Advances in Theoretical and Mathematical Physics

Chiral algebras of (0, 2) models

Junya Yagi

Full-text: Open access


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

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

First available in Project Euclid: 23 January 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Yagi, Junya. Chiral algebras of (0, 2) models. Adv. Theor. Math. Phys. 16 (2012), no. 1, 1--37.

Export citation