Advances in Theoretical and Mathematical Physics

Chiral algebras of (0, 2) models

Junya Yagi

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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


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