Special Issue "Higher Spin Gauge Theories"

A special issue of Universe (ISSN 2218-1997).

Deadline for manuscript submissions: closed (31 October 2017).

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Special Issue Editors

Prof. Dr. Nicolas Boulanger
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Guest Editor
Service de Mécanique et Gravitation, Université de Mons – UMONS 20 Place du Parc, B-7000 Mons, Belgium
Interests: higher spin gauge theories; supergravity and duality; fractional spin fields and anyons; BRST-BV formalism; Weyl invariance in gravity; Poisson Sigma Models; AKSZ quantization; AdS/CFT
Special Issues and Collections in MDPI journals
Dr. Andrea Campoleoni
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Guest Editor
Institut für Theoretische Physik ETH Zurich Wolfgang-Pauli-Str. 27 8093 Zürich, Switzerland
Interests: Higher spin gauge theories; gravitational theories in three space-time dimensions; AdS/CFT

Special Issue Information

Dear Colleagues,

Vasiliev's equations are, to this day, the only known set of consistent and non-linear equations that describe, after linearisation around four dimensional (anti-)de Sitter spacetime, the free propagation of an infinite set of higher-spin gauge fields featuring the graviton. These last two years, new results have been derived in Higher Spin (HS) theory. They partly confirmed some expectations on the subject and they also showed that more work is required for a better understanding of the weak-field expansion of Vasiliev's equations around (A)dS4. On the one hand, the holographic reconstruction of a theory from the free O(N) model in three dimensions seems to reproduce, as expected from the HS/CFT conjecture, a non-abelian gauge theory of higher spin fields in (A)dS4. On the other hand, the Vasiliev equations display some seemingly unavoidable non-localities in their perturbative regime around (A)dS4. These last results raise some questions regarding the status of the HS4/CFT3 duality. In parallel, recent works performed in the light-cone gauge bring back to the scene some results obtained by Metsaev in the early nineties, pointing to the existence of a consistent and interacting HS theory in flat background. This special issue is intended to gather together contributions analyzing these and similar exciting and timely questions on Higher Spin Gauge Theories.

Prof. Dr. Nicolas Boulanger
Dr. Andrea Campoleoni
Guest Editors

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Published Papers (17 papers)

