This project addresses mathematical structures in the space of all possible quantum theories. The space of all QFTs is infinite-dimensional, with CFT fixed-points linked by paths corresponding to RG flows. These CFTs are the building blocks of all possible quantum theories (including theories of quantum gravity and black holes). Our goal is to understand the space of all theories by first understanding some special subsets. We use complementary approaches, such as Resurgent Analysis, Bootstrap Techniques, and Localisation. These approaches solve quantum theories described by random matrix models, CFTs in diverse dimensions, and quantum theories with localisable observables. The very same theory may be approachable using these different techniques, leading to complementary information. By solving different special sets of quantum theories, we expect to describe geometrical and algebraic structures on local patches of the full space of quantum theories.


Mathematical and Geometrical aspects of Superconformal Field Theories

5-6 September 2019
IST Lisbon

  • Vasilis Niarchos (Durham University)
    "Deconstruction of 4d QFTs from 3d QFTs"
  • Costis Papageorgakis (Queen Mary University of London)
    "Exact dimensional deconstruction of the 6D (2,0) theory"
  • Wolfger Peelaers (Oxford University)
    VOAs and rank-two instanton SCFTs

Quantization in fibering polarizations, Mabuchi rays and geometric Peter-Weyl theorem

Thomas Baier, Joachim Hilgert, Oğuzhan Kaya, José M. Mourão, João P. Nunes
In this paper we use techniques of geometric quantization to give a geometric interpretation of the Peter-Weyl theorem. We present a novel approach to half-form corrected geometric quantization in a specific type of non-Kähler polarizations and study one important class of examples, namely cotangent bundles of compact semi-simple groups K. Our main results state that this canonically defined polarization occurs in the geodesic boundary of the space of K×K-invariant Kähler polarizations equipped with Mabuchi's metric, and that its half-form corrected quantization is isomorphic to the Kähler case. read more


João P. Nunes - The geometric interpretation of the Peter-Weyl theorem

22 November 2022
Geometry in Lisbon seminar - IST Lisbon


Ricardo Schiappa - De que é que é feito o espaço?

3 October 2020
Explica-me como se tivesse 5 anos - LINK (in Portuguese)