arXiv subjects

Xavier Bekaert

Publications and source records attributed to Xavier Bekaert.

At least 55 records · Page 3Linked to original sources

arXiv2015

Quartic AdS Interactions in Higher-Spin Gravity from Conformal Field Theory

Clarifying the locality properties of higher-spin gravity is a pressing task, but notoriously difficult due to the absence of a weakly-coupled flat regime. The simplest non-trivial case where this question can be addressed is the quartic self-interaction of the AdS scalar field present in the higher-spin multiplet. We investigate this issue in the context of the holographic duality between the minimal bosonic higher-spin theory on AdS$_4$ and the free $O\left(N\right)$ vector model in three dimensions. In particular, we determine the exact explicit form of the derivative expansion of the bulk scalar quartic vertex. The quartic vertex is obtained from the field theory four-point function of the operator dual to the bulk scalar, by making use of our previous results for the Witten diagrams of higher-spin exchanges. This is facilitated by establishing the conformal block expansions of both the boundary four-point function and the dual bulk Witten diagram amplitudes. We show that the vertex we find satisfies a generalised notion of locality.

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arXiv2015

Connections and dynamical trajectories in generalised Newton-Cartan gravity I. An intrinsic view

The "metric" structure of nonrelativistic spacetimes consists of a one-form (the absolute clock) whose kernel is endowed with a positive-definite metric. Contrarily to the relativistic case, the metric structure and the torsion do not determine a unique Galilean (i.e. compatible) connection. This subtlety is intimately related to the fact that the timelike part of the torsion is proportional to the exterior derivative of the absolute clock. When the latter is not closed, torsionfreeness and metric-compatibility are thus mutually exclusive. We will explore generalisations of Galilean connections along the two corresponding alternative roads in a series of papers. In the present one, we focus on compatible connections and investigate the equivalence problem (i.e. the search for the necessary data allowing to uniquely determine connections) in the torsionfree and torsional cases. More precisely, we characterise the affine structure of the spaces of such connections and display the associated model vector spaces. In contrast with the relativistic case, the metric structure does not single out a privileged origin for the space of metric-compatible connections. In our construction, the role of the Levi-Civita connection is played by a whole class of privileged origins, the so-called torsional Newton-Cartan (TNC) geometries recently investigated in the literature. Finally, we discuss a generalisation of Newtonian connections to the torsional case.

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arXiv2014

Embedding nonrelativistic physics inside a gravitational wave

Gravitational waves with parallel rays are known to have remarkable properties: Their orbit space of null rays possesses the structure of a non-relativistic spacetime of codimension-one. Their geodesics are in one-to-one correspondence with dynamical trajectories of a non-relativistic system. Similarly, the null dimensional reduction of Klein-Gordon's equation on this class of gravitational waves leads to a Schroedinger equation on curved space. These properties are generalized to the class of gravitational waves with a null Killing vector field, of which we propose a new geometric definition, as conformally equivalent to the previous class and such that the Killing vector field is preserved. This definition is instrumental for performing this generalization, as well as various applications. In particular, results on geodesic completeness are extended in a similar way. Moreover, the classification of the subclass with constant scalar invariants is investigated.

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arXiv2014

Towards holographic higher-spin interactions: Four-point functions and higher-spin exchange

Within holography, we calculate the contribution of an arbitrary spin-s gauge boson exchange in $AdS_{d+1}$ to the four-point function with scalar operators on the boundary. As an important ingredient, we first compute the complete bulk-to-bulk propagators for massless bosonic higher-spin fields in the metric-like formulation, in any dimension and in various gauges. The split representation of the bulk-to-bulk propagators in terms of bulk-to-boundary propagators allows to present the higher-spin exchange diagram in the form of a conformal partial wave expansion. Our results provide a step towards the larger goal of the holographic reconstruction of bulk interactions, and of clarifying bulk locality.

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arXiv2014

Flato-Fronsdal theorem for higher-order singletons

We prove a generalised Flato-Fronsdal theorem for higher-order, scalar and spinor, singletons. In the resulting infinite tower of bulk higher-spin fields, we point out the occurrence of partially-massless fields of all depths. This leads us to conjecture a holographic duality between a higher-spin gravity theory around $AdS_{d+1}$ with the aforementioned spectrum of fields, and a free $CFT_d$ of fundamental (higher-order) scalar and spinor singletons. As a first check of this conjecture, we find that the total Casimir energy vanishes at one loop.