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Open AccessArticle
Asymptotic Charges at Null Infinity in Any Dimension
Universe 2018, 4(3), 47; https://doi.org/10.3390/universe4030047 - 02 Mar 2018
Cited by 23
Abstract
We analyse the conservation laws associated with large gauge transformations of massless fields in Minkowski space. Our aim is to highlight the interplay between boundary conditions and finiteness of the asymptotically conserved charges in any space-time dimension, both even and odd, greater than [...] Read more.
We analyse the conservation laws associated with large gauge transformations of massless fields in Minkowski space. Our aim is to highlight the interplay between boundary conditions and finiteness of the asymptotically conserved charges in any space-time dimension, both even and odd, greater than or equal to three. After discussing nonlinear Yang–Mills theory and revisiting linearised gravity, our investigation extends to cover the infrared behaviour of bosonic massless quanta of any spin. Full article
(This article belongs to the Special Issue Higher Spin Gauge Theories) Printed Edition available
Open AccessArticle
Higher Spin Extension of Fefferman-Graham Construction
Universe 2018, 4(2), 17; https://doi.org/10.3390/universe4020017 - 29 Jan 2018
Cited by 16
Abstract
Fefferman-Graham ambient construction can be formulated as sp ( 2 ) -algebra relations on three Hamiltonian constraint functions on ambient space. This formulation admits a simple extension that leads to higher-spin fields, both conformal gauge fields and usual massless fields on anti-de Sitter [...] Read more.
Fefferman-Graham ambient construction can be formulated as sp ( 2 ) -algebra relations on three Hamiltonian constraint functions on ambient space. This formulation admits a simple extension that leads to higher-spin fields, both conformal gauge fields and usual massless fields on anti-de Sitter spacetime. For the bulk version of the system, we study its possible on-shell version which is formally consistent and reproduces conformal higher-spin fields on the boundary. Interpretation of the proposed on-shell version crucially depends on the choice of the functional class. Although the choice leading to fully interacting higher-spin theory in the bulk is not known, we demonstrate that the system has a vacuum solution describing general higher-spin flat backgrounds. Moreover, we propose a functional class such that the system describes propagation of higher-spin fields over any higher-spin flat background, reproducing all the structures that determine the known nonlinear higher-spin equations. Full article
(This article belongs to the Special Issue Higher Spin Gauge Theories) Printed Edition available
Open AccessEditor’s ChoiceArticle
The ABC of Higher-Spin AdS/CFT
Universe 2018, 4(1), 18; https://doi.org/10.3390/universe4010018 - 19 Jan 2018
Cited by 16
Abstract
In recent literature, one-loop tests of the higher-spin AdS d + 1 /CFT d correspondences were carried out. Here, we extend these results to a more general set of theories in d > 2 . First, we consider the Type B higher spin [...] Read more.
In recent literature, one-loop tests of the higher-spin AdS d + 1 /CFT d correspondences were carried out. Here, we extend these results to a more general set of theories in d > 2 . First, we consider the Type B higher spin theories, which have been conjectured to be dual to CFTs consisting of the singlet sector of N free fermion fields. In addition to the case of N Dirac fermions, we carefully study the projections to Weyl, Majorana, symplectic and Majorana–Weyl fermions in the dimensions where they exist. Second, we explore theories involving elements of both Type A and Type B theories, which we call Type AB. Their spectrum includes fields of every half-integer spin, and they are expected to be related to the U ( N ) / O ( N ) singlet sector of the CFT of N free complex/real scalar and fermionic fields. Finally, we explore the Type C theories, which have been conjectured to be dual to the CFTs of p-form gauge fields, where p = d 2 1 . In most cases, we find that the free energies at O ( N 0 ) either vanish or give contributions proportional to the free-energy of a single free field in the conjectured dual CFT. Interpreting these non-vanishing values as shifts of the bulk coupling constant G N 1 / ( N k ) , we find the values k = 1 , 1 / 2 , 0 , 1 / 2 , 1 , 2 . Exceptions to this rule are the Type B and AB theories in odd d; for them, we find a mismatch between the bulk and boundary free energies that has a simple structure, but does not follow from a simple shift of the bulk coupling constant. Full article
(This article belongs to the Special Issue Higher Spin Gauge Theories) Printed Edition available
Open AccessArticle
Higher Spin Superfield Interactions with the Chiral Supermultiplet: Conserved Supercurrents and Cubic Vertices
Universe 2018, 4(1), 6; https://doi.org/10.3390/universe4010006 - 10 Jan 2018
Cited by 31
Abstract
We investigate cubic interactions between a chiral superfield and higher spin superfields corresponding to irreducible representations of the 4 D , N = 1 super-Poincaré algebra. We do this by demanding an invariance under the most general transformation, linear in the chiral superfield. [...] Read more.
We investigate cubic interactions between a chiral superfield and higher spin superfields corresponding to irreducible representations of the 4 D , N = 1 super-Poincaré algebra. We do this by demanding an invariance under the most general transformation, linear in the chiral superfield. Following Noether’s method we construct an infinite tower of higher spin supercurrent multiplets which are quadratic in the chiral superfield and include higher derivatives. The results are that a single, massless, chiral superfield can couple only to the half-integer spin supermultiplets ( s + 1 , s + 1 / 2 ) and for every value of spin there is an appropriate improvement term that reduces the supercurrent multiplet to a minimal multiplet which matches that of superconformal higher spins. On the other hand a single, massive, chiral superfield can couple only to higher spin supermultiplets of type ( 2 l + 2 , 2 l + 3 / 2 ) (only odd values of s, s = 2 l + 1 ) and there is no minimal multiplet. Furthermore, for the massless case we discuss the component level higher spin currents and provide explicit expressions for the integer and half-integer spin conserved currents together with a R-symmetry current. Full article
