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Register a new userOff-shell superconformal higher spin multiplets in four dimensions
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We formulate off-shell N=1 superconformal higher spin multiplets in four spacetime dimensions and briefly discuss their coupling to conformal supergravity. As an example, we explicitly work out the coupling of the superconformal gravitino multiplet to conformal supergravity. The corresponding action is super-Weyl invariant for arbitrary supergravity backgrounds. However, it is gauge invariant only if the supersymmetric Bach tensor vanishes. This is similar to linearised conformal supergravity in curved background.
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We propose generalised $mathcal{N}=1$ superconformal higher-spin (SCHS) gauge multiplets of depth $t$, $Upsilon_{alpha(n)dot{alpha}(m)}^{(t)}$, with $ngeq m geq 1$. 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 $Upsilon_{alpha(n)dot{alpha}(m)}^{(t)}$ 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 $Upsilon^{(t)}_{alpha(n)dot{alpha}(m)}$, 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.
Within the framework of six-dimensional ${cal N}=(1,0)$ conformal supergravity, we introduce new off-shell multiplets ${cal O}{}^{*}(n)$, where $n=3,4,dots,$ and use them to construct higher-rank extensions of the linear multiplet action. The ${cal O}{}^{*}(n)$ multiplets may be viewed as being dual to well-known superconformal ${cal O}(n)$ multiplets. We provide prepotential formulations for the ${cal O}(n)$ and ${cal O}{}^{*}(n)$ multiplets coupled to conformal supergravity. For every ${cal O}{}^{*}(n)$ multiplet, we construct a higher derivative invariant which is superconformal on arbitrary superconformally flat backgrounds. We also show how our results can be used to construct new higher derivative actions in supergravity.
Using the off-shell formulation for ${mathcal N}=2$ conformal supergravity in four dimensions, we propose superconformal higher-spin multiplets of conserved currents and 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.
We develop superspace techniques to construct general off-shell N=1,2,3,4 superconformal sigma-models in three space-time dimensions. The most general N=3 and N=4 superconformal sigma-models are constructed in terms of N=2 chiral superfields. Several superspace proofs of the folklore statement that N=3 supersymmetry implies N=4 are presented both in the on-shell and off-shell settings. We also elaborate on (super)twistor realisations for (super)manifolds on which the three-dimensional N-extended superconformal groups act transitively and which include Minkowski space as a subspace.
We study the constraints of superconformal symmetry on codimension two defects in four-dimensional superconformal field theories. We show that the one-point function of the stress tensor and the two-point function of the displacement operator are related, and we discuss the consequences of this relation for the Weyl anomaly coefficients as well as in a few examples, including the supersymmetric Renyi entropy. Imposing consistency with existing results, we propose a general relation that could hold for sufficiently supersymmetric defects of arbitrary dimension and codimension. Turning to $mathcal{N}=(2,2)$ surface defects in $mathcal{N} geqslant 2$ superconformal field theories, we study the associated chiral algebra. We work out various properties of the modules introduced by the defect in the original chiral algebra. In particular, we find that the one-point function of the stress tensor controls the dimension of the defect identity in chiral algebra, providing a novel way to compute it, once the defect identity is identified. Studying a few examples, we show explicitly how these properties are realized.
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