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arXiv2014

Partition function of free conformal higher spin theory

We compute the canonical partition function Z of non-interacting conformal higher spin (CHS) theory viewed as a collection of free spin s CFT's in R^d. We discuss in detail the 4-dimensional case (where s=1 is the standard Maxwell vector, s=2 is the Weyl graviton, etc.), but also present a generalization for all even dimensions d. Z may be found by counting the numbers of conformal operators and their descendants (modulo gauge identities and equations of motion) weighted by scaling dimensions. This conformal operator counting method requires a careful analysis of the structure of characters of relevant (conserved current, shadow field and conformal Killing tensor) representations of the conformal algebra so(d,2). There is also a close relation to massless higher spin partition functions with alternative boundary conditions in AdS_{d+1}. The same partition function Z may also be computed from the CHS path integral on a curved S^1 x S^{d-1} background. This allows us to determine a simple factorized form of the CHS kinetic operator on this conformally flat background. Summing the individual conformal spin contributions Z_s over all spins we obtain the total partition function of the CHS theory. We also find the corresponding Casimir energy and show that it vanishes if one uses the same regularization prescription that implies the cancellation of the total conformal anomaly a-coefficient. This happens to be true in all even dimensions d >= 2.

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arXiv2013

Higher order singletons, partially massless fields and their boundary values in the ambient approach

Using ambient space we develop a fully gauge and o(d,2) covariant approach to boundary values of AdS(d+1) gauge fields. It is applied to the study of (partially) massless fields in the bulk and (higher-order) conformal scalars, i.e. singletons, as well as (higher-depth) conformal gauge fields on the boundary. In particular, we identify the corresponding Fradkin-Tseytlin equations as obstructions to the extension of the off-shell boundary value to the bulk, generalizing the usual considerations for the holographic anomalies to the partially massless fields. We also relate the background fields for the higher-order singleton to the boundary values of partially massless fields and prove the appropriate generalization of the Flato-Fronsdal theorem, which is in agreement with the known structure of symmetries for the higher-order wave operator. All these facts support the following generalization of the higher-spin holographic duality: the O(N) model at a multicritical isotropic Lifshitz point should be dual to the theory of partially massless symmetric tensor fields described by the Vasiliev equations based on the higher-order singleton symmetry algebra.

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arXiv2013

Notes on the ambient approach to boundary values of AdS gauge fields

The ambient space of dimension d+2 allows to formulate both fields on AdS(d+1) and conformal fields in d dimensions such that the symmetry algebra o(d,2) is realized linearly. We elaborate an ambient approach to the boundary analysis of gauge fields on anti de Sitter spacetime. More technically, we use its parent extension where fields are still defined on AdS or conformal space through arbitrary intrinsic coordinates while the ambient construction works in the target space. In this way, a manifestly local and o(d,2)-covariant formulation of the boundary behaviour of massless symmetric tensor gauge fields on AdS(d+1) spacetime is obtained. As a byproduct, we identify some useful ambient formulation for Fronsdal fields, conformal currents and shadow fields along with a concise generating-function formulation of the Fradkin-Tseytlin conformal fields somewhat similar to the one obtained by Metsaev. We also show how this approach extends to more general gauge theories and discuss its relation to the unfolded derivation of the boundary dynamics recently proposed by Vasiliev.

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arXiv2012

Towards a gravity dual of the unitary Fermi gas

Inspired by the method of null dimensional reduction and by the holographic correspondence between Vasiliev's higher-spin gravity and the critical O(N) model, a bulk dual of the unitary and the ideal non-relativistic Fermi gases is proposed.

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arXiv2012

Comments on higher-spin holography

The conjectured holographic duality between vector models with quartic interaction and higher-spin field theory in the bulk is reviewed, with emphasis on some versions and generalisations (higher dimensions, beyond the singlet sector, etc) which have not been much investigated yet. The strongest form of the conjecture assumes that it holds for any (not necessarily large) number of massless scalar fields and for any value of the coupling constant. Since the quartic interaction is of double-trace type, the exact duality (for any value of the coupling constant) automatically follows from its validity at the Gaussian fixed point (for vanishing coupling constant). The validity of the latter also implies that unbroken higher spin symmetries should prevent quantum corrections in the bulk.

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arXiv2012

Symmetries and currents of the ideal and unitary Fermi gases

The maximal algebra of symmetries of the free single-particle Schroedinger equation is determined and its relevance for the holographic duality in non-relativistic Fermi systems is investigated. This algebra of symmetries is an infinite dimensional extension of the Schroedinger algebra, it is isomorphic to the Weyl algebra of quantum observables, and it may be interpreted as a non-relativistic higher-spin algebra. The associated infinite collection of Noether currents bilinear in the fermions are derived from their relativistic counterparts via a light-like dimensional reduction. The minimal coupling of these currents to background sources is rewritten in a compact way by making use of Weyl quantisation. Pushing forward the similarities with the holographic correspondence between the minimal higher-spin gravity and the critical O(N) model, a putative bulk dual of the unitary and the ideal Fermi gases is discussed.

