**Xiang ZHAO **soutiendra publiquement ses travaux de thèse le **jeudi 25 novembre 2021 à 10h00** au CPHT, Salle de conférence Louis Michel.

**Titre de la thèse : "Aspects of Conformal Field Theories and Quantum Fields in AdS"**

Directeur de thèse : Balt Van Rees

**Participer à la réunion Zoom pour la soutenance de thèse :**

https://us06web.zoom.us/j/87068486326?pwd=a0JMRkZBdEpkYzVDR0h4N2piQ1hNUT09

Meeting ID: 870 6848 6326

Passcode: 245657

**Composition du Jury**

(1) Christopher BEEM, Associate Professor, Oxford University (Rapporteur)

(2) Nikolay BOBEV, Associate Professor, KU Leuven (Rapporteur)

(3)Costas BACHAS, Directeur de Recherche, ENS (Examinateur)

(4) Christoph KOPPER, Professeur, Ecole Polytechnique (CPHT) (Examinateur)

(5) Eric PERLMUTTER, Assistant Professor, Saclay (IPHT) (Examinateur)

(6) Balt VAN REES, Professeur, Ecole Polytechnique (CPHT) (Directeur de thèse)

**Abstract**

"This thesis studies the structure and the space of conformal ﬁeld theories (CFTs), and more generally various properties of conformal correlation functions. It extends into multiple directions, both perturbative and non-perturbative, local and non-local, with and without supersymmetry.

The first aspect concerns the conformal correlation functions in d-dimensional spacetime and their relation to ﬂat-space S-matrices in (d+1)-dimensional spacetime. The connection is built up by considering a quantum ﬁeld theory (QFT) in a fixed (d+1)-dimensional Anti-de Sitter (AdS) background and sending the radius of the AdS curvature to infinity. That is, the central object to study is the ﬂat-space limit of QFT in AdS. The analysis starts from taking the ﬂat-space limit of the building blocks of Witten diagrams, namely the bulk-boundary and bulk-bulk propagators. This analysis leads to conjectural generic prescriptions to extracting ﬂat-space physics from conformal correlators. Interestingly, the intuitional picture that a Witten diagram simply reduces to the corresponding Feynman diagram does not always hold, and the origin of this discrepancy lies in the bulk-bulk propagators: they could have two different ﬂat-space limits. One of the limits always exists and reduces to Feynman propagator, while the other, when present, can diverge in the ﬂat-space limit. This observation is tested by explicit examples, including fourpoint scalar contact, exchange and triangle Witten diagrams and the conjectures are expected to work whenever the scattering energy is large enough.

The second aspect studies the classification problem of conformal defects. The goal is to partially answer the question: given a bulk CFT and consistency conditions such as crossing symmetry and unitarity, what are the allowed conformal defects with a non-trivial coupling to the bulk? Analytic bootstrap techniques are applied to study a simpliﬁed version of this problem where in the bulk only a single free scalar ﬁeld is considered. Analysis of various three-point functions among bulk and defect ﬁelds leads to the conclusion that almost all the n-point correlation functions of defect ﬁelds are completely ﬁxed up to a potentially unﬁxed one-point function. This analysis also leads to an intermediate result in which it is proven that the n-point correlation functions of a conformal theory with a generalised free spectrum must be those of the generalised free ﬁeld theory."

The third aspect studies the interplay between analyticity in spin in CFTs and supersymmetry. Operator spectrum in a general unitary CFT is expected to be captured by a function analytic for spin J>1, and the operators are organised into various Regge trajectories. The presence of supersymmetry in general extends the region of analyticity in spin. The 6d N=(2,0) superconformal ﬁeld theories (SCFTs) is considered as a concrete example, in which analyticity in spin is expected to hold down to J>−3. Detailed analysis of the four-point function of the the stress tensor supermultiplet uncovers an unexpected interplay between unprotected and protected multiplets: the stress tensor multiplet can be found on a long (unprotected) Regge trajectory when analytically continued to spin J=−2. In this study a general iterative bootstrap program is also established, which applies to all SCFTs that have a chiral algebra subsector.