Shailesh Lal (Porto), Machine Learning Symmetries using Neural Networks

We demonstrate how simple neural networks are able to recognize symmetry in physical systems to near-hundred percent precision and accuracy. In addition, we find they estimate the results of Lie algebra representation theory computations again to high precision and accuracy, with minimal computational time compared to standard algorithms. The talk will be largely based on 2006.16114 and 2011.00871.

Tadashi Okazaki (Durham), Dualities of boundary-corner configurations in supersymmetric gauge theories and branes in string theory

Dualities have been changing our view of quantum field theories. In the presence of boundary and corner configurations, fascinating actions of dualities on theories in different dimensions have been recently discovered by directly studying boundary conditions in supersymmetric gauge theories and their brane constructions in string theory. The dualities with boundaries and corners can be stringently tested by computing generalized supersymmetric indices which count local operators living in the bulk, on the boundary and at the corner. The indices can be identified with interesting mathematical objects including graded characters of the algebras formed by the local operators and they also can play a key role in algebraic constructions of the partition functions on compact manifolds. I will discuss dualities of boundary and corner configurations in 4d N=4 and 3d N=4 gauge theories, their mathematical applications and their brane constructions in string theory based on my recent works.

Zhi-Wei Wang (CP3-Origins), Novel Results for QFT via Large Quantum Number Limits and Applications to Standard Model Physics and Beyond

Solving QFT is key to a more profound understanding of present and next generation of theories of Nature. In fact, both the large number-of-flavour 1/Nf and charge (1/Q) expansion have been useful tools to go beyond Feynman diagrammatic computations. In this talk, I will discuss not only the theoretical perspectives of these two methods but, in particular, also their important applications in particle physics phenomenology. I will show that by using the large number-of-flavour 1/Nf summation techniques, the Standard Model can achieve an interacting ultraviolet fixed point, addressing the famous UV Landau Pole problem. I will implement the large charge (1/Q) approach to determine the scaling dimensions of a class of fixed charge operators to the next-to-leading-order in the charge expansion but to all orders in their couplings.

Paul-Konstantin Oehlmann (Uppsala), Sections, Multi-Sections and Mirror-Symmetry in F-theory

In this talk we consider torus-fibered Calabi-Yau spaces with additional structures namely non-trivial Mordell-Weil groups and so called multi-sections and discuss their connection to the physics of F-theory. In F-theory, these structures are relevant for encoding Abelian, gauged discrete center 1-form symmetries- as well as discrete groups. The full classification of all those structures is yet unknown which makes them interesting from a geometric perspective but also in physics as in the swampland program. Moreover we highlight their relevance via the construction of MSSM like models and 6D SCFTs that exhibit such symmetries. In compact n(>2)-folds we argue that discrete center-one form symmetries must always be subgroups of finite Abelian subgroups of E8 by using the modular curves of certain congruence subgroups. Finally we give evidence, that the classification of gauged center 1-form symmetries is connected to discrete gauge symmetries via the action of mirror symmetry.

Sarthak Parikh (Caltech), Higher-point holography

Conformal blocks are theory-independent, non-perturbative basic building blocks of local observables in CFTs. Higher-point global conformal blocks play a central role in the study of higher-point AdS diagrams and conformal correlators. In turn, higher-point AdS diagrams enable a systematic analysis of loop corrections to conformal correlators, and higher-point conformal correlators can help constrain the space of CFTs in general spacetime dimensions via a more powerful conformal bootstrap program. Thus higher-point global conformal blocks are important objects to study. Until recently, knowledge of higher-point blocks was restricted to an extremely limited set of examples. In this talk I will present a simple set of "Feynman rules" for constructing all possible conformal blocks (i.e. arbitrary-point blocks of any topology in general spacetime dimensions) involving external and exchanged scalars. The Feynman vertex factors are given in terms of Lauricella hypergeometric functions of one, two or three variables, and the Feynman rules furnish an explicit power-series expansion in powers of cross-ratios. I will describe how to obtain this result via holography using position- and Mellin-space methods, as well as crucial input from a discrete variant of the AdS/CFT correspondence based on p-adic numbers.

Achilleas Passias (Oxford), N=2 AdS(4) IIA solutions

We present two new families of analytic N=2 AdS(4) solutions of type IIA supergravity with non-zero Romans mass.　The first family contains all previously known numeric solutions and is dual to Chern-Simons theories coupled to matter.　The second family is dual to three-dimensional superconformal field theories obtained by compactifying a five-dimensional one on a Riemann surface.

Yongchao Lu (Uppsala), Crystallographic elliptic Calogero-Moser systems and Seiberg-Witten integrable systems

We propose to identify crystallographic elliptic Calogero-Moser systems attached to complex reflection groups G(m,1,n) with m = 2, 3, 4, 6 as Seiberg-Witten integrable systems for 4d N=2 rank n D₄ and Minahan-Nemeschansky's (MN) E₆, E₇, and E₈ theories, respectively. Our proposal can be viewed as a natural generalization of the identification of elliptic Calogero Moser system of A_n-1 type as the Seiberg-Witten integrable system of 4d N=2* U(n) gauge theory (which we call A₀ theory). The physical data of these 4d N=2 SCFTs perfectly matches the complex reflection group data. As a special case, we identify the 4 (+1) -parameter Inozemtsev BC_n system as the Seiberg-Witten integrable system of 4d N=2 USp(2n) gauge theories with four fundamental and (for n>1) one antisymmetric hypermultiplets.

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