Spinning Witten Diagrams

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$_{d+1}$.Comment: 41 pages, many figures. v2: Three self-contained pages removed from section 4, to be restored elsewhere. Main results unaffected. Refs added and typos fixe

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

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.Comment: v2: 32 pages, typos fixed, refs adde

Higher-Spin Gauge Theories and Bulk Locality

We present a no-go result on consistent Noether interactions among higher-spin gauge fields on anti-de Sitter space-times. We show that there is a non-local obstruction at the classical level to consistent interacting field theory descriptions of massless higher-spin particles that are described in the free limit by the free Fronsdal action, under the assumption that such theories arise from the gauging of a global higher-spin symmetry. Our result suggests that the Fronsdal programme for introducing interactions among higher-spin gauge fields cannot be completed without introducing new guiding principles, which could lie beyond the framework of classical field theory.Comment: 10 pages + refs. v2: Improved presentation, clarifications and references added. Some parts removed which just reviewed previous published work. To appear in Physical Review Letter

Spinning AdS Loop Diagrams: Two Point Functions

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.Comment: 54+23 pages, 15 figures. v2: Section 2.2 added with more details on the analytic evaluation of anomalous dimensions from bubble diagrams. References added, matches published versio

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.Comment: 40 pages plus appendices, 8 figure

Bulk quartic vertices from boundary four-point correlators

We present arguments which suggest that the bulk higher-spin gravity duals of weakly-coupled conformal field theories obey some refined notion of locality. In particular, we discuss the Mellin amplitude programme in this context. We focus on the $O(N)$ vector model and minimal higher-spin gravity as a paradigmatic example of such holographic dual pairs. We restrict ourselves to three- and four-point functions of scalar primary operators, but the qualitative conclusions are expected to hold for the generic case.Comment: 13 pages. Contribution to the proceedings of the "International Workshop on Higher Spin Gauge Theories" (4-6 November 2015, Singapore

Cell Type and Gene Regulatory Network Approaches in the Evolution of Spiralian Biomineralisation

Thanks to Kara Layton for expert advice on nudibranch biology, ecology and spicules, and to Namitha Paul for sea lemon collection and histology. Thanks to all members of the Sleight Lab and colleagues who joined our biomineralisation workshop at the Marine Biological Laboratory in Woods Hole in March 2023 for constructive discussion on the topics raised in this review. Thanks to Maryna P. Lesoway for inspiring conversations on spiralian evo-devo that contributed to some of the early ideas in this review. Thanks to Jessica A. Goodheart, Carmel McDougall, Molly Rivers and Danielle Jordan for critical reading of an early version of the manuscript. Thanks to two anonymous reviewers whose comments improved the final version of this manuscript. FUNDING V.A.S. is supported by research funds from the UKRI Biotechnology and Biological Sciences Research Council (BB/X511973/1), the Royal Society (RGS\R1\211204) and the Royal Society of Edinburgh.Peer reviewedPublisher PD

