Extended superconformal higher-spin gauge theories in four dimensions

Using the off-shell formulation for $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ N = 2 results are then generalised to the $$ \mathcal{N} $$ N -extended case. We also present the gauge-invariant field strengths for on-shell massless higher-spin $$ \mathcal{N} $$ N = 2 supermultiplets in anti-de Sitter space. These field strengths prove to furnish representations of the $$ \mathcal{N} $$ N = 2 superconformal group.

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

We present $$ \mathcal{N} $$ N = 2 superconformal 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 $$ \mathcal{N} $$ N = 4 SU(N) super-Yang-Mills (SYM) theory on its Coulomb branch where (i) the gauge group SU(N) is spontaneously broken to SU(N − 1) × U(1); and (ii) the dynamics is captured by a single $$ \mathcal{N} $$ N = 2 vector multiplet associated with the U(1) factor of the unbroken group. Additionally, a local U(1) duality-invariant action generating the $$ \mathcal{N} $$ N = 2 super-Weyl anomaly is proposed. By providing a new derivation of the recently constructed U(1) duality-invariant $$ \mathcal{N} $$ N = 1 superconformal electrodynamics, we introduce its SL(2, ℝ) duality-invariant coupling to the dilaton-axion multiplet.

Higher-derivative supergravity, AdS4 holography, and black holes

We use conformal supergravity techniques to study four-derivative corrections in four-dimensional gauged supergravity. We show that the four-derivative Lagrangian for the propagating degrees of freedom of the $$ \mathcal{N} $$ N = 2 gravity multiplet is determined by two real dimensionless constants. We demonstrate that all solutions of the two-derivative equations of motion in the supergravity theory also solve the four-derivative equations of motion. These results are then applied to explicitly calculate the regularized on-shell action for any asymptotically locally AdS4 solution of the two-derivative equations of motion. The four-derivative terms in the supergravity Lagrangian modify the entropy and other thermodynamic observables for the black hole solutions of the theory. We calculate these corrections explicitly and demonstrate that the quantum statistical relation holds for general stationary black holes in the presence of the four-derivative corrections. Employing an embedding of this supergravity model in M-theory we show how to use supersymmetric localization results in the holographically dual three-dimensional SCFT to determine the unknown coefficients in the four-derivative supergravity action. This in turn leads to new detailed results for the first subleading $$ {N}^{\frac{1}{2}} $$ N 1 2 correction to the large N partition function of a class of three-dimensional SCFTs on compact Euclidean manifolds. In addition, we calculate explicitly the first subleading correction to the Bekenstein-Hawking entropy of asymptotically AdS4 black holes in M-theory. We also discuss how to add matter multiplets to the supergravity theory in the presence of four-derivative terms and to generalize some of these results to six- and higher-derivative supergravity.

Superconformal geometries and local twistors

Superconformal geometries in spacetime dimensions D = 3, 4, 5 and 6 are discussed in terms of local supertwistor bundles over standard superspace. These natually admit superconformal connections as matrix-valued one-forms. In order to make contact with the standard superspace formalism it is shown that one can always choose gauges in which the scale parts of the connection and curvature vanish, in which case the conformal and S-supersymmetry transformations become subsumed into super-Weyl transformations. The number of component fields can be reduced to those of the minimal off-shell conformal supergravity multiplets by imposing constraints which in most cases simply consists of taking the even covariant torsion two-form to vanish. This must be supplemented by further dimension-one constraints for the maximal cases in D = 3, 4. The subject is also discussed from a minimal point of view in which only the dimension-zero torsion is introduced. Finally, we introduce a new class of supermanifolds, local super Grassmannians, which provide an alternative setting for superconformal theories.

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

General $$ \mathcal{N} $$ 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) 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 ϵα, which proves to generate extended superconformal transformations. Among its cousins are the conformal Killing vector ξa and tensor ζa(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 a limited class of backgrounds, including all conformally flat ones.

Local supertwistors and conformal supergravity in six dimensions

The local supertwistor formalism, which involves a superconformal connection acting on the bundle of such objects over superspace, is used to investigate superconformal geometry in six dimensions. The geometry corresponding to (1, 0) and (2, 0) off-shell conformal supergravity multiplets, as well the associated finite super-Weyl transformations, are derived.

Super heat kernel and one-loop divergence of super Yang–Mills theory in conformal supergravity

We consider super Yang–Mills (SYM) theory in $N=1$ conformal supergravity. Using the background field method and the Faddeev–Popov procedure, the quantized action of the theory is presented. Its one-loop effective action is studied using the heat kernel method. We shall develop a non-iterative scheme, generalizing the non-supersymmetric case, to obtain the super heat kernel coefficients. In particular, the first three coefficients, which govern the one-loop divergence, will be calculated. We shall also demonstrate how to schematically derive the higher-order coefficients. The method presented here can be readily applied to various quantum theories. We shall, as an application, derive the full one-loop divergence of SYM in conformal supergravity.