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Holomorphic Blocks in Quantum Field Theory: New Constructions of Exact Results

Objective

A central challenge in theoretical physics is to develop non-perturbative or exact methods to describe quantitatively the dynamics of strongly coupled quantum fields. This proposal aims to establish new exact methods for the study of supersymmetric quantum field theories thereby unveiling new integrable structures and fostering new correspondences and dualities. We will develop a new cut-and-sew formalism to compute partition functions and expectation values of observables of supersymmetric gauge theories on compact manifolds through the gluing of a fundamental set of building blocks, the holomorphic blocks. The decomposition of partition functions into holomorphic blocks corresponds to
the geometric decomposition of compact manifolds into standard simpler pieces. Similarly the gluing rules for the holomorphic blocks correspond to the geometric gluing rules. The key insight required to exploit the holomorphic block formalism is the deep connection between supersymmetric gauge theories and low dimensional exactly solvable systems such as 2d CFTs, TQFTs and spin chains. Two and four dimensional holomorphic blocks can be reinterpreted as conformal blocks in Liouville theory through an established correspondence between supersymmetric gauge theories and Liouville theory. We will provide a similar realisation of three and five dimensional holomorphic blocks in a new theory,
a q-deformed version of Liouville theory where the Virasoro algebra is replaced by the q-deformed Virasoro algebra.
We will develop this theory classifying the symmetries of correlation functions. These symmetries will be realised as gauge theory dualities, while the language of the q-deformed Liouville theory will become a new powerful tool to investigate supersymmetric gauge theories.

Field of science

  • /natural sciences/physical sciences/theoretical physics/particle physics
  • /natural sciences/physical sciences/theoretical physics/string theory
  • /natural sciences/mathematics/pure mathematics/algebra
  • /natural sciences/physical sciences/condensed matter physics
  • /natural sciences/physical sciences/quantum physics/quantum field theory

Call for proposal

ERC-2014-STG
See other projects for this call

Funding Scheme

ERC-STG - Starting Grant
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Host institution

UNIVERSITA' DEGLI STUDI DI MILANO-BICOCCA
Address
Piazza Dell'ateneo Nuovo 1
20126 Milano
Italy
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 1 253 334,65

Beneficiaries (2)

UNIVERSITA' DEGLI STUDI DI MILANO-BICOCCA
Italy
EU contribution
€ 1 253 334,65
Address
Piazza Dell'ateneo Nuovo 1
20126 Milano
Activity type
Higher or Secondary Education Establishments
UNIVERSITY OF SURREY

Participation ended

United Kingdom
EU contribution
€ 33 753,35
Address
Stag Hill
GU2 7XH Guildford
Activity type
Higher or Secondary Education Establishments