Non-invertible symmetries are refined notions of symmetries intensively studied recently. I will show that non-invertible symmetries sometimes lead to a surprising consequence on scattering amplitudes --- a modification of crossing symmetry. I will demonstrate this using example of integrable field theories in 1+1 dimensions although the argument holds more generally; also for non-integrable theories. I will also present the results of S-matrix bootstrap, which constrains the space of physically consistent scattering amplitudes with categorical symmetries.

We propose a (bosonic) worldsheet description of two-dimensional Yang-Mills. We also argue that similar worldsheet actions provide candidate duals to the symmetric product orbifolds for arbitrary seed CFTs.

I will discuss the fundamentals of quantum field theory on a rigid de Sitter space. First, I will show that the perturbative expansion of late-time correlation functions to all orders can be equivalently generated by a non-unitary Lagrangian on a Euclidean AdS geometry. This finding simplifies dramatically perturbative computations, as well as allows us to establish basic properties of these correlators, which comprise a Euclidean CFT. Second, I use this to infer the analytic structure of the spectral density that captures the conformal partial wave expansion of a late-time four-point function, to derive an OPE expansion, and to constrain the operator spectrum. Third, I will prove that unitarity of the de Sitter theory manifests itself as the positivity of the spectral density. This statement does not rely on the use of Euclidean AdS Lagrangians and holds non-perturbatively. Zoom link: https://us06web.zoom.us/j/82867324531?pwd=cXBkMUNpQlE4M3h2UEdabWpOZkNIdz09

I will discuss two topics on the large charge limit and holography. First, I will discuss general features of the large-charge limit of superconformal field theories at large N. In particular, I will point out a simple setup to analyze the large charge expansion of the planar N=4 super Yang-Mills and discuss its holographic interpretation. Second, I will discuss the large-charge limit of the defect CFT on the Wilson line and its relation to the matrix model. Zoom link: https://us06web.zoom.us/j/82867324531?pwd=cXBkMUNpQlE4M3h2UEdabWpOZkNIdz09

In his paper in 1979, Polyakov envisaged a possibility of reformulating the gauge theory as a Principal Chiral Model defined on a space of loops and discussed "the loop-space integrability". This idea, together with a closely related idea of the loop equation, led to numerous important results in matrix models and 2d gauge theories, but its application to four-dimensional gauge theories had only limited success. Now, after 50 years, we have a concrete example of integrable four-dimensional gauge theory, N=4 SYM. However integrability in N=4 SYM is formulated mostly in terms of local operators, although important progress has been made in constructing the Yangian for the Wilson loops. In this talk, I will present a framework which would bridge these two distant notions of integrabililty. The key player in the story is a correlation function of a local operator and the Wilson loop. I reformulate the gauge-theory computation of this observable as an overlap between an energy eigenstate of a spin chain and a matrix product state (MPS). Unlike standard MPS's discussed in the literature, our MPS has infinite bond dimensions in order to accommodate infinite dimensionality of the space of loops. It provides an "intertwiner" between integrable structures of the local operators and the Wilson loops, and in particular implies the existence of a special set of deformations of the Wilson loop which satisfy the QQ-relation. I will also explain how to formulate a nonperturbative bootstrap program based on the results obtained in this framework and compute the correlator of the circular BPS Wilson loop and general non-BPS operators at finite coupling, emphasizing the relation to and the difference from other observables that were computed by a similar approach. ----------------- Part of London Integrability Journal Club. Please register using the form at integrability-london.weebly.com