Jiaxin Qiao

A bstract: We initiate the study of flux tubes in confining gauge theories placed in a rigid AdS background, which serves as an infrared regulator. Varying the AdS radius from large to small allows us to interpolate between the flat space confining string, and a weakly coupled string-like object which is held together by the AdS gravitational potential. At any radius, the string preserves a subgroup of AdS isometries equivalent to the one-dimensional conformal group and hence, from the boundary point of view, can be thought of as a conformal defect. The defect hosts a protected operator, called displacement, which nonlinearly realizes the broken AdS isometries. At small radius the displacement corresponds to the gauge field strength inserted at the boundary, while at large radius it is mapped to the Goldstone mode living on the string worldsheet. This relates gauge field and worldsheet degrees of freedom. We propose a hypothesis according to which the large and small radius perturbative expansions can be smoothly matched with each other. As a test, we calculate the leading order corrections to the scaling dimensions and OPE coefficients of a set of defect operators at weak coupling in planar 3D Yang-Mills.

On the Wick rotation of the four-point function in conformal field theories: Les théories des champs conformes (CFTs) en signature euclidienne satisfont plusieurs règles bien acceptées, telles que l'invariance conforme et la convergence de l'expansion du produit d'opérateurs (OPE) en signature euclidienne. De nos jours, il est courant de supposer l'existence des fonctions de corrélation d'une CFT et d'assumer diverses propriétés en signature lorentzienne. Certaines de ces propriétés peuvent représenter des hypothèses supplémentaires, et leur validité reste incertaine dans les CFT de physique statistique familières telles que le modèle d'Ising critique en trois dimensions. Dans cette thèse, nous clarifions qu'au niveau des fonctions de corrélation à quatre points, les axiomes CFT euclidiens impliquent les axiomes standards de la théorie quantique des champs tels que les axiomes d'Osterwalder-Schrader (en signature euclidienne) et les axiomes de Wightman (en signature lorentzienne).

A bstract: We study bulk locality constraints in quantum field theories in AdS ₂ . The known derivation of locality sum rules in AdS _{d +1} does not apply for d = 1 due to the different singularity structure of the conformal blocks and the inequivalence of operator orderings on the boundary. Assuming unitarity and a mild growth condition, we establish power-law bounds for correlators, derive dispersion relations and an expansion in terms of “even” and “odd” local blocks that converges in the entire AdS ₂ . These yield two novel families of symmetric and antisymmetric locality sum rules. We test these sum rules explicitly in the free scalar field theory.

We study a conformal field theory that arises in the infinite-volume limit of a spin chain with U_q(sl_2) U q ( s l 2 ) global symmetry. Most operators in the theory are defect-ending operators which allows U_q(sl_2) U q ( s l 2 ) symmetry transformations to act on them in a consistent way. We use Coulomb gas techniques to construct correlation functions and compute all OPE coefficients of the model in closed form, as well as to prove that the properties imposed by the quantum group symmetry are indeed satisfied by the correlation functions. In particular, we treat the non-chiral operators present in the theory. Free boson realization elucidates the origin of the defects attached to the operators. We also comment on the role of quantum group in generalized minimal models.

We study quantum field theories which have quantum groups as global internal symmetries. We show that in such theories operators are generically non-local, and should be thought as living at the ends of topological lines. We describe the general constraints of the quantum group symmetry, given by Ward identities, that correlation functions of the theory should satisfy. We also show that generators of the symmetry can be represented by topological lines with some novel properties. We then discuss a particular example of U _q (sl ₂) symmetric CFT, which we solve using bootstrap techniques and relying on the symmetry. We finally show strong evidence that for a special value of q a subsector of this theory reproduces the fermionic formulation of the Ising model. This suggests that a quantum group can act on local operators as well, however, it generically transforms them into non-local ones.

We introduce a “radial” two-point invariant for quantum field theory in de Sitter (dS) analogous to the radial coordinate used in conformal field theory. We show that the two-point function of a free massive scalar in the Bunch-Davies vacuum has an exponentially convergent series expansion in this variable with positive coefficients only. Assuming a convergent Källén-Lehmann decomposition, this result is then generalized to the two-point function of any scalar operator non-perturbatively. A corollary of this result is that, starting from two-point functions on the sphere, an analytic continuation to an extended complex domain is admissible. dS two-point configurations live inside or on the boundary of this domain, and all the paths traced by analytic continuation between dS and the sphere or between dS and Euclidean Anti-de Sitter are also contained within this domain.