Two-Dimensional Gravity and Nonlinear Gauge Theory

Abstract

We review nonlinear gauge theory and its application to two-dimensional gravity. We construct a gauge theory based on nonlinear Lie algebras, which is an extension of the usual gauge theory based on Lie algebras. It is a new approach to generalization of the gauge theory. The two-dimensional gravity is derived from nonlinear Poincar{\' e} algebra, which is the new Yang-Mills like formulation of the gravitational theory. As typical examples, we investigate $R^2$ gravity with dynamical torsion and generic form of 'dilaton' gravity. The supersymmetric extension of this theory is also discussed.

35 pages, phyzzx, RIMS-953

Cited by in corpus (215)

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• Solvable Models of Quantum Black Holes: A Review on Jackiw-Teitelboim Gravity
• Nonabelian noncommutative gauge theory via noncommutative extra dimensions
• Spherically Symmetric Quantum Geometry: States and Basic Operators
• WZW-Poisson manifolds
• Deformed General Relativity and Effective Actions from Loop Quantum Gravity
• Classical and Quantum Gravity in 1+1 Dimensions, Part I: A Unifying Approach
• Non-existence of a dilaton gravity action for the exact string black hole
• Current Algebras and Differential Geometry
• Membrane Sigma-Models and Quantization of Non-Geometric Flux Backgrounds
• Lagrange structure and quantization
• Generalized complex manifolds and supersymmetry
• On the Completeness of the Black Hole Singularity in 2d Dilaton Theories
• Menagerie of AdS${}_2$ boundary conditions
• Flat space holography and complex SYK
• The Classical Solutions of the Dimensionally Reduced Gravitational Chern-Simons Theory
• Poisson sigma models and symplectic groupoids
• Topological Open P-Branes
• Lie algebroid morphisms, Poisson Sigma Models, and off-shell closed gauge symmetries
• Target space symmetries in topological theories I
• Introduction to supergeometry
• Geometric Interpretation and Classification of Global Solutions in Generalized Dilaton Gravity
• Poisson sigma models and deformation quantization
• Limits of JT gravity
• Generalized complex geometry, generalized branes and the Hitchin sigma model
• On the Globalization of Kontsevich's Star Product and the Perturbative Poisson Sigma Model
• Towards a bulk description of higher spin SYK
• Higher-dimensional BF theories in the Batalin-Vilkovisky formalism: The BV action and generalized Wilson loops
• General Yang-Mills type gauge theories for p-form gauge fields: From physics-based ideas to a mathematical framework OR From Bianchi identities to twisted Courant algebroids
• A Poincare lemma for sigma models of AKSZ type
• Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model
• A sigma model field theoretic realization of Hitchin's generalized complex geometry
• Algebroid Yang-Mills Theories
• A higher stacky perspective on Chern-Simons theory
• Carroll black holes
• Lectures on AKSZ Sigma Models for Physicists
• A minimal BV action for Vasiliev's four-dimensional higher spin gravity
• Dirac Sigma Models
• On Nonlinear Gauge Theory from a Deformation Theory Perspective
• A higher Chern-Weil derivation of AKSZ sigma-models
• Dynamical actions and q-representation theory for double-scaled SYK
• Matrix Models and Deformations of JT Gravity
• From Quantum Groups to Liouville and Dilaton Quantum Gravity
• On the AKSZ formulation of the Poisson sigma model
• Poisson geometry of sigma models with extended supersymmetry
• Signature change in 2-dimensional black-hole models of loop quantum gravity
• Deformations of JT Gravity and Phase Transitions
• Lie Algebroid Yang Mills with Matter Fields
• $T\bar{T}$ in JT Gravity and BF Gauge Theory
• The Poisson sigma model on closed surfaces
• Poisson sigma model on the sphere
• Graded Poisson-Sigma Models and Dilaton-Deformed 2D Supergravity Algebra
• Topological Open Membranes
• Supergroup Structure of Jackiw-Teitelboim Supergravity
• Positive specific heat of the quantum corrected dilaton black hole
• Anti-de Sitter holography for gravity and higher spin theories in two dimensions
• Gravity from Lie algebroid morphisms
• Generalized Poisson sigma models
• Nambu-Sigma model and effective membrane actions
• Generalizing Geometry - Algebroids and Sigma Models
• Target-Superspace in 2d Dilatonic Supergravity
• Effective descriptions of branes on non-geometric tori
• Effective Batalin--Vilkovisky theories, equivariant configuration spaces and cyclic chains
• Free differential algebras and generic 2D dilatonic (super)gravities
• Characteristic classes associated to Q-bundles
• Superspin chains from superstring theory
• The Complete Solution of 2D Superfield Supergravity from graded Poisson-Sigma Models and the Super Pointparticle
• Lectures on Batalin-Vilkovisky formalism and its applications in topological quantum field theory
