Friday, April 4th, 2025
Workshop: Heluani Reimundo
Time: 9:30 AM - 10:30 AM
Location: SCGP 102
Title: The (lack of) progress on chiral homology and extensions of vertex algebra modules
Speaker: Heluani Reimundo
Abstract: We will describe the connection between the degree 1 chiral homology of the projective line with coefficients in two vertex algebra modules, and the extension group between these modules. We then will report on the (lack of) progress towards extending this to higher degrees. This is a report of joint work with T. Cardoso, J. V. Ekeren, and J. Guzmán
Title: The (lack of) progress on chiral homology and extensions of vertex algebra modules
Speaker: Heluani Reimundo
Abstract: We will describe the connection between the degree 1 chiral homology of the projective line with coefficients in two vertex algebra modules, and the extension group between these modules. We then will report on the (lack of) progress towards extending this to higher degrees. This is a report of joint work with T. Cardoso, J. V. Ekeren, and J. Guzmán
Workshop: Mitch Weaver
Time: 11:00 AM - 12:00 PM
Location: SCGP 102
Title: Higher Products of the Vertex Operator Algebra of 4d N = 2 SCFTs
Speaker: Mitch Weaver
Abstract: Every 4d N=2 superconformal field theory contains a BPS protected sub- algebra of local operators that has the structure of a vertex operator algebra (VOA). This VOA is identified by passing to the cohomology of a nilpotent supercharge, T, whose local operator cohomology is represented by twist-translations of Schur operators within a Euclidean two-plane. When working in 4d Minkowski space, this cohomology admits extended operators — so-called descent operators — that are constructed from Schur operators, have worldvolumes extending in the transverse Lorentzian two-plane (so they are point-like w.r.t. the plane supporting the VOA), and subsequently behave like chiral operators supported in the VOA plane. The result is the extended vertex algebra (EVA): a universal extension of the VOA that naturally has the structure of a quasi-VOA, i.e. a vertex algebra (VA) with no conformal vector but which still possesses a representation of sl(2). In Minkowski space, the T-cohomology theory also admits a set of higher products that act on the space of Schur operators and represent higher dimensional versions of mode operators for the fields of a 2d Euclidean chiral algebra. I will describe the construction and basic properties of these higher products along with their relation to the descent operators that give rise to the EVA. These results suggest the VOA of Schur operators in Minkowski space can be equipped with (novel) structures that are commonly found in the higher dimensional chiral algebras describing the minimal twist of 3d N =2 and 4d N =1 theories. This talk is based on 2211.04410 and forthcoming work.
Title: Higher Products of the Vertex Operator Algebra of 4d N = 2 SCFTs
Speaker: Mitch Weaver
Abstract: Every 4d N=2 superconformal field theory contains a BPS protected sub- algebra of local operators that has the structure of a vertex operator algebra (VOA). This VOA is identified by passing to the cohomology of a nilpotent supercharge, T, whose local operator cohomology is represented by twist-translations of Schur operators within a Euclidean two-plane. When working in 4d Minkowski space, this cohomology admits extended operators — so-called descent operators — that are constructed from Schur operators, have worldvolumes extending in the transverse Lorentzian two-plane (so they are point-like w.r.t. the plane supporting the VOA), and subsequently behave like chiral operators supported in the VOA plane. The result is the extended vertex algebra (EVA): a universal extension of the VOA that naturally has the structure of a quasi-VOA, i.e. a vertex algebra (VA) with no conformal vector but which still possesses a representation of sl(2). In Minkowski space, the T-cohomology theory also admits a set of higher products that act on the space of Schur operators and represent higher dimensional versions of mode operators for the fields of a 2d Euclidean chiral algebra. I will describe the construction and basic properties of these higher products along with their relation to the descent operators that give rise to the EVA. These results suggest the VOA of Schur operators in Minkowski space can be equipped with (novel) structures that are commonly found in the higher dimensional chiral algebras describing the minimal twist of 3d N =2 and 4d N =1 theories. This talk is based on 2211.04410 and forthcoming work.