Super-Laplacians and their symmetries

We put forward new explicit realisations of dS/CFT that relate N = 2 supersymmetric Euclidean vector models with reversed spin-statistics in three dimensions to specific supersymmetric Vasiliev theories in four-dimensional de Sitter space. The partition function of the free supersymmetric vector model deformed by a range of low spin deformations that preserve supersymmetry appears to specify a well-defined wave function with asymptotic de Sitter boundary conditions in the bulk. In particular we find the wave function is globally peaked at undeformed de Sitter space, with a low amplitude for strong deformations. This suggests that supersymmetric de Sitter space is stable in higher-spin gravity and in particular free from ghosts. We speculate this is a limiting case of the de Sitter realizations in exotic string theories.

Section: Dualitymentioning

confidence: 99%

Supersymmetric dS/CFT

Hertog

Tartaglino‐Mazzucchelli

Riet

et al. 2018

“…A full derivation of the solutions of the conformal Killing equations (3.23) will be given elsewhere (see also [68] for related work based on superspace techniques). Here we assume that the pattern emerged in the rank 0 and 1 examples extends to arbitrary values of the rank.…”

Section: Conformal Killing Spinor-tensorsmentioning

confidence: 99%

Higher-spin charges in Hamiltonian form. II. Fermi fields

Campoleoni

Henneaux

Hörtner

et al. 2017

Abstract:We build the asymptotic higher-spin charges associated with "improper" gauge transformations for fermionic higher-spin gauge fields on Anti de Sitter backgrounds of arbitrary dimension. This is achieved within the canonical formalism. We consider massless fields of spin s+1/2, described by a symmetric spinor-tensor of rank s in the Fang-Fronsdal approach. We begin from a detailed analysis of the spin 5/2 example, for which we cast the Fang-Fronsdal action in Hamiltonian form, we derive the charges and we propose boundary conditions on the canonical variables that secure their finiteness. We then extend the computation of charges and the characterisation of boundary conditions to arbitrary halfinteger spin. Our construction generalises to higher-spin fermionic gauge fields the known Hamiltonian derivation of supercharges in AdS supergravity.

“…Time has come to understand the higher symmetries of supersymmetric extensions of the d'Alembertian. To the best of our knowledge, so far there has appeared only one work on the topic, written by Howe and Lindström [51].…”

Section: Symmetries Of the Massless Wess-zumino Operatormentioning

confidence: 99%

“…In 2016, Howe and Lindström [50] (see also [51]) generalised the notion of a conformal Killing tensor to superspace. In the case of N = 1 AdS supersymmetry, their definition is equivalent to imposing the condition (1.4a).…”

mentioning

confidence: 99%

Symmetries of supergravity backgrounds and supersymmetric field theory

Kuzenko

Raptakis

2020

In four spacetime dimensions, all N = 1 supergravity-matter systems can be formulated in the so-called U(1) superspace proposed by Howe in 1981. This paper is devoted to the study of those geometric structures which characterise a background U(1) superspace and are important in the context of supersymmetric field theory in curved space. We introduce (conformal) Killing tensor superfields ℓ (α 1 ...αm)(α 1 ...αn) , with m and n non-negative integers, m + n > 0, and elaborate on their significance in the following cases: (i) m = n = 1; (ii) m − 1 = n = 0; and (iii) m = n > 1. The (conformal) Killing vector superfields ℓ αα generate the (conformal) isometries of curved superspace, which are symmetries of every (conformal) supersymmetric field theory. The (conformal) Killing spinor superfields ℓ α generate extended (conformal) supersymmetry transformations. The (conformal) Killing tensor superfields with m = n > 1 prove to generate all higher symmetries of the (massless) massive Wess-Zumino operator.