# Contents

## Idea

The space of infinitesimal loops in a given space.

## Properties

### Relation to chiral differential operators

With $X$ a suitable scheme, its formal loop space$L_inf X$ in the sense of (Kapranov-Vasserot I) has a Tate structure? and hence an associated determinantal gerbe $Det_{L_{inf} X}$ with band? $\mathcal{O}^\ast_{L_{inf} X}$. According to (Kapranov-Vasserot IV) this gerbe is essentially identified with the gerbe $CDO_X$ of chiral differential operators on $X$.

## References

In the context of algebraic geometry formal loop spaces have been introduced and studied in

Tentative aspects of a generalization to differential geometry are discussed in

Created on June 2, 2012 21:35:00 by Urs Schreiber (94.136.12.233)