• Topological Poisson Sigma models on Poisson-Lie groups
• OFF-SHELL (4,4) SUPERSYMMETRIC SIGMA MODELS WITH TORSION AS GAUGE THEORIES IN HARMONIC SUPERSPACE
• Hamiltonian BRST deformation of a class of n-dimensional BF-type theories
• A note on the Poisson bracket of 2d smeared fluxes in loop quantum gravity
• Beyond the standard gauging: gauge symmetries of Dirac Sigma Models
• Odd Scalar Curvature in Anti-Poisson Geometry
• Towards holography in the BV-BFV setting
• Poisson Geometry in Constrained Systems
• Edge States and Entropy of 2d Black Holes
• Supergravity in Two Spacetime Dimensions
• Supersymmetric black holes in 2D dilaton supergravity: baldness and extremality
• Dirac Sigma Models from Gauging
• Introduction to the BV-BFV formalism
• Topological Field Theories and Geometry of Batalin-Vilkovisky Algebras
• Universal conservation law and modified Noether symmetry in 2d models of gravity with matter
• The Hitchin Model, Poisson-quasi-Nijenhuis Geometry and Symmetry Reduction
• Gauging the Poisson sigma model
• 2d Gauge Theories and Generalized Geometry
• Hamiltonian Algebroid Symmetries in W-gravity and Poisson sigma-model
• Aspects of AdS${}_2$ holography with non-constant dilaton
• 2D sigma models and differential Poisson algebras
• Quantization of 2D dilaton supergravity with matter
• Dilaton Gravity, Poisson Sigma Models and Loop Quantum Gravity
• Black holes and thermodynamics - The first half century
• Double field theory for the A/B-models and topological S-duality in generalized geometry
• Long time black hole evaporation with bounded Hawking flux
• Classical and Quantum Integrability of 2D Dilaton Gravities in Euclidean space
• On the harmonic superspace geometry of $(4,4)$ supersymmetric sigma models with torsion
• Topological Field Theories induced by twisted R-Poisson structure in any dimension
• Poisson sigma model over group manifolds
• Chemistry of Chern-Simons Supergravity: reduction to a BPS kink, oxidation to M-theory and thermodynamical aspects
• Lie algebroids, Lie groupoids and TFT
• Globalization for Perturbative Quantization of Nonlinear Split AKSZ Sigma Models on Manifolds with Boundary
• Strings in Singular Space-Times and their Universal Gauge Theory
• Consistent interactions of dual linearized gravity in D=5: couplings with a topological BF model
• $Ad{S}_2$ holography is (non-)trivial for (non-)constant dilaton
• Wilson surface observables from equivariant cohomology
• p-Brane Actions and Higher Roytenberg Brackets
• PT-symmetry breaking hamiltonian interactions in BF models
• K-symplectic formalism on Lie algebroids
• AKSZ constructions for topological membranes on $G_2$-manifolds
• Two-dimensional interactions between a BF-type theory and a collection of vector fields
• On the Globalization of the Poisson Sigma Model in the BV-BFV Formalism
• dS${}_2$ as excitation of AdS${}_2$
• Formality theorems for Hochschild complexes and their applications
• Formality and Star Products
• Poisson reduction and branes in Poisson-Sigma models
• Deformation of Batalin-Vilkovisky Structures
• Lie-Poisson gauge theories and $\kappa$-Minkowski electrodynamics
• Two-dimensional gravity with an invariant energy scale
• Couplings of a collection of BF models to matter theories
• Canonical Transformations of Local Functionals and sh-Lie Structures
• The BV action of 3D twisted R-Poisson sigma models
• Topological Membranes, Current Algebras and H-flux - R-flux Duality based on Courant Algebroids
• Gauge Transformation of Double Field Theory for Open String
• Classical Solutions for Poisson Sigma Models on a Riemann surface
• Algebraic formulation of higher gauge theory
• Deformed graded Poisson structures, Generalized Geometry and Supergravity
• Jacobi sigma models
• The topological structure of supergravity: an application to supersymmetric localization
• On Globalized Traces for the Poisson Sigma Model
• Gauged sigma-models with nonclosed 3-form and twisted Jacobi structures
• Dimensional Reduction of the Generalized DBI
• Two-dimensional metric-affine gravity
• Four-dimensional couplings among BF and massless Rarita-Schwinger theories: a BRST cohomological approach
• Current algebras from QP-manifolds in general dimensions
• Dimensional Reduction of Nonlinear Gauge Theories
• Self-interactions in a topological BF-type model in D=5
• The Lie algebroid Poisson sigma model
• Higher Gauge Theory
• BV and BFV Formulation of a Gauge Theory of Quadratic Lie Algebras in 2-d and a Construction of W3 Topological Gravity
• BRST operators for W algebras
• On the generalized Freedman-Townsend model
• Couplings between a collection of BF models and a set of three-form gauge fields
• On self-gravitating kinks in two-dimensional pseudo-riemannian universes
• Equivalences between 2D dilaton gravities, their asymptotic symmetries, and their holographic duals
