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This is the first of a series of papers dedicated to the study of the partition function of three-dimensional quantum gravity on the twisted solid torus with the aim to deepen our understanding of holographic dualities from a non-perturbative quantum gravity perspective.
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Regge, T, · 1961
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1974 Role of surface integrals in the Hamiltonian formulation of general relativity
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1977 Action integrals and partition functions in quantum gravity
Gibbons, G. W & Hawking, S. W, · 1977
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1980 The use of anticommuting variable integrals in statistical mechanics. III. Unsolved models
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1981 Boundary terms in the action for the Regge calculus
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1981 QUANTUM REGGE CALCULUS
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1983 Global Aspects of Current Algebra
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1983 Wave Function of the Universe
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1984 Current Algebra and Wess-Zumino Model in Two-Dimensions
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1985 NONPERTURBATIVE SIMPLICIAL QUANTUM GRAVITY
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1986 Boundary terms in the action principles of general relativity
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1986 Central charges in the canonical realization of asymptotic symmetries: An example from three dimensional gravity
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1988 2 + 1 Dimensional Gravity As an Exactly Soluble System
Witten, E, · 1988
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1988 Topological quantum field theory
Witten, E, · 1988
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Topological Quantum Field Theory
Atiyah, M, 1988 · 1988
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1989 Exactly soluble diffeomorphism invariant theories
Horowitz, G. T, · 1989
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1989 A new class of topological field theories and the Ray-Singer torsion
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1991 Invariants of three manifolds via link polynomials and quantum groups
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1991 On Witten’s 3-manifold Invariants
Walker, K, · 1991
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1991 3-dimensional Gravity from the Turaev-Viro Invariant [ arxiv:hep-th/9110057 ]
Mizoguchi, S & Tada, T, · 1991
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1992 State sum invariants of 3 manifolds and quantum 6j symbols
Turaev, V. G & Viro, O. Y, · 1992
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1992 The Black Hole in Three Dimensional Space Time
Bañados, M, Teitelboim, C, & Zanelli, J, · 1992
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1992 Regge calculus: a brief review and bibliography
Williams, R. M & Tuckey, P. A, · 1992
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1992 A Model of three-dimensional lattice gravity
Boulatov, D. V, · 1992
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1993 The Basis of the Ponzano-Regge-Turaev-Viro-Ooguri quantum gravity model in the loop representation basis
Rovelli, C, · 1993
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1993 Semi-Classical Limits of Simplicial Quantum Gravity
Barrett, J. W & Foxon, T. J, · 1993
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1995 Skein theory and Turaev-Viro invariants
Roberts, J, · 1995
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1995 Discreteness of area and volume in quantum gravity
Rovelli, C & Smolin, L, · 1995
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1995 Spin networks and quantum gravity
Rovelli, C & Smolin, L, · 1995
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1995 On the moduli space of polygons in the Euclidean plane
Kapovich, M & Millson, J, · 1995
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1995 Aspects of black hole quantum mechanics and thermodynamics in 2+1 dimensions
Carlip, S & Teitelboim, C, · 1995
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1996 The symplectic geometry of polygons in Euclidean space
Kapovich, M & Millson, J. J, · 1996
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1997 ’Sum over surfaces’ form of loop quantum gravity
Reisenberger, M. P & Rovelli, C, · 1997
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1997 Asymptotic structure of symmetry reduced general relativity
Ashtekar, A, Bicak, J, & Schmidt, B. G, · 1997
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1997 An Algebraic interpretation of the Wheeler-DeWitt equation
Barrett, J. W & Crane, L, · 1997
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1998 Spin foam models
Baez, J. C, · 1998
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1998 Note on covariant action integrals in three dimensions
Bañados, M & Méndez, F, · 1998
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1998 Anti de sitter space and holography
Witten, E, · 1998
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1998 Quantum tetrahedra and simplicial spin networks
Barbieri, A, · 1998
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Spin foam models and the classical action principle
Freidel, L & Krasnov, K, 1999 · 1999
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1999 Discrete space-time volume for three-dimensional BF theory and quantum gravity
Freidel, L & Krasnov, K, · 1999
