2025/02/04 by Andoni De Arriba de La Hera, Mateo Galdeano, de La Hera, Andoni De Arriba +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2502.02769
openalex publication_date 2025/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct representations of the deformed Shatashvili-Vafa vertex algebra SVa, with parameter a ∈ ℂ, as recently proposed in the physics literature by Fiset and Gaberdiel. The geometric input for our construction are integrable G2-structures with closed torsion, solving the heterotic G2 system with α'=0 on the group manifolds S3× T4 and S3× S3× S1. From considerations in string theory, one expects the chiral algebra of these backgrounds to include SVa, and we provide a mathematical realization of this expectation by obtaining embeddings of SVa in the corresponding superaffine vertex algebra and the chiral de Rham complex. In our examples, the parameter a is proportional to the scalar torsion class of the G2 structure, a ∼ τ0, as expected from previous work in the semi-classical limit by the second author, jointly with De la Ossa and Marchetto.