(This article belongs to the Special Issue Higher Spin Gauge Theories) Printed Edition available
Open AccessArticle
A Note on Rectangular Partially Massless Fields
Universe 2018, 4(1), 4; https://doi.org/10.3390/universe4010004 - 01 Jan 2018
Cited by 4
Abstract
We study a class of non-unitary so ( 2 , d ) representations (for even values of d), describing mixed-symmetry partially massless fields which constitute natural candidates for defining higher-spin singletons of higher order. It is shown that this class of so [...] Read more.
We study a class of non-unitary so ( 2 , d ) representations (for even values of d), describing mixed-symmetry partially massless fields which constitute natural candidates for defining higher-spin singletons of higher order. It is shown that this class of so ( 2 , d ) modules obeys of natural generalisation of a couple of defining properties of unitary higher-spin singletons. In particular, we find out that upon restriction to the subalgebra so ( 2 , d - 1 ) , these representations branch onto a sum of modules describing partially massless fields of various depths. Finally, their tensor product is worked out in the particular case of d = 4 , where the appearance of a variety of mixed-symmetry partially massless fields in this decomposition is observed. Full article
(This article belongs to the Special Issue Higher Spin Gauge Theories) Printed Edition available
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Open AccessFeature PaperArticle
A Note on (Non)-Locality in Holographic Higher Spin Theories
Universe 2018, 4(1), 2; https://doi.org/10.3390/universe4010002 - 01 Jan 2018
Cited by 30
Abstract
It was argued recently that the holographic higher spin theory features non-local interactions. We further elaborate on these results using the Mellin representation. The main difficulty previously encountered in this method is that the Mellin amplitude for the free theory correlator is ill-defined. [...] Read more.
It was argued recently that the holographic higher spin theory features non-local interactions. We further elaborate on these results using the Mellin representation. The main difficulty previously encountered in this method is that the Mellin amplitude for the free theory correlator is ill-defined. To resolve this problem, instead of literally applying the standard definition, we propose to define this amplitude by linearity using decompositions, where each term has the associated Mellin amplitude well-defined. Up to a sign, the resulting amplitude is equal to the Mellin amplitude for the singular part of the quartic vertex in the bulk theory and, hence, can be used to analyze bulk locality. From this analysis we find that the scalar quartic self-interaction vertex in the holographic higher spin theory has a singularity of a special form, which can be distinguished from generic bulk exchanges. We briefly discuss the physical interpretation of such singularities and their relation to the Noether procedure. Full article
(This article belongs to the Special Issue Higher Spin Gauge Theories) Printed Edition available
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Open AccessArticle
Gauge Non-Invariant Higher-Spin Currents in AdS4
Universe 2017, 3(4), 78; https://doi.org/10.3390/universe3040078 - 16 Nov 2017
Cited by 4
Abstract
Conserved currents of any spin t > 0 built from bosonic symmetric massless gauge fields of arbitrary integer spins s 1 + s 2 > t in A d S 4 are found. Analogous to the case of 4 d Minkowski space, currents [...] Read more.
Conserved currents of any spin t > 0 built from bosonic symmetric massless gauge fields of arbitrary integer spins s 1 + s 2 > t in A d S 4 are found. Analogous to the case of 4 d Minkowski space, currents considered in this paper are not gauge invariant, but generate gauge-invariant conserved charges. Full article
(This article belongs to the Special Issue Higher Spin Gauge Theories) Printed Edition available
Open AccessArticle
Exploring Free Matrix CFT Holographies at One-Loop
Universe 2017, 3(4), 77; https://doi.org/10.3390/universe3040077 - 09 Nov 2017
Cited by 7
Abstract
We extend our recent study on the duality between stringy higher spin theories and free conformal field theories (CFTs) in the S U ( N ) adjoint representation to other matrix models, namely the free S O ( N ) and S p [...] Read more.
We extend our recent study on the duality between stringy higher spin theories and free conformal field theories (CFTs) in the S U ( N ) adjoint representation to other matrix models, namely the free S O ( N ) and S p ( N ) adjoint models as well as the free U ( N ) × U ( M ) bi-fundamental and O ( N ) × O ( M ) bi-vector models. After determining the spectrum of the theories in the planar limit by Polya counting, we compute the one loop vacuum energy and Casimir energy for their respective bulk duals by means of the Character Integral Representation of the Zeta Function (CIRZ) method, which we recently introduced. We also elaborate on possible ambiguities in the application of this method. Full article
(This article belongs to the Special Issue Higher Spin Gauge Theories) Printed Edition available
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Open AccessArticle
Higher Spin Matrix Models
Universe 2017, 3(4), 74; https://doi.org/10.3390/universe3040074 - 30 Oct 2017
Abstract
We propose a hybrid class of theories for higher spin gravity and matrix models, i.e., which handle simultaneously higher spin gravity fields and matrix models. The construction is similar to Vasiliev’s higher spin gravity, but part of the equations of motion are provided [...] Read more.
