Higher-order singletons, partially massless fields, and their boundary values in the ambient approach
TL;DR: In this paper, a fully-gauge and o(d, 2 ) -covariant approach to boundary values of AdS d + 1 gauge fields is presented.
About: This article is published in Nuclear Physics.The article was published on 2013-11-11 and is currently open access. It has received 161 citations till now. The article focuses on the topics: Boundary value problem & Symmetry (physics).
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TL;DR: In this article, the authors consider general-symmetry higher spin fields in AdS5 and derive the expressions for their one-loop corrections to vacuum energy and the associated 4d boundary conformal anomaly a-coefficient.
Abstract: We consider general-symmetry higher spin fields in AdS5 and derive the expressions for their one-loop corrections to vacuum energy E
c
and the associated 4d boundary conformal anomaly a-coefficient. We propose a similar expression for the second conformal anomaly c-coefficient. We show that all the three quantities (E
c
, a, c) computed for $$ \mathcal{N}=8 $$
gauged 5d supergravity are equal to $$ -\frac{1}{2} $$
of their values for $$ \mathcal{N}=4 $$
conformal 4d supergravity and also to twice the values for $$ \mathcal{N}=4 $$
Maxwell multiplet. This gives a 5d derivation of the fact that the system of $$ \mathcal{N}=4 $$
conformal supergravity and four $$ \mathcal{N}=4 $$
Maxwell multiplets is anomaly free. The values of (E
c
, a, c) for the states at level p of Kaluza-Klein tower of 10d type IIB supergravity compactified on S
5 turn out to be equal to those for p copies of $$ \mathcal{N}=4 $$
Maxwell multiplets. This may be related to the fact that these states appear in the tensor product of p superdoubletons. Under a natural regularization of the sum over p, the full 10d supergravity contribution is then minus that of one Maxwell multiplet, in agreement with the standard adjoint AdS/CFT duality (SU(N) SYM contribution is N
2 − 1 times that of one Maxwell multiplet). We also verify the matching of (E
c
, a, c) for spin 0 and $$ \frac{1}{2} $$
boundary theory cases of vectorial AdS/CFT duality. The consistency conditions for vectorial AdS/CFT turn out to be equivalent to the cancellation of anomalies in the closely related 4d conformal higher spin theories. In addition, we study novel example of the vectorial AdS/CFT duality when the boundary theory is described by free spin 1 fields and is dual to a particular higher spin theory in AdS5 containing fields in mixed-symmetry representations. We also discuss its supersymmetric generalizations.
171 citations
TL;DR: In this article, the authors studied 4-dimensional higher-derivative conformal higher-spin (CHS) fields generalizing Weyl graviton and conformal gravitino on curved Einstein-space backgrounds like (A)dS or sphere and Ricci-flat spaces.
163 citations
Cites background from "Higher-order singletons, partially ..."
...A discussion of this field and some hints of its connection to CHS fields appear in [49]....
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...“Partially massless” (PM) higher spin fields in (A)dSD exist also for s > 2 [36, 37, 38, 39, 40, 41, 42, 43] (see also [44, 45, 49]) and, as we shall suggest, are directly related to the factorization of the CHS operators on (A)dS4 background for all s....
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TL;DR: In this paper, the authors consider general-symmetry higher spin fields in AdS_5 and derive expressions for their one-loop corrections to vacuum energy E and the associated 4d boundary conformal anomaly a-coefficient.
Abstract: We consider general-symmetry higher spin fields in AdS_5 and derive expressions for their one-loop corrections to vacuum energy E and the associated 4d boundary conformal anomaly a-coefficient. We a propose a similar expression for the second conformal anomaly c-coefficient. We show that all the three quantities (E, a, c) computed for N=8 gauged 5d supergravity are -1/2 of the values for N=4 conformal 4d supergravity and also twice the values for N=4 Maxwell multiplet. This gives 5d derivation of the fact that the system of N=4 conformal supergravity and four N=4 Maxwell multiplets is anomaly free. The values of (E, a, c) for the states at level p of Kaluza-Klein tower of 10d type IIB supergravity compactified on S^5 turn out to be equal to those for p copies of N=4 Maxwell multiplets. This may be related to the fact that these states appear in the tensor product of p superdoubletons. Under a natural regularization of the sum over p, the full 10d supergravity contribution is then minus that of the Maxwell multiplet, in agreement with the standard adjoint AdS/CFT duality (SU(n) SYM contribution is n^2-1 of one Maxwell multiplet). We also verify the matching of (E, a, c) for spin 0 and 1/2 boundary theory cases of vectorial AdS/CFT duality. The consistency conditions for vectorial AdS/CFT turn out to be equivalent to the cancellation of anomalies in the closely related 4d conformal higher spin theories. In addition, we study novel example of vectorial AdS/CFT duality when the boundary theory is described by free spin 1 fields and is dual to a particular higher spin theory in AdS_5 containing fields in mixed-symmetry representations. We also discuss its supersymmetric generalizations.
