ dimensions.

hep-th↗
arXiv2023

Nonlinear realisation approach to topologically massive supergravity

We develop a nonlinear realisation approach to topologically massive supergravity in three dimensions, with and without a cosmological term. It is a natural generalisation of a similar construction for ${\cal N}=1$ supergravity in four dimensions, which was recently proposed by one of us. At the heart of both formulations is the nonlinear realisation approach to gravity which was given by Volkov and Soroka fifty years ago in the context of spontaneously broken local supersymmetry. In our setting, the action for cosmological topologically massive supergravity is invariant under two different local supersymmetries. One of them acts on the Goldstino, while the other supersymmetry leaves the Goldstino invariant. The former can be used to gauge away the Goldstino, and then the resulting action coincides with that given in the literature.

hep-th↗
arXiv2023

The $\mathcal{N}=2$ superconformal gravitino multiplet

We propose a new gauge prepotential $Υ_i$ describing the four-dimensional ${\mathcal N}=2$ superconformal gravitino multiplet. The former naturally arises via a superspace reduction of the ${\mathcal N}=3$ conformal supergravity multiplet. A locally superconformal chiral action for $Υ_i$, which is gauge-invariant in arbitrary conformally-flat backgrounds, is derived. This construction readily yields a new superprojector, which maps an isospinor superfield $Ψ_i$ to a multiplet characterised by the properties of a conformal supercurrent associated with $Υ_i$. Our main results are also specialised to ${\mathcal N}=2$ anti-de Sitter superspace.

hep-th↗
arXiv2023

On higher-spin ${\mathcal{N}=2}$ supercurrent multiplets

We elaborate on the structure of higher-spin $\mathcal{N}=2$ supercurrent multiplets in four dimensions. It is shown that associated with every conformal supercurrent $J_{α(m) \dotα(n)}$ (with $m,n$ non-negative integers) is a descendant $J^{ij}_{α(m+1) \dotα(n+1)}$ with the following properties: (a) it is a linear multiplet with respect to its $\mathsf{SU}(2)$ indices, that is $ D_β^{(i} J^{ jk)}_{α(m+1) \dotα(n+1) }=0$ and $ \bar D_{\dot β}^{(i} J^{jk)}_{ α(m+1) \dotα(n+1) }=0$; and (b) it is conserved, $\partial^{β\dotβ} J^{ij}_{βα(m) \dotβ \dotα(n)}=0$. Realisations of the conformal supercurrents $J_{α(s) \dotα(s)}$, with $s=0,1, \dots$, are naturally provided by a massless hypermultiplet and a vector multiplet. It turns out that such supercurrents and their linear descendants $J^{ij}_{α(s+1) \dotα(s+1)}$ do not occur in the harmonic-superspace framework recently described in arXiv:2212.14114. Making use of a massive hypermultiplet, we derive non-conformal higher-spin $\mathcal{N}=2$ supercurrent multiplets. Additionally, we derive the higher symmetries of the kinetic operators for both a massive and massless hypermultiplet. Building on this analysis, we sketch the construction of higher-derivative gauge transformations for the off-shell arctic multiplet $Υ^{(1)}$, which are expected to be vital in the framework of consistent interactions between $Υ^{(1)}$ and superconformal higher-spin gauge multiplets.

hep-th↗
arXiv2023

Embedding formalism for $(p,q)$ AdS superspaces in three dimensions

We develop an embedding formalism for $(p,q)$ anti-de Sitter (AdS) superspaces in three dimensions by using a modified version of their supertwistor description given in the literature. A coset construction for these superspaces is worked out. We put forward a program of constructing a supersymmetric analogue of the Bañados metric, which is expected to be a deformation of the $(p,q)$ AdS superspace geometry by a two-dimensional conformal $(p,q)$ supercurrent multiplet.

