# nLab super Riemann surface

superalgebra

and

supergeometry

## Applications

complex geometry

### Examples

#### Manifolds and cobordisms

manifolds and cobordisms

# Contents

## Idea

A super Riemann surface is the analog of a Riemann surface in supergeometry.

## Examples

A Riemann surface with spin structure that is also a branched cover of $\mathbb{C}P^{(1 \vert 1)}$ is canonically endowed with the structure of a super Riemann surface with Ramond punctures? (Donagi-Witten 15). This implies that adinkras encode certain very special super Riemann surfaces Doran & Iga & Landweber & Mendez-Diez 13.

## References

The concept of super Riemann surfaces originates with the following articles:

• Daniel Friedan, Notes On String Theory and 2-Dimensional Conformal Field Theory. 1986

• M.A. Baranov, Albert Schwarz, On the Multiloop Contribution to the String Theory Int.J.Mod.Phys., A2:1773, 1987

• Yuri Manin, Critical Dimensions of String Theories and the Dualizing Sheaf on the Moduli Space of (Super) Curves, Funct.Anal.Appl., 20:244-245, 1987

• S. B. Giddings and P. Nelson, The Geometry of super Riemann surfaces, Commun. Math. Phys., 116, (1988), 607

Further discussion of the moduli space of super Riemann surfaces includes the following:

Discussion of super Riemann surfaces induced by supermultiplets for $N$-extended $d = 1$ supersymmetry – via adinkra symbols, is due to

Revised on February 13, 2017 10:02:45 by Urs Schreiber (46.183.103.8)