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arXiv2012

How higher-spin gravity surpasses the spin two barrier: no-go theorems versus yes-go examples

Aiming at non-experts, we explain the key mechanisms of higher-spin extensions of ordinary gravity. We first overview various no-go theorems for low-energy scattering of massless particles in flat spacetime. In doing so we dress a dictionary between the S-matrix and the Lagrangian approaches, exhibiting their relative advantages and weaknesses, after which we high-light potential loop-holes for non-trivial massless dynamics. We then review positive yes-go results for non-abelian cubic higher-derivative vertices in constantly curved backgrounds. Finally we outline how higher-spin symmetry can be reconciled with the equivalence principle in the presence of a cosmological constant leading to the Fradkin--Vasiliev vertices and Vasiliev's higher-spin gravity with its double perturbative expansion (in terms of numbers of fields and derivatives).

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arXiv2011

Manifestly Conformal Descriptions and Higher Symmetries of Bosonic Singletons

The usual ambient space approach to conformal fields is based on identifying the d-dimensional conformal space as the Dirac projective hypercone in a flat d+2-dimensional ambient space. In this work, we explicitly concentrate on singletons of any integer spin and propose an approach that allows one to have both locality and conformal symmetry manifest. This is achieved by using the ambient space representation in the fiber rather than in spacetime. This approach allows us to characterize a subalgebra of higher symmetries for any bosonic singleton, which is a candidate higher-spin algebra for mixed symmetry gauge fields on anti de Sitter spacetime. Furthermore, we argue that this algebra actually exhausts all higher symmetries.

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arXiv2011

Effective action in a higher-spin background

We consider a free massless scalar field coupled to an infinite tower of background higher-spin gauge fields via minimal coupling to the traceless conserved currents. The set of Abelian gauge transformations is deformed to the non-Abelian group of unitary operators acting on the scalar field. The gauge invariant effective action is computed perturbatively in the external fields. The structure of the various (divergent or finite) terms is determined. In particular, the quadratic part of the logarithmically divergent (or of the finite) term is expressed in terms of curvatures and related to conformal higher-spin gravity. The generalized higher-spin Weyl anomalies are also determined. The relation with the theory of interacting higher-spin gauge fields on anti de Sitter spacetime via the holographic correspondence is discussed.

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arXiv2010

Higher spin interactions with scalar matter on constant curvature spacetimes: conserved current and cubic coupling generating functions

Cubic couplings between a complex scalar field and a tower of symmetric tensor gauge fields of all ranks are investigated on any constant curvature spacetime of dimension d>2. Following Noether's method, the gauge fields interact with the scalar field via minimal coupling to the conserved currents. A symmetric conserved current, bilinear in the scalar field and containing up to r derivatives, is obtained for any rank r from its flat spacetime counterpart in dimension d+1, via a radial dimensional reduction valid precisely for the mass-square domain of unitarity in (anti) de Sitter spacetime of dimension d. The infinite collection of conserved currents and cubic vertices are summarized in a compact form by making use of generating functions and of the Weyl/Wigner quantization on constant curvature spaces.

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arXiv2010

Strong obstruction of the Berends-Burgers-van Dam spin-3 vertex

In the eighties, Berends, Burgers and van Dam (BBvD) found a nonabelian cubic vertex for self-interacting massless fields of spin three in flat spacetime. However, they also found that this deformation is inconsistent at higher order for any multiplet of spin-three fields. For arbitrary symmetric gauge fields, we severely constrain the possible nonabelian deformations of the gauge algebra and, using these results, prove that the BBvD obstruction cannot be cured by any means, even by introducing fields of spin higher (or lower) than three.

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arXiv2009

On higher spin interactions with matter

Cubic couplings between a complex scalar field and a tower of symmetric tensor gauge fields of all ranks are investigated. A symmetric conserved current, bilinear in the scalar field and containing r derivatives, is provided for any rank r>0 and is related to the corresponding rigid symmetry of Klein-Gordon's Lagrangian. Following Noether's method, the tensor gauge fields interact with the scalar field via minimal coupling to the conserved currents. The corresponding cubic vertex is written in a compact form by making use of Weyl's symbols. This enables the explicit computation of the non-Abelian gauge symmetry group, the current-current interaction between scalar particles mediated by any gauge field and the corresponding four-scalar elastic scattering tree amplitude. The exact summation of these amplitudes for an infinite tower of gauge fields is possible and several examples for a definite choice of the coupling constants are provided where the total amplitude exhibits fast (e.g. exponential) fall-off in the high-energy limit. Nevertheless, the long range interaction potential is dominated by the exchange of low-spin particles in the low-energy limit.

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arXiv2009

An infinite supermultiplet of massive higher-spin fields

The representation theory underlying the infinite-component relativistic wave equation written by Majorana is revisited from a modern perspective. On the one hand, the massless solutions of this equation are shown to form a supermultiplet of the superPoincare algebra with tensorial central charges; it can also be obtained as the infinite spin limit of massive solutions. On the other hand, the Majorana equation is generalized for any space-time dimension and for arbitrary Regge trajectories. Inspired from these results, an infinite supermultiplet of massive fields of all spins and of equal mass is constructed in four dimensions and proved to carry an irreducible representation of the orthosymplectic group OSp(1|4) and of the superPoincare group with tensorial charges.

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