We propose a hybrid class of theories for higher spin gravity and matrix models, i.e., which handle simultaneously higher spin gravity fields and matrix models. The construction is similar to Vasiliev’s higher spin gravity, but part of the equations of motion are provided by the action principle of a matrix model. In particular, we construct a higher spin (gravity) matrix model related to type IIB matrix models/string theory that have a well defined classical limit, and which is compatible with higher spin gravity in A d S space. As it has been suggested that higher spin gravity should be related to string theory in a high energy (tensionless) regime, and, therefore to M-Theory, we expect that our construction will be useful to explore concrete connections. Full article
(This article belongs to the Special Issue Higher Spin Gauge Theories) Printed Edition available
Open AccessArticle
Three Point Functions in Higher Spin AdS3 Holography with 1/N Corrections
Universe 2017, 3(4), 70; https://doi.org/10.3390/universe3040070 - 09 Oct 2017
Cited by 7
Abstract
We examine three point functions with two scalar operators and a higher spin current in 2d W N minimal model to the next non-trivial order in 1 / N expansion. The minimal model was proposed to be dual to a 3d higher spin [...] Read more.
We examine three point functions with two scalar operators and a higher spin current in 2d W N minimal model to the next non-trivial order in 1 / N expansion. The minimal model was proposed to be dual to a 3d higher spin gauge theory, and 1 / N corrections should be interpreted as quantum effects in the dual gravity theory. We develop a simple and systematic method to obtain three point functions by decomposing four point functions of scalar operators with Virasoro conformal blocks. Applying the method, we reproduce known results at the leading order in 1 / N and obtain new ones at the next leading order. As confirmation, we check that our results satisfy relations among three point functions conjectured before. Full article
(This article belongs to the Special Issue Higher Spin Gauge Theories) Printed Edition available
Open AccessArticle
Induced Action for Conformal Higher Spins from Worldline Path Integrals
Universe 2017, 3(3), 64; https://doi.org/10.3390/universe3030064 - 04 Sep 2017
Cited by 20
Abstract
Conformal higher spin (CHS) fields, yet being non unitary, provide a remarkable example of a consistent interacting higher spin theory in flat space background, that is local to all orders. The non-linear action is defined as the logarithmically UV divergent part of a [...] Read more.
Conformal higher spin (CHS) fields, yet being non unitary, provide a remarkable example of a consistent interacting higher spin theory in flat space background, that is local to all orders. The non-linear action is defined as the logarithmically UV divergent part of a one-loop scalar effective action. In this paper we take a particle model, that describes the interaction of a scalar particle to the CHS background, and compute its path integral on the circle. We thus provide a worldline representation for the CHS action, and rederive its quadratic part. We plan to come back to the subject, to compute cubic and higher vertices, in a future work. Full article
(This article belongs to the Special Issue Higher Spin Gauge Theories) Printed Edition available
Open AccessArticle
Infinite Spin Fields in d = 3 and Beyond
Universe 2017, 3(3), 63; https://doi.org/10.3390/universe3030063 - 30 Aug 2017
Cited by 22
Abstract
In this paper, we consider the frame-like formulation for the so-called infinite (continuous) spin representations of the Poincare algebra. In the three-dimensional case, we give explicit Lagrangian formulation for bosonic and fermionic infinite spin fields (including the complete sets of the gauge-invariant objects [...] Read more.
In this paper, we consider the frame-like formulation for the so-called infinite (continuous) spin representations of the Poincare algebra. In the three-dimensional case, we give explicit Lagrangian formulation for bosonic and fermionic infinite spin fields (including the complete sets of the gauge-invariant objects and all the necessary extra fields). Moreover, we find the supertransformations for the supermultiplet containing one bosonic and one fermionic field, leaving the sum of their Lagrangians invariant. Properties of such fields and supermultiplets in four and higher dimensions are also briefly discussed. Full article
(This article belongs to the Special Issue Higher Spin Gauge Theories) Printed Edition available
Open AccessArticle
AdS/CFT in Fractional Dimension and Higher-Spins at One Loop
Universe 2017, 3(3), 61; https://doi.org/10.3390/universe3030061 - 14 Aug 2017
Cited by 18
Abstract
Large-N, ϵ -expansion or the conformal bootstrap allow one to make sense of some of conformal field theories in non-integer dimension, which suggests that AdS/CFT may also extend to fractional dimensions. It was shown recently that the sphere free energy and [...] Read more.
Large-N, ϵ -expansion or the conformal bootstrap allow one to make sense of some of conformal field theories in non-integer dimension, which suggests that AdS/CFT may also extend to fractional dimensions. It was shown recently that the sphere free energy and the a-anomaly coefficient of the free scalar field can be reproduced as a one-loop effect in the dual higher-spin theory in a number of integer dimensions. We extend this result to all integer and also to fractional dimensions. Upon changing the boundary conditions in the higher-spin theory the sphere free energy of the large-N Wilson-Fisher CFT can also be reproduced from the higher-spin side. Full article
(This article belongs to the Special Issue Higher Spin Gauge Theories) Printed Edition available
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Review

