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Related papers: Notes On Super Riemann Surfaces And Their Moduli

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In this note we give a summary of some elementary results in the theory of super Riemann surfaces (SUSY curves).

Algebraic Geometry · Mathematics 2013-06-11 R. Fioresi , S. D. Kwok

The symmetric spaces that appear as moduli spaces in string theory and supergravity can be decomposed with explicit metrics using parabolic subgroups. The resulting isometry between the original moduli space and this decomposition can be…

High Energy Physics - Theory · Physics 2024-07-31 Paul S. Aspinwall

Complex geometry and supergeometry are closely entertwined in superstring perturbation theory, since perturbative superstring amplitudes are formulated in terms of supergeometry, and yet should reduce to integrals of holomorphic forms on…

High Energy Physics - Theory · Physics 2007-08-30 Eric D'Hoker , D. H. Phong

The moduli spaces of compact and connected Riemann surfaces has been a central topic in modern mathematics in recent years. Thus their homological dimensions become important invariants. Motivated by the emergence mathematical counterparts…

Quantum Algebra · Mathematics 2020-03-30 Hao Yu

We establish the equivalence between two formulations of superstring perturbation theory, one based on integration over the supermoduli space of super Riemann surfaces (SRS), the other based on integration over the bosonic moduli space with…

High Energy Physics - Theory · Physics 2023-04-05 Charles Wang , Xi Yin

We define analytic maps between super Riemann surfaces which extend the notion of branched covering maps to a supersymmetric setting. We show that these super covering maps appear naturally both in symmetric product orbifolds of…

High Energy Physics - Theory · Physics 2026-02-06 Beat Nairz

In these lecture notes, we provide an introduction to the moduli space of Riemann surfaces, a fundamental concept in the theories of 2D quantum gravity, topological string theory, and matrix models. We begin by reviewing some basic results…

Algebraic Geometry · Mathematics 2026-03-02 Alessandro Giacchetto , Danilo Lewański

In this note we reformulate topological string theory using supermanifolds and supermoduli spaces, following the approach worked out by Witten for superstring perturbation theory in arXiv:1209.5461. We intend to make the construction…

High Energy Physics - Theory · Physics 2016-08-29 Bei Jia

This article is an introduction to newly discovered relations between volumes of moduli spaces of Riemann surfaces or super Riemann surfaces, simple models of gravity or supergravity in two dimensions, and random matrix ensembles. (The…

Symplectic Geometry · Mathematics 2020-07-07 Edward Witten

We generalize the result of Voronov (1988) to give an expression for the super Mumford form $\mu$ on the moduli spaces of super Riemann surfaces with Ramond and Neveu-Schwarz punctures in the limit where the number of punctures is large…

Mathematical Physics · Physics 2019-07-17 Daniel Diroff

A new $(1,1)$-dimensional super vector bundle which exists on any super Riemann surface is described. Cross-sections of this bundle provide a new class of fields on a super Riemann surface which closely resemble holomorphic functions on a…

High Energy Physics - Theory · Physics 2010-04-06 Alice Rogers , Mark Langer

The article surveys published and not yet published results about moduli spaces of algebraic surfaces.

Algebraic Geometry · Mathematics 2008-12-24 Fabrizio Catanese

We generalize the result of Voronov (1988) to give an expression for the super Mumford form $\mu$ on the moduli spaces of super Riemann surfaces with Ramond and Neveu-Schwarz punctures. In the Ramond case we take the number of punctures to…

Mathematical Physics · Physics 2019-07-18 Daniel J. Diroff

Generically, string models with $N=1$ supersymmetry are not expected to have moduli beyond perturbation theory; stringy non-perturbative effects as well as low energy field-theoretic phenomena such as gluino condensation will lift any flat…

High Energy Physics - Theory · Physics 2009-10-28 Tom Banks , Michael Dine

We describe some results on moduli space of logarithmic connections equipped with framings on a $n$-pointed compact Riemann surface.

Algebraic Geometry · Mathematics 2021-03-24 Indranil Biswas , Michi-aki Inaba , Arata Komyo , Masa-Hiko Saito

This article provides a brief discussion of the functional of super Riemann surfaces from the point of view of classical (i.e. not "super-) differential geometry. The discussion is based on symmetry considerations and aims to clarify the…

Differential Geometry · Mathematics 2016-10-10 Enno Keßler , Jürgen Tolksdorf

The moduli associated with boundaries in a Riemann surface are parametrized by the positions and strengths of electric charges. This suggests a method for summing over orientable Riemann surfaces with Dirichlet boundary conditions on the…

High Energy Physics - Theory · Physics 2009-10-09 Michael B. Green , Joe Polchinski

In this paper we relate volumes of moduli spaces of super Riemann surfaces to integrals over the moduli space of stable Riemann surfaces $\overline{\cal M}_{g,n}$. This allows us to prove via algebraic geometry a recursion between the…

Algebraic Geometry · Mathematics 2025-12-24 Paul Norbury

We construct a moduli space for Riemann surfaces that is universal in the sense that it represents compact Riemann surfaces of any finite genus. This moduli space is stratifed according to genus, and it carries a metric and a measure that…

Algebraic Geometry · Mathematics 2017-02-01 Lizhen Ji , Juergen Jost

We consider two problems associated to the space of Riemann surfaces that are closely related to string theory. We first consider the problem of existence of heterotic-string and type-II-superstring field theory vertices in the product of…

High Energy Physics - Theory · Physics 2019-11-13 Seyed Faroogh Moosavian , Yehao Zhou