125 citations
TL;DR: In this paper, it was shown that the partition function of the set of all free massless higher spins s = 0, 1, 2, 3,... in flat space is equal to one: the ghost determinants cancel against the 'physical' ones or, equivalently, the (regularized) total number of degrees of freedom vanishes.
Abstract: We observe that the partition function of the set of all free massless higher spins s = 0, 1, 2, 3,... in flat space is equal to one: the ghost determinants cancel against the 'physical' ones or, equivalently, the (regularized) total number of degrees of freedom vanishes. This reflects large underlying gauge symmetry and suggests analogy with supersymmetric or topological theory. The Z = 1 property extends also to the AdS background, i.e. the 1-loop vacuum partition function of Vasiliev theory is equal to 1 (assuming a particular regularization of the sum over spins); this was noticed earlier as a consistency requirement for the vectorial AdS/CFT duality. We find that Z = 1 is true also in the conformal higher spin theory (with higher-derivative kinetic terms) expanded near flat or conformally flat S4 background. We also consider the partition function of free conformal theory of symmetric traceless rank s tensor field which has 2-derivative kinetic term but only scalar gauge invariance in flat 4d space. This non-unitary theory has Weyl-invariant action in curved background and it corresponds to 'partially massless' field in AdS5. We discuss in detail the special case of s = 2 (or 'conformal graviton'), compute the corresponding conformal anomaly coefficients and compare them with previously found expressions for generic representations of conformal group in 4 dimensions.
116 citations
TL;DR: In this paper, the authors generalize this connection to any classical Lie algebra and consider the corresponding higher-spin algebras relevant to Vasiliev's equations in various dimensions, which can be interpreted as the symmetries of the minimal representation of the isometry algebra.
Abstract: The higher-spin (HS) algebras relevant to Vasiliev’s equations in various dimensions can be interpreted as the symmetries of the minimal representation of the isometry algebra After discussing this connection briefly, we generalize this concept to any classical Lie algebra and consider the corresponding HS algebras For $ \mathfrak{s}{{\mathfrak{p}}_{2N }} $
and $ \mathfrak{s}{{\mathfrak{o}}_N} $
, the minimal representations are unique so we get unique HS algebras For $ \mathfrak{s}{{\mathfrak{l}}_N} $
, the minimal representation has one-parameter family, so does the corresponding HS algebra The $ \mathfrak{s}{{\mathfrak{o}}_N} $
HS algebra is what underlies the Vasiliev theory while the $ \mathfrak{s}{{\mathfrak{l}}_2} $
one coincides with the 3D HS algebra hs[λ] Finally, we derive the explicit expression of the structure constant of these algebras — more precisely, their bilinear and trilinear forms Several consistency checks are carried out for our results
105 citations
Cites background from "Higher-order singletons, partially ..."
...Actually these have been already explored by a number of authors: see [30–32] for the mathematics literature and [33] for the physics one....
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References
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TL;DR: In this article, the authors review the formalism of holographic renormalization and apply it to holographic RG flows, including the derivation of the on-shell renormalized action, holographic Ward identities, anomalies and renormalisation group (RG) equations.
Abstract: We review the formalism of holographic renormalization. We start by discussing mathematical results on asymptotically anti-de Sitter (AdS) spacetimes. We then outline the general method of holographic renormalization. The method is illustrated by working all details in a simple example: a massive scalar field on anti-de Sitter spacetime. The discussion includes the derivation of the on-shell renormalized action, holographic Ward identities, anomalies and renormalization group (RG) equations, and the computation of renormalized one-, two- and four-point functions. We then discuss the application of the method to holographic RG flows. We also show that the results of the near-boundary analysis of asymptotically AdS spacetimes can be analytically continued to apply to asymptotically de Sitter spacetimes. In particular, it is shown that the Brown–York stress energy tensor of de Sitter spacetime is equal, up to a dimension-dependent sign, to the Brown–York stress energy tensor of an associated AdS spacetime.
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TL;DR: In this article, a general relation between theories of infinite number of higher-spin massless gauge fields in AdS d + 1 and large N conformal theories in d dimensions containing N -component vector fields was proposed.
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TL;DR: In this article, nonlinear field equations for totally symmetric bosonic massless fields of all spins in any dimension are presented, and a nonlinear nonlinear model of the field equations is proposed.
756 citations
TL;DR: In this paper, it was shown that there is a bijective correspondence between equivalence classes of asymptotic reducibility parameters and (n−2)-forms in the context of Lagrangian gauge theories.
744 citations
"Higher-order singletons, partially ..." refers background in this paper
...ions. The space of global reducibility parameters is an invariant characteristic of a gauge system, i.e. independent of the chosen (equivalent) descriptions. This is known in a rather general context [51] and will be explicitly demonstrated shortly in the case of free systems. In particular, one can use any equivalent formulation to identify it. For instance, in the case of PM fields it is convenient t...
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...ously, higher global reducibilities are described by Ω-cohomology at ghost degree−2,−3 etc. Note that reducibility parameters are directly related to surface charges (see [52] for AdS gauge fields and [51] for the general case) and these notions remain meaningful at nonlinear level as well. To make contact with the literature, let us mention that in the unfolded formulation of HS fields the module of 1-...
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