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1999 On the relation between 2+1 Einstein gravity and Chern-Simons theory
Matschull, H.-J, · 1999
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Conformal field theory: A Case study
Gawedzki, K, 1999 · 1999
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1999 Three-dimensional quantum geometry and black holes
Banados, M, · 1999
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Classical 6j symbols and the tetrahedron
Roberts, J, 1999 · 1999
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The symplectic geometry of polygons in hyperbolic 3-space
Kapovich, M, Millson, J. J, & Treloar, T, 1999 · 1999
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2000 Discrete structures in gravity
Regge, T & Williams, R. M, · 2000
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2000 A Holographic formulation of quantum general relativity
Smolin, L, · 2000
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The Symplectic Geometry of Polygons in the 3-sphere
Treloar, T, 2000 · 2000
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Loops, knots, gauge theories and quantum gravity
Gambini, R & Pullin, J, 2000 · 2000
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2000 A Ponzano-Regge model of Lorentzian 3-dimensional gravity
Freidel, L, · 2000
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2001 Implementing holographic projections in Ponzano-Regge gravity
Arcioni, G, Carfora, M, Marzuoli, A, & O’Loughlin, M, · 2001
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2001 A Spin foam model without bubble divergences
Perez, A & Rovelli, C, · 2001
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Haggard, H. M, Han, M, & Riello, A, · 2001
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Quantum gravity in 2+ 1 dimensions
Carlip, S, 2003 · 2003
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Spin foam models of quantum space-time
Oriti, D, 2003 · 2003
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6j symbols for U_q(sl_2) and non-Euclidean tetrahedra
Taylor, Y. U & Woodward, C. T, 2003 · 2003
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The general boundary approach to quantum gravity
Oeckl, R, 2003 · 2003
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2003 Exploring the holographic principle in asymptotically flat space-times via the BMS group
Arcioni, G & Dappiaggi, C, · 2003
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1993 Geometry of the (2+1) black hole
Banados, M, Henneaux, M, Teitelboim, C, & Zanelli, J, · 2013
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2013 Dual dynamics of three dimensional asymptotically flat Einstein gravity at null infinity
Barnich, G & González, H. A, · 2013
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Barnich, G, Gomberoff, A, & González, H. A, · 2013
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Dittrich, B & Hnybida, J, 2013 · 2013
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2013 Divergences and Orientation in Spinfoams
Christodoulou, M, Langvik, M, Riello, A, Roken, C, & Rovelli, C, · 2013
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2003 Spin foam models for quantum gravity
Perez, A, · 2003
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2003 Geometrical measurements in three-dimensional quantum gravity
Barrett, J. W, · 2003
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Ponzano-Regge model revisited II: Equivalence with Chern-Simons
Freidel, L & Louapre, D, 2004 · 2004
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2004 Ponzano-Regge model revisited: I. Gauge fixing, observables and interacting spinning particles
Freidel, L & Louapre, D, · 2004
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2004 Background independent quantum gravity: A Status report
Ashtekar, A & Lewandowski, J, · 2004
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2004 Holography in asymptotically flat space-times and the BMS group
Arcioni, G & Dappiaggi, C, · 2004
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2013 Deformations of Polyhedra and Polygons by the Unitary Group
Livine, E. R, · 2013
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Topological lattice field theories from intertwiner dynamics
Dittrich, B & Kaminski, W, 2013 · 2013
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2013 Coarse graining of spin net models: dynamics of intertwiners
Dittrich, B, Mart�n-Benito, M, & Schnetter, E, · 2013
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2014 Turaev-Viro amplitudes from 2+1 Loop Quantum Gravity
Pranzetti, D, · 2014
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2014 Observables in Loop Quantum Gravity with a cosmological constant
Dupuis, M & Girelli, F, · 2014
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Deformed phase space for 3d loop gravity and hyperbolic discrete geometries
Bonzom, V, Dupuis, M, Girelli, F, & Livine, E. R, 2014 · 2014
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2014 Towards the Turaev-Viro amplitudes from a Hamiltonian constraint
Bonzom, V, Dupuis, M, & Girelli, F, · 2014
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2014 Deformed Spinor Networks for Loop Gravity: Towards Hyperbolic Twisted Geometries
Dupuis, M, Girelli, F, & Livine, E. R, · 2014
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2014 Notes on the BMS group in three dimensions: I. Induced representations
Barnich, G & Oblak, B, · 2014
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2014 Discretization independence implies non-locality in 4D discrete quantum gravity
Dittrich, B, Kaminski, W, & Steinhaus, S, · 2014
