## Advances in Theoretical and Mathematical Physics

- Adv. Theor. Math. Phys.
- Volume 16, Number 1 (2012), 1-37.

### Chiral algebras of (0, 2) models

#### Abstract

We explore two-dimensional sigma models with (0, 2) supersymmetry through their chiral algebras. Perturbatively, the chiral algebras of (0, 2) models have a rich infinite-dimensional structure described by the cohomology of a sheaf of chiral differential operators. Nonperturbatively, instantons can deform this structure drastically. We show that under some conditions they even annihilate the whole algebra, thereby triggering the spontaneous breaking of supersymmetry. For a certain class of Kähler manifolds, this suggests that there are no harmonic spinors on their loop spaces and gives a physical proof of the Höhn–Stolz conjecture.

#### Article information

**Source**

Adv. Theor. Math. Phys., Volume 16, Number 1 (2012), 1-37.

**Dates**

First available in Project Euclid: 23 January 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.atmp/1358950849

**Mathematical Reviews number (MathSciNet)**

MR2985352

**Zentralblatt MATH identifier**

1165.81038

#### Citation

Yagi, Junya. Chiral algebras of (0, 2) models. Adv. Theor. Math. Phys. 16 (2012), no. 1, 1--37. https://projecteuclid.org/euclid.atmp/1358950849