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. Fields of science natural sciencesphysical sciencestheoretical physicsparticle physicsnatural sciencesphysical sciencesquantum physicsquantum field theorynatural sciencesmathematicspure mathematicsalgebranatural sciencesphysical sciencestheoretical physicsstring theorynatural sciencesmathematicsapplied mathematicsmathematical physicsconformal field theory Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Topic(s) ERC-StG-2014 - ERC Starting Grant Call for proposal ERC-2014-STG See other projects for this call Funding Scheme ERC-STG - Starting Grant Host institution UNIVERSITA' DEGLI STUDI DI MILANO-BICOCCA Net EU contribution € 1 253 334,65 Address PIAZZA DELL'ATENEO NUOVO 1 20126 MILANO Italy See on map Region Nord-Ovest Lombardia Milano Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 1 253 334,65 Beneficiaries (2) Sort alphabetically Sort by Net EU contribution Expand all Collapse all UNIVERSITA' DEGLI STUDI DI MILANO-BICOCCA Italy Net EU contribution € 1 253 334,65 Address PIAZZA DELL'ATENEO NUOVO 1 20126 MILANO See on map Region Nord-Ovest Lombardia Milano Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 1 253 334,65 UNIVERSITY OF SURREY Participation ended United Kingdom Net EU contribution € 33 753,35 Address Stag Hill GU2 7XH Guildford See on map Region South East (England) Surrey, East and West Sussex West Surrey Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 33 753,35