Mirror symmetry in two steps: A-I-B

Abstract

We suggest an interpretation of mirror symmetry for toric varieties via an equivalence of two conformal field theories. The first theory is the twisted sigma model of a toric variety in the infinite volume limit (the A-model). The second theory is an intermediate model, which we call the I-model. The equivalence between the A-model and the I-model is achieved by realizing the former as a deformation of a linear sigma model with a complex torus as the target and then applying to it a version of the T-duality. On the other hand, the I-model is closely related to the twisted Landau-Ginzburg model (the B-model) that is mirror dual to the A-model. Thus, the mirror symmetry is realized in two steps, via the I-model. In particular, we obtain a natural interpretation of the superpotential of the Landau-Ginzburg model as the sum of terms corresponding to the components of a divisor in the toric variety. We also relate the cohomology of the supercharges of the I-model to the chiral de Rham complex and the quantum cohomology of the underlying toric variety.

50 pages; revised version

References in corpus (3)

• Chiral de Rham complex and the half-twisted sigma-model
• Two-Dimensional Models With (0,2) Supersymmetry: Perturbative Aspects
• On First Order Formalism in String Theory

Cited by in corpus (26)

• Multiloop Superstring Amplitudes from Non-Minimal Pure Spinor Formalism
• Lectures on curved beta-gamma systems, pure spinors, and anomalies
• Supersymmetry of the Chiral de Rham Complex
• Poisson sigma model on the sphere
• A topological sigma model of biKaehler geometry
• On the B-twisted topological sigma model and Calabi-Yau geometry
• Stringy ER=EPR
• Symmetries and Covering Maps for the Minimal Tension String on $\mathbf{Ad}{\mathbf{S}}_3\times {\mathbf{S}}^3\times {\mathbf{T}}^4$
• 2D sigma models and differential Poisson algebras
• Partition Functions, Localization, and the Chiral de Rham complex
• Chiral de Rham complex on Riemannian manifolds and special holonomy
• Large-N Solution of the Heterotic CP(N-1) Model with Twisted Masses
• Two-Dimensional Twisted Sigma Models, the Mirror Chiral de Rham Complex, and Twisted Generalised Mirror Symmetry
• Lagrangian approach to sheaves of vertex algebras
• Two-Dimensional Twisted Sigma Models And The Theory of Chiral Differential Operators
• BPS Spectrum of Supersymmetric CP(N-1) Theory with Z_N Twisted Masses
• Two-dimensional abelian BF theory in Lorenz gauge as a twisted N=(2,2) superconformal field theory
• New observables in topological instantonic field theories
• Theory of holomorphic maps of two-dimensional complex manifolds to toric manifolds and type A multi-string theory
• On a Logarithmic Deformation of the Supersymmetric bc-system on Curved Manifolds
• Little Strings, Quasi-topological Sigma Model on Loop Group, and Toroidal Lie Algebras
• Partition function of beta-gamma system on orbifolds
• Grobner Bases for Finite-temperature Quantum Computing and their Complexity
• Tropical Mirror
• Non-linear sigma models via the chiral de Rham complex
• Mixed anomalies of chiral algebras compactified to smooth quasi-projective surfaces