Chiral Deformations of Conformal Field Theories

Abstract

We study general perturbations of two-dimensional conformal field theories by holomorphic fields. It is shown that the genus one partition function is controlled by a contact term (pre-Lie) algebra given in terms of the operator product expansion. These models have applications to vertex operator algebras, two-dimensional QCD, topological strings, holomorphic anomaly equations and modular properties of generalized characters of chiral algebras such as the $W_{1+\infty }$ algebra, that is treated in detail.

28 pages, latex

References in corpus (11)

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• Large N 2D Yang-Mills Theory and Topological String Theory
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• Toda Lattice Hierarchy and the Topological Description of the c=1 String Theory
• The String Partition Function for QCD on the Torus
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Cited by in corpus (42)

• $T\bar{T}$ deformed partition functions
• Chiral Scale and Conformal Invariance in 2D Quantum Field Theory
• A pedagogical review on solvable irrelevant deformations of 2d quantum field theory
• Two Dimensional Yang-Mills, Black Holes and Topological Strings
• Baby Universes in String Theory
• Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions
• Correlation functions of the CFTs on torus with $T\bar{T}$ deformation
• Modular covariance and uniqueness of $J\bar{T}$ deformed CFTs
• Two Dimensional Kodaira-Spencer Theory and Three Dimensional Chern-Simons Gravity
• Probing higher spin black holes from CFT
• Novikov structures on solvable Lie algebras
• Thermal Correlation Functions of KdV Charges in 2D CFT
• Holography for chiral scale-invariant models
• A universal correction to higher spin entanglement entropy
• Boundary Conditions and Partition Functions in Higher Spin AdS${}_3$/CFT${}_2$
• A universe field theory for JT gravity
• Conformal perturbation theory and higher spin entanglement entropy on the torus
• Chern-Simons Theory in Lens Spaces from 2d Yang-Mills on the Cylinder
• Quantum Hall Bilayers and the Chiral Sine-Gordon Equation
• Vertex algebras and quantum master equation
• W(1+infinity) algebra as a symmetry behind AGT relation
• $T\bar{T}$-flow effects on torus partition functions
• Hamiltonian Formulation of the W-Infinity Minimal Models
• Modular Properties of 3D Higher Spin Theory
• From Zwiebach invariants to Getzler relation
• Tautological relations in Hodge field theory
• Gravitational Corrections for Supersymmetric Gauge Theories with Flavors via Matrix Models
• Resurgence analysis of 2d Yang-Mills theory on a torus
• Diagrammatic Expansion of Non-Perturbative Little String Free Energies
• Free fermions, KdV charges, generalised Gibbs ensembles and modular transforms
• Two-Dimensional Yang-Mills Theory and Moduli Spaces of Holomorphic Differentials
• The phase diagram of $T\bar{T}$-deformed Yang-Mills theory on the sphere
• On some (integrable) structures in low-dimensional holography
• Holomorphic anomaly of 2d Yang-Mills theory on a torus revisited
• Counting functions for branched covers of elliptic curves and quasi-modular forms
• Regularized Integrals on Riemann Surfaces and Modular Forms
• Regularized Integrals on Elliptic Curves and Holomorphic Anomaly Equations
• Modular Properties of Generalised Gibbs Ensembles
• W-(infinity)-algebras in n complex dimensions and Kodaira-Spencer deformations : a symplectic approach
• Some remarks on mirror symmmetry and noncommutative elliptic curves
• On scalar propagators of three-dimensional higher-spin black holes
• Boson-Fermion Correspondence and Holomorphic Anomaly Equation in 2d Yang-Mills Theory on Torus