Tue, 18 Nov 2025
13:00
L2

An N=4 SYM Collider at Finite Rank and Finite Coupling

Robin Karlsson
(Oxford )
Abstract

Energy correlations characterise the energy flux through detectors at infinity produced in a collision event. In CFTs, these detectors are examples of light-ray operators and, in particular, the stress tensor operator integrated over future null infinity. In N=4 SU(N_c) SYM, we combine perturbation theory, holography, integrability, supersymmetric localisation, and modern conformal bootstrap techniques to obtain predictions for such a collider experiment at finite coupling, both at finite number of colours, and in the planar limit. In QCD, the coupling runs with the angle between detectors, and there is a transition from perturbative to non-perturbative QCD. In N=4 SYM, a similar transition occurs when the coupling is varied, which we explore quantitatively. I will describe the physics underlying this observable and some of the methods used, particularly in regimes with analytical control.


 

Tue, 28 Oct 2025
13:00
L2

Periods, the Hodge structure and the arithmetic of Calabi-Yau manifolds

Xenia de la Ossa
(Oxford )
Abstract

It is well known to mathematicians that there is a deep relationship between the arithmetic of algebraic varieties and their geometry.  

These areas of mathematics have a fascinating connection with physical theories and vice versa.  Examples include Feynman graphs and black hole physics.  There are very many relationships however I will focus on the structure of black hole solutions of superstring theories on Calabi-Yau manifolds. 

 
The main quantities of interest in the arithmetic context are the numbers of points of the variety, considered as varieties over finite fields, and how these numbers vary with the parameters of the varieties. The generating function for these numbers is the zeta function, about which much is known in virtue of the Weil conjectures. The first surprise, for a physicist, is that the numbers of these points, and so the zeta function, are given by expressions that involve the periods of the manifold.  These same periods determine also many aspects of the physical theory, including the properties of black hole solutions. 

 
I will discuss a number of interesting topics related to the zeta function, the corresponding L-function, and the appearance of modularity for one parameter families of Calabi-Yau manifolds. I will focus on an example for which the quartic numerator of the zeta function of a one parameter family factorises into two quadrics at special values of the parameter. These special values, for which the underlying manifold is smooth, satisfy an algebraic equation with coefficients in Q, so independent of any particular prime.  The significance of these factorisations is that they are due to the existence of black hole attractor points in the sense of type II supergravity which predict the splitting of the Hodge structure over Q at these special values of the parameter.  Modular groups and modular forms arise in relation to these attractor points, in a way that is familiar to mathematicians as a consequence of the Langland’s Program, but which is a surprise to a physicist.  To our knowledge, the rank two attractor points that were  found together with Mohamed  Elmi and Duco van Straten by the application of  number theoretic techniques, provide the first explicit examples of such attractor points for Calabi-Yau manifolds.  
Tue, 21 Oct 2025
13:00
L2

Linking chaos and geometry

Zhenbin Yang
(Tsinghua University)
Abstract

In recent years, there has been increasing evidence for a geometric representation of quantum chaos within Einstein's theory of general relativity. Despite the lack of a complete theoretical framework, this overview will explore various examples of this phenomenon. It will also discuss the lessons we have learned from it to address several existing puzzles in quantum gravity, such as the black hole information paradox and off-shell wormhole geometries.

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