The Super Mumford Form and Sato Grassmannian

2020/02/16 by Maxwell, Katherine A.
#Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2002.06625

Abstract

We describe a supersymmetric generalization of the construction of Kontsevich and Arbarello, De Concini, Kac, and Procesi, which utilizes a relation between the moduli space of curves with the infinite-dimensional Sato Grassmannian. Our main result is the existence of a flat holomorphic connection on the line bundle λ_3/2⊗λ_1/2^-5 on the moduli space of triples: a super Riemann surface, a Neveu-Schwarz puncture, and a formal coordinate system. We also prove a superconformal Noether normalization lemma for families of super Riemann surfaces.

Related

• The Super Mumford Form in the Presence of Ramond and Neveu-Schwarz Punctures
• The Neveu-Schwarz group and Schwarz's extended super Mumford form
• Toward the Universal Mumford form on Sato Grassmannians
• Notes On Super Riemann Surfaces And Their Moduli
• Goldman form, flat connections and stable vector bundles