Related papers: Notes On Super Riemann Surfaces And Their Moduli
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.
It is in general very subtle to integrate over the odd moduli of super Riemann surfaces in perturbative superstring computations. We study how these subtleties go away in favorable cases, including the embedding of N=0 string to N=1 string…
Riemann surfaces are two-dimensional manifolds with a conformal class of metrics. It is well known that the harmonic action functional and harmonic maps are tools to study the moduli space of Riemann surfaces. Super Riemann surfaces are an…
The goal of this paper is to develop some aspects of the deformation theory of piecewise flat structures on surfaces and use this theory to construct new geometric structures on the moduli space of Riemann surfaces.
The known (explicit) examples of Riemann surfaces not definable over their field of moduli are not real whose field of moduli is a subfield of the reals. In this paper we provide explicit examples of real Riemann surfaces which cannot be…
This article is devoted to an overview of superstring perturbation theory from the point of view of super Riemann surfaces. We aim to elucidate some of the subtleties of superstring perturbation that caused difficulty in the early…
We consider the moduli problem of stable maps from a Riemann surface into a supermanifold; in twistor-string theory, this is the instanton moduli space. By developing the algebraic geometry of supermanifolds to include a treatment of…
We review some aspects of moduli in string theory. We argue that one should focus on {\it approximate moduli spaces}, and that there is evidence that such spaces exist non-perturbatively. We ask what it would mean for string theory to…
Our goal is to describe superconformal structures on super Riemann surfaces (SRS), based on data assigned to a fatgraph. We start from the complex structures on punctured $(1|1)$-supermanifolds, characterizing the corresponding moduli and…
One of the subtleties that has made superstring perturbation theory intricate at high string loop order is the fact that as shown by Donagi and Witten, supermoduli space is not holomorphically projected, nor is it holomorphically split. In…
Differentials on Riemann surfaces correspond to translation surfaces with conical singularities, and affine transformations acting on them preserve the orders of these singularities. This viewpoint allows the moduli spaces of differentials…
This is an informal set of lecture notes on moduli spaces of curves based on a set of lectures given at the ICTP last summer. It begins at an elementary level and discusses the genus 1 case in detail. The notes then give an informal…
We construct a measure on the moduli space of super Riemann surfaces with Ramond punctures using the super Mumford isomorphism and a super period map.
We prove that for genus greater than or equal to 5, the moduli space of super Riemann surfaces is not projected (and in particular is not split): it cannot be holomorphically projected to its underlying reduced manifold. Physically, this…
Infinite-dimensional Grassmannian manifold contains moduli spaces of Riemann surfaces of all genera. This well known fact leads to a conjecture that non-perturbative string theory can be formulated in terms of Grassmannian. We present new…
We define a kind of moduli space of nested surfaces and mappings, which we call a comparison moduli space. We review examples of such spaces in geometric function theory and modern Teichmueller theory, and illustrate how a wide range of…
We review recent work which has significantly sharpened our geometric understanding and interpretation of the moduli space of certain $N$=2 superconformal field theories. This has resolved some important issues in mirror symmetry and has…
We study matrix string scattering amplitudes and matrix string instantons on a marked Riemann surface in the limit of a vanishing string coupling constant. We give an explicit parameterization of the moduli space of such instantons. We also…
In this article, we consider certain irreducible subvarieties of the moduli space of compact Riemann surfaces determined by the specification of actions of finite groups. We address the general problem of determining which among them are…
The underlying even manifold of a super Riemann surface is a Riemann surface with a spinor valued differential form called gravitino. Consequently infinitesimal deformations of super Riemann surfaces are certain infinitesimal deformations…