The S-Matrix in flat space is a naturally holographic observable. S-Matrix elements thus contain valuable information about the putative dual CFT. In this talk, I will first introduce some basic aspects of Celestial Holography and then explain how these can be inferred directly from scattering amplitudes. I will then focus on how the singularity structure of amplitudes interplays with traditional CFT structures particularly in the context of the operator product expansion (OPE) of the dual CFT. I will conclude with some discussion about the role played by supersymmetry in simplifying the putative dual CFT.
 

The Bethe-Gauge Correspondence (BGC) of Nekrasov and Shatashvili, linking quantum integrable spin chains to two-dimensional supersymmetric gauge theories with N=2 supersymmetry, stands out as a significant instance of the deep connection between supersymmetric gauge theories and integrable models. In this talk, I will delve into this correspondence and its origins for superspin chains. To achieve this, I will first elucidate the Bethe Side and its corresponding Gauge Side of the BGC. Subsequently, it becomes evident that the BGC can be naturally realized within String Theory. I will initially outline the brane configuration for the realization of the Gauge Side. Through the use of string dualities, this brane configuration will be mapped to another, embodying the Bethe Side of the correspondence. The 4D Chern-Simons theory plays a crucial role in this latter duality frame, elucidating the integrability of the Bethe Side. Lastly, I will elaborate on computing the main object of interest for integrable superspin chains—the R-matrix—from the BGC. While this provides a rather comprehensive picture of the correspondence, some important questions remain for further clarification. I will summarize some of the most interesting ones at the end of the talk.

The resolutions of Slodowy slices S͂_e are symplectic varieties that contain the Springer fiber (G/B)_e as a Lagrangian subvariety. In joint work with R. Bezrukavnikov, M. McBreen, and Z. Yun, we construct analogues of these spaces for homogeneous affine Springer fibers. We further understand the categories of microlocal sheaves in these symplectic spaces supported on the affine Springer fiber as some categories of coherent sheaves.

In this talk I will mostly focus on the case of the homogeneous element ts for s a regular semisimple element and will discuss some relations of these categories with the small quantum group providing a categorification of joint work with R.Bezrukavnikov, P. Shan and E. Vasserot.

In this talk, I describe an exact duality between the double scaling limit of the SYK model and quantum geometry of de Sitter spacetime in three dimensions. The duality maps the so-called chord rules that specify the exact SYK correlations functions to the skein relations that govern the topological interactions between world-line operators in 3D de Sitter gravity.

This talk is part of the series of Willis Lamb Lectures in Theoretical Physics. Herman Verlinde is the Lamb Lecturer of 2024.