Showing papers by "Massimo Taronna published in 2017"

Spinning Witten diagrams

Abstract: We develop a systematic framework to compute the conformal partial wave expansions (CPWEs) of tree-level four-point Witten diagrams with totally symmetric external fields of arbitrary mass and integer spin in AdS d+1. As an intermediate step, we identify convenient bases of three-point bulk and boundary structures to invert linear map between spinning three-point conformal structures and spinning cubic couplings in AdS. Given a CFT d , this provides the complete holographic reconstruction of all cubic couplings involving totally symmetric fields in the putative dual theory on AdS d+1. Employing this framework, we determine the CPWE of a generic four-point exchange Witten diagram with spinning exchanged field. As a concrete application, we compute all four-point exchange Witten diagrams in the type A higher-spin gauge theory on AdS d+1, which is conjectured to be dual to the free scalar O (N ) model.

Higher-spin algebras, holography and flat space

Abstract: In this article we study the higher-spin algebra behind the type-A cubic couplings recently extracted from the free O(N ) model in generic dimensions, demonstrating that they coincide with the known structure constants for the unique higher-spin algebra in generic dimensions. This provides an explicit check of the holographic reconstruction and of the duality between higher-spin theories and the free O(N ) model in generic dimensions, generalising the result of Giombi and Yin in AdS4. For completeness, we also address the same problem in the flat space for the cubic couplings derived by Metsaev in 1991, which are recovered from the flat limit of the AdS type-A cubic couplings. We observe that both flat and AdS4 higher-spin Lorentz subalgebras coincide, hinting towards the existence of a full higher-spin symmetry behind the flat-space cubic couplings of Metsaev.

Spinning AdS Loop Diagrams: Two Point Functions

Abstract: We develop a systematic approach to evaluating AdS loop amplitudes based on the spectral (or "split") representation of bulk-to-bulk propagators, which re-expresses loop diagrams in terms of spectral integrals and higher-point tree diagrams. In this work we focus on 2pt one-loop Witten diagrams involving totally symmetric fields of arbitrary mass and integer spin. As an application of this framework, we study the contribution to the anomalous dimension of higher-spin currents generated by bubble diagrams in higher-spin gauge theories on AdS.

Spinning Witten Diagrams

Abstract: We develop a systematic framework to compute the conformal partial wave expansions (CPWEs) of tree-level four-point Witten diagrams with totally symmetric external fields of arbitrary mass and integer spin in AdS$_{d+1}$. Employing this framework, we determine the CPWE of a generic exchange Witten diagram with spinning exchanged field. As an intermediate step, we diagonalise the linear map between spinning three-point conformal structures and spinning cubic couplings in AdS. As a concrete application, we compute all exchange diagrams in the type A higher-spin gauge theory on AdS$_{d+1}$, which is conjectured to be dual to the free scalar $O\left(N\right)$ model. Given a CFT$_d$, our results provide the complete holographic reconstruction of all cubic couplings involving totally symmetric fields in the putative dual theory on AdS$_{d+1}$.

On the non-local obstruction to interacting higher spins in flat space

Abstract: Owing to a renewed interest in flat space higher spin gauge theories, in this note we provide further details and clarifications on the results presented in arXiv:1107.5843 and arXiv: 1209.5755, which investigated their locality properties. Focusing, for simplicity, on quartic couplings with one of the external legs having non-zero integer spin (which can be considered as a prototype for Weinberg-type arguments), we review the appearance of 1/□ non-localities. In particular, we emphasise that it appears to be not possible to eliminate all of the aforementioned non-localities in the general quartic Noether procedure solution with a judicious choice of coupling constants and spectrum. We also discuss the light-cone gauge fixing in d = 4, and argue that the non-local obstruction discussed in the covariant language cannot be avoided using light-cone gauge formalism.

Higher spin gauge theories and bulk locality: a no-go result

Abstract: We present a no-go result on consistent interactions among higher-spin gauge fields in AdS$_{d+1}$ space-times. We show that crossing symmetry with higher-spin gauge fields in the spectrum necessitates the presence of pathological $1/\Box$ non-localities in the bulk. This suggests the breakdown of the field theory picture for interacting higher-spin gauge theories at the classical level.

Feynman rules for higher-spin gauge fields on AdS$_{d+1}$

Abstract: We determine the Feynman rules for the minimal type A higher-spin gauge theory on AdS$_{d+1}$ at cubic order. In particular, we establish the quantum action at cubic order in de Donder gauge, including ghosts. We also give the full de Donder gauge propagators of higher-spin gauge fields and their ghosts. This provides all ingredients needed to quantise the theory at cubic order.

Pseudo-local Theories: A Functional Class Proposal

Abstract: In this article, using the language of jet space, we propose a functional class space for pseudo-local functionals. We test this functional class proposal in a number of examples ranging from string-field-theory to AdS/CFT dualities. Implications of the locality proposal at the quartic order are also discussed.

A note on field redefinitions and higher-spin equations

Abstract: In this note we provide some details on the quasi-local field redefinitions which map interactions extracted from Vasiliev's equations to those obtained via holographic reconstruction. Without loss of generality, we focus on the source to the Fronsdal equations induced by current interactions quadratic in the higher-spin linearised curvatures.

Comments on Higher-Spin Fields in Nontrivial Backgrounds

Abstract: We consider the free propagation of totally symmetric massive bosonic fields in nontrivial backgrounds. The mutual compatibility of the dynamical equations and constraints in flat space amounts to the existence of an Abelian algebra formed by the d'Alembertian, divergence and trace operators. The latter, along with the symmetrized gradient, symmetrized metric and spin operators, actually generate a bigger non-Abelian algebra, which we refer to as the "consistency" algebra. We argue that in nontrivial backgrounds, it is some deformed version of this algebra that governs the consistency of the system. This can be motivated, for example, from the theory of charged open strings in a background gauge field, where the Virasoro algebra ensures consistent propagation. For a gravitational background, we outline a systematic procedure of deforming the generators of the consistency algebra in order that their commutators close. We find that equal-radii AdSp X Sq manifolds, for arbitrary p and q, admit consistent propagation of massive and massless fields, with deformations that include no higher-derivative terms but are non-analytic in the curvature. We argue that analyticity of the deformations for a generic manifold may call for the inclusion of mixed-symmetry tensor fields like in String Theory.

On the Non-Local Obstruction to Interacting Higher Spins in Flat Space

Abstract: Owing to a renewed interest in flat space higher spin gauge theories, in this note we provide further details and clarifications on the results presented in arXiv:1107.5843 and arXiv: 1209.5755, which investigated their locality properties. Focusing, for simplicity, on quartic amplitudes with one of the external legs having non-zero integer spin (which can be considered as a prototype for Weinberg-type arguments), we review the appearance of $1/\Box$ non-localities. In particular, we emphasise that it appears to be not possible to eliminate all of the aforementioned non-localities with a judicious choice of coupling constants and spectrum. We also discuss the light-cone gauge fixing in $d=4$, and argue that the non-local obstruction discussed in the covariant language cannot be avoided using light-cone gauge formalism.