• Topological Dirac Sigma Models and the Classical Master Equation
• Graded geometry in gauge theories and beyond
• Poisson-Dirac branes in Poisson-Sigma models
• Two-Dimensional N=(2,2) Dilaton Supergravity from Graded Poisson-Sigma Models I: Complete Actions and Their Symmetries
• Two-dimensional gravity with an invariant energy scale and arbitrary dilaton potential
• First order gauge field theories from a superfield formulation
• A note on topological brane theories
• Quantum group origins of edge states in double-scaled SYK
• Poisson Structure Induced Field Theories and Models of 1+1 Dimensional Gravity
• Schwarzian quantum mechanics as a Drinfeld-Sokolov reduction of $BF$ theory
• Star products and branes in Poisson-Sigma models
• Les Houches lectures on two-dimensional gravity and holography
• Basic curvature and the Atiyah cocycle in gauge theory
• Jackiw-Teitelboim Gravity Generates Horndeski via Disformal Transformations
• A Lagrangian for Hamiltonian vector fields on singular Poisson manifolds
• Target Space Equivariant Cohomological Structure of the Poisson Sigma Model
• Poisson Sigma Model with branes and hyperelliptic Riemann surfaces
• Coisotropic submanifolds and dual pairs
• Differential Poisson Sigma Models with Extended Supersymmetry
• Sh-Lie algebras Induced by Gauge Transformations
• An Alternative Topological Field Theory of Generalized Complex Geometry
• Generating functions for local symplectic groupoids and non-perturbative semiclassical quantization
• Generalized dilaton gravity in 2d
• Formal Global AKSZ Gauge Observables and Generalized Wilson Surfaces
• Open problems in the Kontsevich graph construction of Poisson bracket symmetries
• Topological and dynamical aspects of Jacobi sigma models
• 2D Poisson Sigma Models with Gauged Vectorial Supersymmetry
• Canonical Functions and Differential Graded Symplectic Pairs in Supergeometry and AKSZ Sigma Models with Boundary
• Poisson-sigma model for 2D gravity with non-metricity
• On Quantum Obstruction Spaces and Higher Codimension Gauge Theories
• Generalized Supergravity in Two Dimensions
• Boundary coupling of Lie algebroid Poisson sigma models and representations up to homotopy
• On the Kontsevich $\star$-product associativity mechanism
• The A_infty de Rham theorem and integration of representations up to homotopy
• Hamiltonian Algebroids and deformations of complex structures on Riemann curves
• Poly-Poisson Sigma models and their relational poly-symplectic groupoids
• $SU(2)\times SU(2)$ harmonic superspace and (4,4) sigma models with torsion
• From BFV to BV and spacetime covariance
• Quantum Systems Exactly
• On Nonlinear Gauge Theories
• From topological field theory to deformation quantization and reduction
• Poisson sigma models on surfaces with boundary: classical and quantum aspects
• Groupoids, Frobenius algebras and Poisson sigma models
• Chern-Simons action for inhomogeneous Virasoro group as an extension of three dimensional flat gravity
• The Background Field Method and the Linearization Problem for Poisson Manifolds
• Lie Algebroids and generalized projective structures on Riemann surfaces
• Jacobi algebroids and Jacobi sigma models
• Gravity from AKSZ-Manin theories in two, three, and four dimensions
• Homotopy Manin Theories: Generalising Third-Way, Yang-Mills and Integrable Sigma Models
• Comment on "New variables for 1+1 dimensional gravity"
• Gauge fields and Sternberg-Weinstein Approximation of Poisson Manifolds
• Poisson-Sigma Models
• The coupling of Poisson sigma models to topological backgrounds
• Wolfgang Kummer and the Vienna School of Dilaton (Super-)Gravity
• Geometric quantization and non-perturbative Poisson sigma model
• Poisson-Lie sigma models over low dimensional real Poisson-Lie groups
• Equivariant BV-BFV Formalism
• Geometry of Membrane Sigma Models
• A so(2,2) extension of JT gravity via the Virasoro-Kac-Moody semidirect product
• Solutions of deformed three-dimensional gravity
• Instances of Higher Geometry in Field Theory
• The universality question for noncommutative quantum field theory
• Formal Global Perturbative Quantization of the Rozansky-Witten Model in the BV-BFV Formalism
• Cotangent paths as coisotropic subsets for local functions
• Convolution algebras for Relational Groupoids and Reduction
• Higher dimensional Lie algebroid sigma model with WZ term
• Lectures on Symplectic Geometry, Poisson Geometry, Deformation Quantization and Quantum Field Theory
• Minimal Factorization of Chern-Simons Theory -- Gravitational Anyonic Edge Modes
• Supersymmetric Poisson and Poisson-supersymmetric sigma models
• On the Explicit Asymptotic Symmetry Breaking of sl(3,R) Jackiw-Teitelboim Gravity
• Computation of Kontsevich Weights of Connection and Curvature Graphs for Symplectic Poisson Structures