2d Sigma Models on Non-compact Calabi-Yau and $\mathcal{N}=2$ Liouville Theory

Abstract

We consider a class of two dimensional conformal $\mathcal{N}=2$ supersymmetric $U(1)$ gauge linear sigma models with $N$ fields of charges $+1$ and $N$ fields of charges $-1$, whose Higgs branches are non-compact toric Calabi-Yau manifolds of complex dimension $2N-1$. We show, starting from large-$N$ approximation, that the Coulomb branch of these models, which opens up at strong coupling, is described by $\mathcal{N}=2$ Liouville theory and then extrapolate it to exact equivalence demanding the central charge of the Liouville theory to be $\hat{c}=2N-1$. Next we concentrate on mostly physically attractive $N=2$ and $N\ge 3$ cases and find there a perfect agreement of the set of complex moduli on the Calabi-Yau side with the marginal deformations in $\mathcal{N}=2$ Liouville theory, supporting proposed exact equivalence.

arXiv comment31 pages, 3 figures; added citations and further clarifications about the studied correspondence

References in corpus (42)

• Phases of $N=2$ Theories In Two Dimensions
• Supergravity and a Confining Gauge Theory: Duality Cascades and $\chi$SB-Resolution of Naked Singularities
• CFT's From Calabi-Yau Four-folds
• Massless Black Holes and Conifolds in String Theory
• A Correspondence Principle for Black Holes and Strings
• Vortices, Instantons and Branes
• On Classification of N=2 Supersymmetric Theories, (e-mail uncorrupted version)
• Nonabelian Superconductors: Vortices and Confinement in $\mathcal{N}=2$ SQCD
• Two-Dimensional Black Hole and Singularities of CY Manifolds
• Liouville Field Theory -- A decade after the revolution
• Solitons in the Higgs phase -- the moduli matrix approach --
• Vortex Strings and Four-Dimensional Gauge Dynamics
• Non-Abelian String Junctions as Confined Monopoles
• Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories
• Duality of the Fermionic 2d Black Hole and N=2 Liouville Theory as Mirror Symmetry
• Little String Theory in a Double Scaling Limit
• c=1 String as the Topological Theory of the Conifold
• Holography for Non-Critical Superstrings
• Operator product expansion and factorization in the $H_3^{+}$-WZNW model
• Branes and N=2 Theories in Two Dimensions
• Phases of Quantum Gravity in AdS3 and Linear Dilaton Backgrounds
• Quantum Vortex Strings: A Review
• LSZ in LST
• On The Conformal Field Theory Of The Higgs Branch
• The No-ghost Theorem for AdS_3 and the Stringy Exclusion Principle
• The BPS Spectra of Gauge Theories in Two and Four Dimensions
• Two dimensional black-hole as a topological coset model of c=1 string theory
• Deformation of Conifold and Intersecting Branes
• Expectation values of local fields for a two-parameter family of integrable models and related perturbed conformal field theories
• Cosets as gauge slices in SU(1,1) strings
• The BPS Spectra of Two-Dimensional Supersymmetric Gauge Theories with Twisted Mass Terms
• Modular Invariance in Superstring on Calabi-Yau n-fold with A-D-E Singularity
• Large-N Solution of the Heterotic N=(0,2) Two-Dimensional CP(N-1) Model
• The long flow to freedom
• Conifold Type Singularities, N=2 Liouville and SL(2;R)/U(1) Theories
• Critical String from Non-Abelian Vortex in Four Dimensions
• Non-Abelian Vortex in Four Dimensions as a Critical String on a Conifold
• D-branes in Singular Calabi-Yau n-fold and N=2 Liouville Theory
• Critical Non-Abelian Vortex in Four Dimensions and Little String Theory
• Hadrons of N=2 Supersymmetric QCD in Four Dimensions from Little String Theory
• Supercoset CFT's for String Theories on Non-compact Special Holonomy Manifolds
• Critical Non-Abelian Vortex and Holography for Little String Theory

Cited by in corpus (1)

• Critical Non-Abelian Vortex String and 2D N=2 Black Hole