GASonSQuaT: Geometrical and Algebraic Structures on the Space of Quantum Theories

Project funded by Fundação para a Ciência e a Tecnologia, I.P. (FCT) (Concurso para Financiamento de Projetos de Investigação Científica e Desenvolvimento Tecnológico em Todos os Domínios Ci), grant PTDC/MAT-OUT/28784/2017. Funded amount: EUR 239,875, as stated by the source. Runs 2018-10-01 to 2022-09-30. Keywords: Resurgent Analysis, Quantization, Bootstrap of Conformal Field Theory, Localization in Random Matrices, Exact sciences. Source: OpenAIRE Graph, from the funder's project data (collected by OpenAIRE on 2026-07-23); national funding data, not CORDIS. Abstract given by the source: One of the most important questions in modern Mathematical Physics deals with understanding the space of all possible quantum theories. Unraveling such "theory space" is bound to have significant impact in both Mathematics (with the emergence of new mathematical structures, as the space of all quantum field theories itself is expected to form a new, or at least very subtle, mathematical structure) and Physics (with the description of all possible quantum phenomena). However, this task is a difficult one. Heuristically, the space of all quantum field theories is expected to be infinite-dimensional, with special fixed points (known as conformal field theories (CFT)) linked by paths corresponding to renormalisation-group flows. Understanding this space, encompassing all its geometrical and algebraic substructures, thus begins with understanding some of its special subsets --- in the sense that these CFTs are precisely the building blocks of all possible quantum theories (including theories of quantum gravity and black hole singularities). Our goal in this project is to pursue this long-term goal of understanding the space of all quantum theories, by first understanding special subsets of this space. Furthermore, we shall use complementary approaches, based on the different expertise of the members of this collaboration, associated to Resurgent Analysis, Bootstrap Techniques, and Localisation, to address these special subsets. These approaches allow for computing the spectrum and correlation functions of quantum theories described by random matrix models, of CFTs in diverse dimensions, and of quantum theories with correlation functions which localize to random matrices. Note that the very same theory may be approachable using these different techniques, and they might lead to complementary information. By solving different special sets of quantum theories, we expect to describe local patches, or local subsets, of the full space of quantum theories. In particular we [shortened; the full text is on the OpenAIRE page]

Original source.

Source: OpenAIRE Graph: projects of national funders, OpenAIRE, from the project data of Fundação para a Ciência e a Tecnologia, I.P. (FCT). Retrieved 2026-10-28. Licence: Creative Commons Attribution 4.0 (OpenAIRE Graph). Selected metadata, adapted presentation; the publisher's record is authoritative. No endorsement by the source is implied. Licence: Creative Commons Attribution 4.0 (CC BY 4.0).

AI-assisted summary: GASonSQuaT is a project funded by FCT with a grant of EUR 239,875, running from 2018-10-01 to 2022-09-30. It focuses on understanding the space of all possible quantum theories, impacting both Mathematics and Physics. Suggested technology pillar: enabling. Generated by AI from the public source text; it may contain errors and the original source is authoritative.