scholarly journals Chern–Simons formulation of three-dimensional gravity with torsion and nonmetricity

2006 ◽  
Vol 56 (12) ◽  
pp. 2523-2543 ◽  
Author(s):  
Sergio L. Cacciatori ◽  
Marco M. Caldarelli ◽  
Alex Giacomini ◽  
Dietmar Klemm ◽  
Diego S. Mansi
Keyword(s):  
Three Dimensional ◽  
Dimensional Gravity ◽  
Chern Simons

scholarly journals RATIONAL CONFORMAL FIELD THEORY AND MULTIWORMHOLE PARTITION FUNCTION IN THREE-DIMENSIONAL GRAVITY

1993 ◽  
Vol 08 (22) ◽  
pp. 3909-3932 ◽  
Author(s):  
SHUN’YA MIZOGUCHI
Keyword(s):  
Partition Function ◽  
Initial Data ◽  
Three Dimensional ◽  
Lens Space ◽  
Conformal Field Theories ◽  
Positive Cosmological Constant ◽  
Modular Invariant ◽  
Conformal Field ◽  
Dimensional Gravity ◽  
Chern Simons

We study the Turaev-Viro (TV) invariant as the Euclidean Chern-Simons-Witten gravity partition function with positive cosmological constant. After explaining why it can be identified as the partition function of three-dimensional gravity, we show that the initial data of the TV invariant can be constructed from the duality data of a certain class of rational conformal field theories, and that, in particular, the original TV initial data are associated with the Ak+1 modular invariant SU(2) WZW model. As a corollary we then show that the partition function Z(M) is bounded from above by [Formula: see text], where g is the smallest genus of handlebodies with which M can be presented by Hegaard splitting. Z(M) is generically very large near Λ~+0 if M is neither S3 nor a lens space, and many-wormhole configurations dominate near Λ~+0 in the sense that Z(M) generically tends to diverge faster as the “number of wormholes” g becomes larger.

ON SL(2, ℝ) AND AdS GRAVITY

2012 ◽  
Vol 27 (23) ◽  
pp. 1250138 ◽  
Author(s):  
SEN HU ◽  
ZHI HU ◽  
RUORAN ZHANG
Keyword(s):  
Fixed Points ◽  
Ricci Flow ◽  
Three Dimensional ◽  
Topological Properties ◽  
Dimensional Gravity ◽  
Chern Simons

In this paper, we first view the three-dimensional gravity as the fixed points of generalized Ricci flow. Next we discuss the linear AdS3 gravity, and show some interesting topological properties in the Bañados, Teitelboim and Zanelli (BTZ) construction by manipulation of the group-theoretic properties of SL(2, ℝ). Finally we embed SL(2, ℝ) into OSp(1|2, ℝ) and consider the corresponding super-Chern–Simons action.

3D MANIFOLDS, GRAPH INVARIANTS AND CHERN-SIMONS THEORY

1992 ◽  
Vol 07 (23) ◽  
pp. 2065-2076 ◽  
Author(s):  
S. KALYANA RAMA ◽  
SIDDHARTHA SEN
Keyword(s):  
Partition Function ◽  
Closed Form ◽  
Three Dimensional ◽  
Simons Theory ◽  
Partition Functions ◽  
Graph Invariants ◽  
Absolute Value ◽  
Dimensional Gravity ◽  
Chern Simons ◽  
Chern Simons Theory

We show how the Turaev-Viro invariant, which is closely related to the partition function of three-dimensional gravity, can be understood within the framework of SU(2) Chern-Simons theory. We also show that, for S3 and RP3, this invariant is equal to the absolute value square of their respective partition functions in SU(2) Chern-Simons theory and give a method of evaluating the latter in a closed form for a class of 3D manifolds, thus in effect obtaining the partition function of three-dimensional gravity for these manifolds. By interpreting the triangulation of a manifold as a graph consisting of crossings and vertices with three lines we also describe a new invariant for certain class of graphs.

scholarly journals Three-dimensional de Sitter horizon thermodynamics

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Dionysios Anninos ◽  
Eleanor Harris
Keyword(s):  
Entanglement Entropy ◽  
Three Dimensional ◽  
Simons Theory ◽  
De Sitter ◽  
Edge Mode ◽  
Mode Theory ◽  
Dimensional Gravity ◽  
Field Fluctuations ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We explore thermodynamic contributions to the three-dimensional de Sitter horizon originating from metric and Chern-Simons gauge field fluctuations. In Euclidean signature these are computed by the partition function of gravity coupled to matter semi-classically expanded about the round three-sphere saddle. We investigate a corresponding Lorentzian picture — drawing inspiration from the topological entanglement entropy literature — in the form of an edge-mode theory residing at the de Sitter horizon. We extend the discussion to three-dimensional gravity with positive cosmological constant, viewed (semi-classically) as a complexified Chern-Simons theory. The putative gravitational edge-mode theory is a complexified version of the chiral Wess-Zumino-Witten model associated to the edge-modes of ordinary Chern-Simons theory. We introduce and solve a family of complexified Abelian Chern-Simons theories as a way to elucidate some of the more salient features of the gravitational edge-mode theories. We comment on the relation to the AdS4/CFT3 correspondence.

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

scholarly journals Fermi gas approach to general rank theories and quantum curves

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Naotaka Kubo
Keyword(s):  
Matrix Models ◽  
Critical Role ◽  
Three Dimensional ◽  
Fermi Gas ◽  
Fermi Gases ◽  
Partition Functions ◽  
Density Matrices ◽  
General Rank ◽  
Chern Simons ◽  
The Ideal

Abstract It is known that matrix models computing the partition functions of three-dimensional $$ \mathcal{N} $$ N = 4 superconformal Chern-Simons theories described by circular quiver diagrams can be written as the partition functions of ideal Fermi gases when all the nodes have equal ranks. We extend this approach to rank deformed theories. The resulting matrix models factorize into factors depending only on the relative ranks in addition to the Fermi gas factors. We find that this factorization plays a critical role in showing the equality of the partition functions of dual theories related by the Hanany-Witten transition. Furthermore, we show that the inverses of the density matrices of the ideal Fermi gases can be simplified and regarded as quantum curves as in the case without rank deformations. We also comment on four nodes theories using our results.

scholarly journals Wilson loop algebras and quantum K-theory for Grassmannians

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Hans Jockers ◽  
Peter Mayr ◽  
Urmi Ninad ◽  
Alexander Tabler
Keyword(s):  
Wilson Loop ◽  
Gauge Theories ◽  
Wilson Line ◽  
Quantum Cohomology ◽  
Three Dimensional ◽  
Loop Algebra ◽  
Loop Algebras ◽  
Verlinde Algebra ◽  
K Theory ◽  
Chern Simons

Abstract We study the algebra of Wilson line operators in three-dimensional $$ \mathcal{N} $$ N = 2 supersymmetric U(M ) gauge theories with a Higgs phase related to a complex Grassmannian Gr(M, N ), and its connection to K-theoretic Gromov-Witten invariants for Gr(M, N ). For different Chern-Simons levels, the Wilson loop algebra realizes either the quantum cohomology of Gr(M, N ), isomorphic to the Verlinde algebra for U(M ), or the quantum K-theoretic ring of Schubert structure sheaves studied by mathematicians, or closely related algebras.

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

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