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2014 A new vacuum for Loop Quantum Gravity
Dittrich, B & Geiller, M, · 2014
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2014 Time evolution as refining, coarse graining and entangling
Dittrich, B & Steinhaus, S, · 2014
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2014
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2014 Quantum group spin nets: refinement limit and relation to spin foams
Dittrich, B, Martin-Benito, M, & Steinhaus, S, · 2014
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2014 A Discrete and Coherent Basis of Intertwiners
Freidel, L & Hnybida, J, · 2014
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Exact Path Integral for 3D Quantum Gravity
Iizuka, N, Tanaka, A, & Terashima, S, 2015 · 2015
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2015 Exact Path Integral for 3D Quantum Gravity II
Honda, M, Iizuka, N, Tanaka, A, & Terashima, S, · 2015
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2015 One loop partition function of three-dimensional flat gravity
Barnich, G, González, H. A, Maloney, A, & Oblak, B, · 2015
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2015 Characters of the BMS Group in Three Dimensions
Oblak, B, · 2015
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2015 Notes on the BMS group in three dimensions: II. Coadjoint representation
Barnich, G & Oblak, B, · 2015
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2015 Symplectic and semiclassical aspects of the Schl�fli identity
Hedeman, A, Haggard, H. M, Kur, E, & Littlejohn, R. G, · 2015
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SL(2,C) Chern-Simons Theory, Flat Connections, and Four-dimensional Quantum Geometry
Haggard, H. M, Han, M, Kaminski, W, & Riello, A, 2015 · 2015
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A new realization of quantum geometry
Bahr, B, Dittrich, B, & Geiller, M, 2015 · 2015
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2015 BTZ Black Hole Entropy and the Turaev-Viro model
Geiller, M & Noui, K, · 2015
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Duality between Spin networks and the 2D Ising model
Bonzom, V, Costantino, F, & Livine, E. R, 2015 · 2015
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2015 3d Lorentzian loop quantum gravity and the spinor approach
Girelli, F & Sellaroli, G, · 2015
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2015 On a generalization of a theorem by Euler
Swanepoel, J. W, · 2015
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2016 Actions, topological terms and boundaries in first-order gravity: A review
Corichi, A, Rubalcava-Garc�a, I, & Vuka�inac, T, · 2016
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The Dynamics of Supertranslations and Superrotations in 2+1 Dimensions
Carlip, S, 2016 · 2016
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2016 3D holography: from discretum to continuum
Bonzom, V & Dittrich, B, · 2016
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A local and operational framework for the foundations of physics
Oeckl, R, 2016 · 2016
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Holographic relations in loop quantum gravity
Smolin, L, 2016 · 2016
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The Bethe ansatz for the six-vertex and XXZ models: an exposition
Duminil-Copin, H, Gagnebin, M, Harel, M, Manolescu, I, & Tassion, V, 2016 · 2016
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2016 Ising Spin Network States for Loop Quantum Gravity: a Toy Model for Phase Transitions
Feller, A & Livine, E. R, · 2016
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Quasi-local holographic dualities in non-perturbative 3d quantum gravity II - From coherent quantum boundaries to BMS 3 characters
Dittrich, B, Goeller, C, Livine, E. R, & Riello, A, 2017 · 2017
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2017 Kitaev Lattice Models as a Hopf Algebra Gauge Theory
Meusburger, C, · 2017
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2017 Fusion basis for lattice gauge theory and loop quantum gravity
Delcamp, C, Dittrich, B, & Riello, A, · 2017
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2017 3d Quantum Gravity: Coarse-Graining and q q -Deformation
Livine, E. R, · 2017
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2017 Quantum gravity kinematics from extended TQFTs
Dittrich, B & Geiller, M, · 2017
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2017 The continuum limit of loop quantum gravity - a framework for solving the theory
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2017 Loop Quantum Gravity, Exact Holographic Mapping, and Holographic Entanglement Entropy
Han, M & Hung, L.-Y, · 2017
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Group Field theory and Tensor Networks: towards a Ryu-Takayanagi formula in full quantum gravity
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On a self-dual phase space for 3+1 lattice Yang-Mills theory
Riello, A, 2017 · 2017
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Discretization of 3d gravity in different polarizations
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Quasi-local holographic dualities in non-perturbative 3d quantum gravity III
Goeller, C, Livine, E. R, & Riello, A, 2017 · 2017
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2013 The Spin Foam Approach to Quantum Gravity
Perez, A, · 2019
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2006 Ponzano-Regge model revisited III: Feynman diagrams and effective field theory
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2011 U(N) Coherent States for Loop Quantum Gravity
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