Chiral Algebras of (0, 2) Models: Beyond Perturbation Theory

  title={Chiral Algebras of (0, 2) Models: Beyond Perturbation Theory},
  author={M. C. Tan and Junya Yagi},
  journal={Letters in Mathematical Physics},
  • M. TanJunya Yagi
  • Published 31 January 2008
  • Mathematics
  • Letters in Mathematical Physics
We show that the chiral algebras of $${\mathcal{N} = (0, 2)}$$ sigma models with no left-moving fermions are totally trivialized by worldsheet instantons for flag manifold target spaces. Consequently, supersymmetry is spontaneously broken in these models. Our results affirm Stolz’s idea (Stolz in Math Ann 304(4):785–800, 1996) that there are no harmonic spinors on the loop spaces of flag manifolds. Moreover, they also imply that the kernels of certain twisted Dirac operators on these target… 

Chiral algebras of (0, 2) models

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

Vanishing Chiral Algebras and H\"ohn-Stolz Conjecture

Given a two-dimensional quantum field theory with (0,2) supersymmetry, one can construct a chiral (or vertex) algebra. The chiral algebra of a (0,2) supersymmetric sigma model is, perturbatively, the

Beta functions in Chirally deformed supersymmetric sigma models in two dimensions

We study two-dimensional sigma models where the chiral deformation diminished the original 𝒩 = (2, 2) supersymmetry to the chiral one, 𝒩 = (0, 2). Such heterotic models were discovered previously

Making Supersymmetric Quivers from N =(0,2) Sigma Models

We show how to construct quiver-like (0,2) sigma models starting from n copies of (2,2) CP(N-1) models (or similar more generic models). These "quivers" present a natural generalization of the

Anomalies of minimal  = ( 0 , 1 ) and  = ( 0 , 2 ) sigma models on homogeneous spaces

We study chiral anomalies in  = ( 0 , 1 ) and ( 0 , 2 ) two-dimensional minimal sigma models defined on the generic homogeneous spaces G/H. Such minimal theories contain only (left) chiral fermions

Quasi-Topological Gauged Sigma Models, The Geometric Langlands Program, And Knots

We construct and study a closed, two-dimensional, quasi-topological (0,2) gauged sigma model with target space a smooth G-manifold, where G is any compact and connected Lie group. When the target

Boundary Chiral Algebras and Holomorphic Twists

We study the holomorphic twist of 3d ${\cal N}=2$ gauge theories in the presence of boundaries, and the algebraic structure of bulk and boundary local operators. In the holomorphic twist, both bulk

Chiral algebras in Landau-Ginzburg models

A bstractChiral algebras in the cohomology of the Q¯+$$ {\overline{Q}}_{+} $$ supercharge of two-dimensional N=02$$ \mathcal{N}=\left(0,2\right) $$ theories on flat spacetime are discussed. Using the

N=(0,2) deformation of the CP(1) model: Two-dimensional analog of N=1 Yang-Mills theory in four dimensions

We consider two-dimensional $\mathcal{N}=(0,2)$ sigma models with the CP(1) target space. A minimal model of this type has one left-handed fermion. Nonminimal extensions contain, in addition, $N_f$



Two-dimensional twisted sigma models and the theory of chiral differential operators

In this paper, we study the perturbative aspects of a twisted version of the two-dimensional $(0,2)$ heterotic sigma model on a holomorphic gauge bundle $\mathcal E$ over a complex, hermitian

Topological heterotic rings

We prove the existence of topological rings in (0,2) theories containing non-anomalous left-moving U(1) currents by which they may be twisted. While the twisted models are not topological, their

Chiral rings in N = 2 superconformal theories

New string vacua from twistor spaces

We find a new family of AdS{sub 4} vacua in IIA string theory. The internal space is topologically either the complex projective space CP{sup 3} or the ''flag manifold'' SU(3)/(U(1)xU(1)), but the

Mirror Symmetry

We prove mirror symmetry for supersymmetric sigma models on Kahler manifolds in 1+1 dimensions. The proof involves establishing the equivalence of the gauged linear sigma model, embedded in a theory

Topological sigma models

A variant of the usual supersymmetric nonlinear sigma model is described, governing maps from a Riemann surfaceΣ to an arbitrary almost complex manifoldM. It possesses a fermionic BRST-like symmetry,

Two-dimensional twisted sigma models, the mirror chiral de Rham complex, and twisted generalised mirror symmetry

In this paper, we study the perturbative aspects of a ``B-twisted" two-dimensional (0,2) heterotic sigma model on a holomorphic gauge bundle over a complex, hermitian manifold X. We show that the

Equivariant cohomology of the chiral de Rham complex and the half-twisted gauged sigma model

In this paper, we study the perturbative aspects of the half-twisted variant of Witten's topological A-model coupled to a non-dynamical gauge field with Kahler target space X being a G-manifold. Our