## Advances in Theoretical and Mathematical Physics

- Adv. Theor. Math. Phys.
- Volume 12, Number 3 (2008), 547-604.

### The half-twisted orbifold sigma model and the Chiral de Rham complex

#### Abstract

In this paper, we study the perturbative aspects of the half-twisted
variant of Witten’s topological A-model on a complex orbifold X/G,
where G is an isometry group of X. The objective is to furnish a
purely physical interpretation of the mathematical theory of the Chiral de
Rham complex on orbifolds recently constructed by Frenkel and Szczesny
in *Chiral de Rham complex and orbifolds*, Preprint, arXiv: math.AG/
0307181. In turn, one can obtain a novel understanding of the holomorphic
(twisted) N = 2 superconformal structure underlying the untwisted
and twisted sectors of the quantum sigma model, purely in terms of an
obstruction (or a lack thereof) to a global definition of the relevant physical
operators which correspond to G-invariant sections of the sheaf of
Chiral de Rham complex on X. Explicit examples are provided to help
illustrate this connection, and comparisons with their non-orbifold counterparts
are also made in an aim to better understand the action of the
G-orbifolding on the original half-twisted sigma model on X.

#### Article information

**Source**

Adv. Theor. Math. Phys., Volume 12, Number 3 (2008), 547-604.

**Dates**

First available in Project Euclid: 7 May 2008

**Permanent link to this document**

https://projecteuclid.org/euclid.atmp/1210167653

**Mathematical Reviews number (MathSciNet)**

MR2399319

**Zentralblatt MATH identifier**

1152.81887

#### Citation

Tan, Meng-Chwan. The half-twisted orbifold sigma model and the Chiral de Rham complex. Adv. Theor. Math. Phys. 12 (2008), no. 3, 547--604. https://projecteuclid.org/euclid.atmp/1210167653