arXiv subjects

Daniel Hutchings

Publications and source records attributed to Daniel Hutchings.

6 recordsLinked to original sources

arXiv2024

Spin-$(s,j)$ projectors and gauge-invariant spin-$s$ actions in maximally symmetric backgrounds

Given a maximally symmetric $d$-dimensional background with isometry algebra $\mathfrak{g}$, a symmetric and traceless rank-$s$ field $ϕ_{a(s)}$ satisfying the massive Klein-Gordon equation furnishes a collection of massive $\mathfrak{g}$-representations with spins $j\in \{0,1,\cdots,s\}$. In this paper we construct the spin-$(s,j)$ projectors, which are operators that isolate the part of $ϕ_{a(s)}$ that furnishes the representation from this collection carrying spin $j$. In the case of an (anti-)de Sitter ((A)dS$_d$) background, we find that the poles of the projectors encode information about (partially-)massless representations, in agreement with observations made earlier in $d=3,4$. We then use these projectors to facilitate a systematic derivation of two-derivative actions with a propagating massless spin-$s$ mode. In addition to reproducing the massless spin-$s$ Fronsdal action, this analysis generates new actions possessing higher-depth gauge symmetry. In (A)dS$_d$ we also derive the action for a partially-massless spin-$s$ depth-$t$ field with $1\leq t \leq s$. The latter utilises the minimum number of auxiliary fields, and corresponds to the action originally proposed by Zinoviev after gauging away all Stückelberg fields. Some higher-derivative actions are also presented, and in $d=3$ are used to construct (i) generalised higher-spin Cotton tensors in (A)dS$_3$; and (ii) topologically-massive actions with higher-depth gauge symmetry. Finally, in four-dimensional $\mathcal{N}=1$ Minkowski superspace, we provide closed-form expressions for the analogous superprojectors.

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arXiv2023

Superspin projection operators and off-shell higher-spin supermultiplets on Minkowski and anti-de Sitter superspace

This thesis is dedicated to the study of (super)spin projection operators and their applications on maximally symmetric (super)space backgrounds in three and four dimensions. On such backgrounds, the irreducible representations of the associated isometry (super)algebra may be realised on the space of tensor (super)fields satisfying certain differential constraints. The (super)spin projectors isolate the component of an unconstrained (super)field which furnishes the irreducible representation with maximal (super)spin. The explicit form of these (super)projectors are found in the following backgrounds: three-dimensional ($3d$) $\mathcal{N}$-extended Minkowski superspace $\mathbb{M}^{3|2 \mathcal{N}}$; $3d$ (anti-)de Sitter space (A)dS$_3$; $3d$ $\mathcal{N} = 1$ anti-de Sitter superspace AdS$^{3|2}$; four-dimensional ($4d$) $\mathcal{N} = 1$ anti-de Sitter superspace AdS$^{4|4}$; and $4d$ $\mathcal{N} = 2$ anti-de Sitter superspace AdS$^{4|8}$. An array of novel applications are investigated, with an emphasis placed on the interplay between (super)projectors and (super)conformal higher-spin theory. Another major component of this thesis consists of a detailed study of massless higher-spin gauge models with $\mathcal{N} = 2$ AdS supersymmetry in three dimensions. We find that every known higher-spin theory with $(1, 1)$ AdS supersymmetry decomposes into a sum of two off-shell $(1, 0)$ supermultiplets which belong to three series of inequivalent higher-spin gauge models.

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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.

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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

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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arXiv2019

Linearised actions for $\cal N$-extended (higher-spin) superconformal gravity

The off-shell actions for $\cal N$-extended conformal supergravity theories in three dimensions were formulated in [1,2] for $1\leq {\cal N} \leq 6$ using a universal approach. Each action is generated by a closed super three-form which is constructed in terms of the constrained geometry of $\cal N$-extended conformal superspace. In this paper we initiate a program to recast these actions (and to formulate their higher-spin counterparts) in terms of unconstrained gauge prepotentials as integrals over the full superspace. We derive transverse projection operators in $\cal N$-extended Minkowski superspace and then use them to construct linearised rank-$n$ super-Cotton tensors and off-shell $\cal N$-extended superconformal actions. We also propose off-shell gauge-invariant actions to describe massive higher-spin supermultiplets in $\cal N$-extended supersymmetry. Our analysis leads to general expressions for identically conserved higher-spin current multiplets in $\cal N$-extended supersymmetry.

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