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Open AccessReview
Frame- and Metric-Like Higher-Spin Fermions
Universe 2018, 4(2), 34; https://doi.org/10.3390/universe4020034 - 11 Feb 2018
Cited by 7
Abstract
Conventional descriptions of higher-spin fermionic gauge fields appear in two varieties: the Aragone–Deser–Vasiliev frame-like formulation and the Fang–Fronsdal metric-like formulation. We review, clarify and elaborate on some essential features of these two. For frame-like free fermions in Anti-de Sitter space, one can present [...] Read more.
Conventional descriptions of higher-spin fermionic gauge fields appear in two varieties: the Aragone–Deser–Vasiliev frame-like formulation and the Fang–Fronsdal metric-like formulation. We review, clarify and elaborate on some essential features of these two. For frame-like free fermions in Anti-de Sitter space, one can present a gauge-invariant Lagrangian description such that the constraints on the field and the gauge parameters mimic their flat-space counterparts. This simplifies the explicit demonstration of the equivalence of the two formulations at the free level. We comment on the subtleties that may arise in an interacting theory. Full article
(This article belongs to the Special Issue Higher Spin Gauge Theories) Printed Edition available
Open AccessReview
Higher Spins without (Anti-)de Sitter
Universe 2018, 4(1), 20; https://doi.org/10.3390/universe4010020 - 19 Jan 2018
Cited by 6
Abstract
Can the holographic principle be extended beyond the well-known AdS/CFT correspondence? During the last couple of years, there has been a substantial amount of research trying to find answers for this question. In this work, we provide a review of recent developments of [...] Read more.
Can the holographic principle be extended beyond the well-known AdS/CFT correspondence? During the last couple of years, there has been a substantial amount of research trying to find answers for this question. In this work, we provide a review of recent developments of three-dimensional theories of gravity with higher spin symmetries. We focus in particular on a proposed holographic duality involving asymptotically flat spacetimes and higher spin extended bms 3 symmetries. In addition, we also discuss developments concerning relativistic and nonrelativistic higher spin algebras. As a special case, Carroll gravity will be discussed in detail. Full article
(This article belongs to the Special Issue Higher Spin Gauge Theories) Printed Edition available
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Open AccessReview
Higher Spin Fields in Hyperspace. A Review
Universe 2018, 4(1), 7; https://doi.org/10.3390/universe4010007 - 03 Jan 2018
Cited by 8
Abstract
We give an introduction to the so-called tensorial, matrix or hyperspace approach to the description of massless higher-spin fields. Full article
(This article belongs to the Special Issue Higher Spin Gauge Theories) Printed Edition available
Open AccessReview
On Exact Solutions and Perturbative Schemes in Higher Spin Theory
Universe 2018, 4(1), 5; https://doi.org/10.3390/universe4010005 - 01 Jan 2018
Cited by 8
Abstract
We review various methods for finding exact solutions of higher spin theory in four dimensions, and survey the known exact solutions of (non)minimal Vasiliev’s equations. These include instanton-like and black hole-like solutions in (A)dS and Kleinian spacetimes. A perturbative construction of solutions with [...] Read more.
We review various methods for finding exact solutions of higher spin theory in four dimensions, and survey the known exact solutions of (non)minimal Vasiliev’s equations. These include instanton-like and black hole-like solutions in (A)dS and Kleinian spacetimes. A perturbative construction of solutions with the symmetries of a domain wall is also described. Furthermore, we review two proposed perturbative schemes: one based on perturbative treatment of the twistor space field equations followed by inverting Fronsdal kinetic terms using standard Green’s functions; and an alternative scheme based on solving the twistor space field equations exactly followed by introducing the spacetime dependence using perturbatively defined gauge functions. Motivated by the need to provide a higher spin invariant characterization of the exact solutions, aspects of a proposal for a geometric description of Vasiliev’s equation involving an infinite dimensional generalization of anti de Sitter space are revisited and improved. Full article
(This article belongs to the Special Issue Higher Spin Gauge Theories) Printed Edition available
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