Interactions in higher-spin gravity

In this thesis we investigate aspects of higher-spin gravity on an anti-de Sitter (AdS) background. Such theories are believed to give an effective description of quantum gravity in its high energy regime, where there have been hints that a large underlying (higher-spin) symmetry may become restored. In particular, through considerations of string theory in the high-energy (tensionless) limit. The study of higher-spin gauge theories is thus of physical relevance, for their infinite dimensional symmetry may serve as a guiding principle to help shed light on the nature of quantum gravity at energies which are beyond the reach of present day experiments. To fulfil this potential, there is much still to be understood about higher-spin theories themselves. To date, the fully non-linear formulations of higher-spin theories include infinitely many additional auxiliary fields. With this work we take steps towards clarifying the nature of interactions amongst higher-spin fields in a metric-like Lagrangian framework, free from such auxiliary fields. To this end, we employ the conjectured holographic duality between higher-spin gravity theories on AdS and certain, solvable, conformal field theories (CFTs). In this way well-known methods in CFT may be applied, and with them we determine completely all cubic interactions and the quartic self-interaction of the scalar in the higher-spin Lagrangian on an AdS background. For this purpose a number of further original results were established, which include: Tools to evaluate three-point amplitudes in AdS space involving external fields of arbitrary integer spin, propagators for gauge fields of arbitrary integer spin on an AdS background, and techniques to determine conformal partial wave expansions of four-point amplitudes in higher-spin theories. Reminiscent of the tail of $\alpha^\prime$ corrections in string theory, higher-spin interactions are non-local in the sense that they are unbounded in their number of derivatives. While in (finite tension) string theory this higher-derivative behaviour does not appear to pose a threat to fundamental properties like causality, in higher-spin theories this remains to be clarified. In the context of the results established in this work, we briefly discuss the implications of the AdS/CFT duality on the locality properties of interactions in higher-spin theory. In particular, by drawing on the holographic interpretation of CFT correlation functions as scattering amplitudes in the dual gravity theory on AdS.Die vorliegende Dissertation widmet sich der Untersuchung der Höhere Spin-Gravitation auf einem Anti-de-Sitter-Raum (AdS). Es gibt Hinweise darauf, dass dem Hochenergiebereich der Quantengravitation eine große (Höhere Spin-) Symmetriegruppe zugrundeliegt und somit eine mögliche effektive Beschreibung dieses Beriechs durch eine Höhere Spin-Theorie gegeben ist. Die Reaslisierung einer Quantengravitation mit dieser Symmetrie ist insbesondere in der String Theorie bei hohen Energien gegeben, wenn die Stringspannung vernachlässigt werden kann. Die Untersuchung der Höhere Spin-Theorien ist von physikalischer Relevanz, weil ihre unendlichdimensionale Symmetrie als Leitprinzip verwendet werden kann, um neue Erkenntnisse über die Quantengravitation bei Energien jenseits der heute experimentall erreichbaren Energieskalen zu gewinnen. Es muss dabei berücksichtigt werden, dass die verfügbaren nichtlinearen Formulierungen der Höhere-Spin-Theorien unendlich viele Hilfsfelder mit einschließen, so dass selbst grundlegende Eigenschaften wie Unitarität oder Kausalität noch nicht vollständig verstanden sind. Zielsetzung dieser Arbeit ist es, die Wechselwirkungen zwischen höheren Spin-Feldern im Rahmen der Lagrangeformulierung zu untersuchen, da dies ohne Hilfsfelder möglich ist. Um dies zu ermöglichen, wird die vermutete Dualität zwischen der Höhere Spin-Gravitation im AdS-Raum und integrablen konformen Feldtheorien benutzt. Durch Anwendung von Techniken der konformen Feldtheorie werden in der Lagrangefunktion der Höheren Spin-Theorie alle Wechselwirkungsterme bis zur dritten Ordnung sowie die Selbstwechselwirkung des Skalarfeldes bis zur vierten Ordnung bestimmt. Zu diesem Zweck werden neue Methoden entwickelt: Diese umfassen eine neue Herangehensweise zur Berechnung von Dreipunktamplituden mit externen Feldern beliebigen Spins und die explizite Form von Propagatoren für Eichfelder mit beliebigem ganzzahligen Spin im AdS-Raum. Weiterhin werden Techniken zur Berechnung konformer partieller Wellenzerlegungen von Vierpunktamplituden in Höhere Spin-Theorien entwichelt. Die $\alpha'$-Korrekturen in der Stringtheorie spiegeln sich in der Nichtlokalität der Wechselwirkungen zwischen Höhere Spin-Feldern wider: Es treten beliebig hohe Ableitungen der Felder auf. In der Stringtheorie bei endlicher Stringspannung bedeuten diese höheren Ableitungsterme offensichtlich keine Einschränkung von fundamentalen Eigenschaften wie etwa der Kausalität. In der Höhere-Spin-Theorie jedoch ist dies Gegenstand aktueller Forschung. Im Kontext der Ergebnisse dieser Arbeit wird die Bedeutung der AdS/CFT Dualität für die Lokalität der Wechselwirkungen zwischen Höhere Spin-Feldern diskutiert. Insbesondere wird auf die holographische Interpretation der Korrelatoren in der konformen Feldtheorie als Streuamplituden der dualen Gravitationstheorie im AdS-Raum eingegangen

Interactions in Higher-Spin Gravity: a Holographic Perspective

This thesis is an elaboration of recent results on the holographic re-construction of metric-like interactions in higher-spin gauge theories on anti-de Sitter space (AdS), employing their conjectured holographic duality with free conformal field theories (CFTs). After reviewing the general approach and establishing the necessary intermediate results, we extract explicit expressions for the complete cubic action on AdS$_{d+1}$ and the quartic self-interaction of the scalar on AdS$_4$ for the type A minimal bosonic higher-spin theory from the three- and four- point correlation functions of single-trace operators in the free scalar $O\left(N\right)$ vector model. For this purpose tools were developed to evaluate tree-level three-point Witten diagrams involving fields of arbitrary integer spin and the conformal partial wave expansions of tree-level four-point Witten diagrams, which are underpinned by the ambient space formulation of AdS space and CFT. We also discuss the implications of the holographic duality on the locality properties of interactions in higher-spin gauge theories.Comment: Ph.D. thesis, 246 pages, 14 figures. Advisor: Prof. Dr. Johanna Erdmenger. v2: Minor edits, refs added and typos fixed. Published as a topical review in Journal of Physics