Towards a mathematical conjecture for the Landau-Ginzburg/conformal field theory correspondence and beyond

Información del proyecto

MACOLAB

Identificador del acuerdo de subvención: 747555

DOI

10.3030/747555

Proyecto finalizado el 1 Agosto 2018

Fecha de la firma de la CE 16 Febrero 2017

Fecha de inicio 1 Agosto 2017

Fecha de finalización 31 Julio 2019

Financiado con arreglo a

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Coste total

€ 165 598,80

Aportación de la UE

€ 165 598,80

Coordinado por

UNIVERSITEIT UTRECHT
Netherlands

Objetivo

Initially a model to describe superconductivity, Landau-Ginzburg (LG) models were promoted in the late 80s to supersymmetric quantum field theories (QFTs) completely characterized by a polynomial W called potential. They gained importance in string theory and algebraic geometry as they play an interesting role in homological mirror symmetry. On the other hand, conformal field theories (CFTs) have been another kind of QFTs which display conformal symmetry. They have focused many efforts to understand the mathematical structures which encode them, e.g. inspiring the definition of vertex operator algebras (Borcherds, Fields medalist ’88) or pushing forward our knowledge of modular tensor categories. Despite seeming two very different topics, LG models and CFTs are intimately related via a result of theoretical physics — the LG/CFT correspondence— stating that the infrared fixed point of a LG model with potential W is a CFT of central charge c(W). Mathematically this implies equivalences of categories of matrix factorizations (which describe defects of LG models) and categories of representations of vertex operator algebras (which describe defects of CFT). Up to date, we lack a complete understanding of the LG/CFT correspondence and we only have a few examples. The main goal of this Marie Curie is to find a mathematical statement for it, via completing a list of examples, exploring their properties (e.g. tensoriality or even modularity of the categories) and then attacking the main goal. Utrecht University (host institution) is one of the few places in Europe hosting experts in representation, category and Galois theory and mathematical physics, providing exactly the necessary and complementary expertise required to achieve this goal. These results will build a surprising bridge between very different areas of mathematics, opening new research gates completely inspired by physics.

Ámbito científico (EuroSciVoc)

• ciencias naturales › ciencias físicas › física cuántica › teoría cuántica de campos
• ciencias naturales › ciencias físicas › física teórica › teoría de cuerdas
• ciencias naturales › matemáticas › matemáticas aplicadas › física matemática › teoría de campos conformes
• ciencias naturales › matemáticas › matemáticas puras › álgebra › geometría algebraica
• ciencias naturales › ciencias físicas › electromagnetismo y electrónica › superconductor

Palabras clave

• Landau-Ginzburg models
• conformal field theory
• matrix factorizations
• vertex operator algebras

Programa(s)

• H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions PROGRAMA PRINCIPAL
  
• H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility
  

Tema(s)

• MSCA-IF-2016 - Individual Fellowships
  

Régimen de financiación

MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)

Convocatoria de propuestas

H2020-MSCA-IF-2016

Coordinador

UNIVERSITEIT UTRECHT

• Aportación neta de la UEn: € 165 598,80
• Dirección: HEIDELBERGLAAN 8 ; 3584 CS Utrecht ; Países Bajos
• Tipo de actividad: Higher or Secondary Education Establishments
• Coste total: € 165 598,80