Notes on super Riemann surfaces and their moduli

@article{Witten2019NotesOS,
  title={Notes on super Riemann surfaces and their moduli},
  author={Edward Witten},
  journal={Pure and Applied Mathematics Quarterly},
  year={2019}
}
  • E. Witten
  • Published 11 September 2012
  • Physics, Mathematics
  • Pure and Applied Mathematics Quarterly
These are notes on the theory of super Riemann surfaces and their moduli spaces, aiming to collect results that are useful for a better understanding of superstring perturbation theory in the RNS formalism. 
Notes on supermanifolds and integration
  • E. Witten
  • Physics, Mathematics
  • Pure and Applied Mathematics Quarterly
  • 2019
These are notes on the theory of supermanifolds and integration on them, aiming to collect results that are useful for a better understanding of superstring perturbation theory in the RNS formalism.
On Closed Twistor String Theory
The Heterotic twistor string theory of Mason and Skinner is investigated with particular attention given to the role of topological gravity on the world-sheet. The general structure of scatteringExpand
A Local Torelli's Theorem for SUSY curves
SUSY curves, or super Riemann surfaces, are the generalization of Riemann surfaces in the context of super geometry. The main goal of this paper is to construct some explicit families of SUSY curvesExpand
Analytic and Algebraic Deformations of Super Riemann Surfaces
By analytic deformations of complex structures, we mean perturbations of the Dolbeault operator. By algebraic deformations of complex structures, we mean deformations of holomorphic glueing data. ForExpand
Pluri-Canonical Models of Supersymmetric Curves
This paper is about pluri-canonical models of supersymmetric (susy) curves. Susy curves are generalisations of Riemann surfaces in the realm of super geometry. Their moduli space is a key object inExpand
More On Superstring Perturbation Theory
This article is devoted to an overview of some of the subtleties of superstring perturbation theory in the RNS framework, focusing on a concrete example { the SO(32) heterotic string compactied on aExpand
Topological String Theory Revisited I: The Stage
  • B. Jia
  • Physics, Mathematics
  • 2016
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.Expand
Aspects of String Perturbation Theory
In this thesis we study the string perturbation theory for closed bosonic strings and closed superstrings in RNS formalism. For bosonic string we review the classic approach, and also discuss anExpand
On SUSY curves
We give a summary of some elementary results in the theory of super Rie-mann surfaces (SUSY curves), which are mostly known, but are not readily available in the literature. In particular, we giveExpand
The projective linear supergroup and the SUSY-preserving automorphisms of ℙ1|1
The purpose of this paper is to describe the projective linear supergroup, its relation with the automorphisms of the projective superspace and to determine the supergroup of SUSY preservingExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 63 REFERENCES
Moduli of super Riemann surfaces
The basic properties of super Riemann surfaces are presented, and their supermoduli spaces are constructed, in a manner suitable for the application of algebro-geometric techniques to string theory.
Notes on supermanifolds and integration
  • E. Witten
  • Physics, Mathematics
  • Pure and Applied Mathematics Quarterly
  • 2019
These are notes on the theory of supermanifolds and integration on them, aiming to collect results that are useful for a better understanding of superstring perturbation theory in the RNS formalism.
Superconformal geometry and string theory
We give a formula for the determinant of the super Laplace operator in a holomorphic hermitian line bundle over a superconformal manifold. This is then used to obtain an expression for the fermionExpand
Geometry of superconformal manifolds
The main facts about complex curves are generalized to superconformal manifolds. The results thus obtained are relevant to the fermion string theory and, in particular, they are useful forExpand
The super GAGA principle and families of super Riemann surfaces
We extend the GAGA principle, the Kodaira embedding theorem, and Chow's lemma to supergeometry and conclude that families of super Riemann surfaces are locally algebraic
Supermoduli spaces
The connection between different supermoduli spaces is studied. It is shown that the coincidence of the moduli space of (1/1) dimensional complex manifolds andN=2 superconformal moduli space isExpand
N = 2 super-Riemann surfaces
Abstract Super-Riemann surfaces are generalized to N ⩾ 2. Basis differentials and tensors are defined. For even N , a distinction between general O( N ) surfaces and SO( N ) (untwisted) surfacesExpand
The Geometry of String Perturbation Theory
This paper is devoted to recent progress made towards the understanding of closed bosonic and fermionic string perturbation theory, formulated in a Lorentz-covariant way on Euclidean space-time.Expand
Supergravity and the spinor dual model
Abstract We find that the spinor dual model is locally supersymmetric not only in the two-dimensional surface spanned by the string, but also with respect to the embedding space-time.
A superanalog of the Selberg trace formula and multiloop contributions for fermionic strings
An analog of the classical Selberg trace formula is given for discrete groups, acting on the upper complex half-superplane. Applications to the fermionic string measure on the moduli superspace areExpand
...
1
2
3
4
5
...