PIRSA:26020031

Video URL

https://pirsa.org/26020031

2+2=4: a 2d/2d unitary/non-unitary correspondence

Sacchi, M. (2026). 2+2=4: a 2d/2d unitary/non-unitary correspondence. Perimeter Institute for Theoretical Physics. https://pirsa.org/26020031

Sacchi, Matteo. 2+2=4: a 2d/2d unitary/non-unitary correspondence. Perimeter Institute for Theoretical Physics, Feb. 03, 2026, https://pirsa.org/26020031 

          @misc{ scivideos_PIRSA:26020031,
            doi = {10.48660/26020031},
            url = {https://pirsa.org/26020031},
            author = {Sacchi, Matteo},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {2+2=4: a 2d/2d unitary/non-unitary correspondence},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2026},
            month = {feb},
            note = {PIRSA:26020031 see, \url{https://scivideos.org/pirsa/26020031}}
          }

Matteo Sacchi

Talk numberPIRSA:26020031
DOI10.48660/26020031
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

Motivated by the observation that 2 + 2 = 4, we consider 4d N=2 SCFTs on S^2 x Sigma. On the one hand, reduction of a 4d theory T on a Riemann surface Sigma leads to a family F[T;Sigma] of 2d (2,2) unitary SCFTs, a 2d analog of the 4d theories of class S. On the other hand, reduction on S^2 yields a non-unitary two-dimensional CFT C[T] whose chiral algebra is the same as the one associated to T by the standard SCFT/VOA correspondence. This construction upgrades the vertex operator algebra to a full-fledged 2d CFT. What's more, it leads to a novel 2d/2d correspondence, a "2 + 2 = 4" analog of the "4 + 2 = 6" AGT correspondence: the S^2 partition function of F[T;Sigma] is computed by correlation functions of C[T] on Sigma. We discuss some structural aspects of this correspondence, and present an example where T is the (A1,A2) Argyres-Douglas SCFT and Sigma a four-punctured sphere. We also show how the elliptic genus of the F[T;Sigma] theories is captured by a TQFT on Sigma.