hep-th↗
arXiv2023

A supersymmetric nonlinear sigma model analogue of the ModMax theory

A decade ago, it was shown that associated with any model for $\mathsf{U}(1)$ duality-invariant nonlinear electrodynamics there is a unique $\mathsf{U}(1)$ duality-invariant supersymmetric nonlinear sigma model formulated in terms of chiral and complex linear superfields. Here we study the ${\cal N}=1$ superconformal $σ$-model analogue of the conformal duality-invariant electrodynamics known as the ModMax theory. We derive its dual formulation in terms of chiral superfields and show that the target space is a Kähler cone with $\mathsf{U}(1)\times \mathsf{U}(1)$ being the connected component of the isometry group.

hep-th↗
arXiv2023

Local supersymmetry: Variations on a theme by Volkov and Soroka

We revisit the work by Volkov and Soroka on spontaneously broken local supersymmetry. It is demonstrated for the first time that, for specially chosen parameters of the theory, the Volkov-Soroka action is invariant under two different local supersymmetries. One of them is present for arbitrary values of the parameters and acts on the Goldstino, while the other supersymmetry emerges only in a special case and leaves the Goldstino invariant. The former can be used to gauge away the Goldstino, and then the resulting action coincides with that proposed by Deser and Zumino for consistent supergravity in the first-order formalism. In this sense, pure $\mathcal{N} = 1$ supergravity is a special case of the Volkov-Soroka theory, although it was not discovered by these authors. We also explain how the Volkov-Soroka approach allows one to naturally arrive at the 1.5 formalism. Our analysis provides a nonlinear realisation approach to construct unbroken $\mathcal{N} = 1$ Poincaré supergravity.

hep-th↗
arXiv2023

Induced action for superconformal higher-spin multiplets using SCFT techniques

Recently, the interacting $\mathcal{N}=1$ superconformal higher-spin theory in four dimensions has been proposed within the induced action approach. In this paper we initiate a program of computing perturbative corrections to the corresponding action and explicitly evaluate all quadratic terms. This is achieved by employing standard techniques from superconformal field theory.

hep-th↗
arXiv2023

Effective actions in supersymmetric gauge theories: heat kernels for non-minimal operators

We study the quantum dynamics of a system of $n$ Abelian ${\cal N}=1$ vector multiplets coupled to $\frac 12 n(n+1)$ chiral multiplets which parametrise the Hermitian symmetric space $\mathsf{Sp}(2n, {\mathbb R})/ \mathsf{U}(n)$. In the presence of supergravity, this model is super-Weyl invariant and possesses the maximal non-compact duality group $\mathsf{Sp}(2n, {\mathbb R})$ at the classical level. These symmetries should be respected by the logarithmically divergent term (the ``induced action'') of the effective action obtained by integrating out the vector multiplets. In computing the effective action, one has to deal with non-minimal operators for which the known heat kernel techniques are not directly applicable, even in flat (super)space. In this paper we develop a method to compute the induced action in Minkowski superspace. The induced action is derived in closed form and has a simple structure. It is a higher-derivative superconformal sigma model on $\mathsf{Sp}(2n, {\mathbb R})/ \mathsf{U}(n)$. The obtained ${\cal N}=1$ results are generalised to the case of ${\cal N}=2$ local supersymmetry: a system of $n$ Abelian ${\cal N}=2$ vector multiplets coupled to ${\cal N}=2$ chiral multiplets $X^I$ parametrising $\mathsf{Sp}(2n, {\mathbb R})/ \mathsf{U}(n)$. The induced action is shown to be proportional to $ \int {\rm d}^4x {\rm d}^4 θ{\rm d}^4 \bar θ\, E \, {\mathfrak K}(X, \bar X )$, where ${\mathfrak K}(X, \bar X )$ is the Kähler potential for $\mathsf{Sp}(2n, {\mathbb R})/ \mathsf{U}(n)$. We also apply our method to compute DeWitt's $a_2 $ coefficients in some non-supersymmetric theories with non-minimal operators.

hep-th↗