scholarly journals Partition functions of three-dimensional pure gravity

2008 ◽  
Vol 2 (2) ◽  
pp. 285-324 ◽  
Author(s):  
Xi Yin
Keyword(s):  
Three Dimensional ◽  
Partition Functions ◽  
Pure Gravity

scholarly journals Three dimensional pure gravity and generalized Hecke operators

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
M. Ashrafi
Keyword(s):  
Symmetry Group ◽  
Central Charge ◽  
Three Dimensional ◽  
Gravitational Theory ◽  
Hecke Operators ◽  
Simons Theory ◽  
Partition Functions ◽  
Integer Multiple ◽  
Pure Gravity ◽  
Modular Covariance

Abstract In this paper, we study mathematical functions of relevance to pure gravity in AdS3. Modular covariance places stringent constraints on the space of such functions; modular invariance places even stronger constraints on how they may be combined into physically viable candidate partition functions. We explicitly detail the list of holomorphic and anti-holomorphic functions that serve as candidates for chiral and anti-chiral partition functions and note that modular covariance is only consistent with such functions when the left (resp. right) central charge is an integer multiple of 8, c ∈ 8ℕ. We then find related constraints on the symmetry group of the corresponding topological, Chern-Simons, theory in the bulk of AdS. The symmetry group of the theory can be one of two choices: either SO(2; 1) × SO(2; 1) or its three-fold diagonal cover. We introduce the generalized Hecke operators which map the modular covariant functions to the modular covariant functions. With these mathematical results, we obtain conjectural partition functions for extremal CFT2s, and the corresponding microcanonical entropies, when the chiral central charges are multiples of eight. Finally, we compute subleading corrections to the Beckenstein-Hawking entropy in the bulk gravitational theory with these conjectural partition functions.

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 Three-dimensional 𝒩 = 2 supersymmetric gauge theories and partition functions on Seifert manifolds: A review

2019 ◽  
Vol 34 (23) ◽  
pp. 1930011 ◽  
Author(s):  
Cyril Closset ◽  
Heeyeon Kim
Keyword(s):  
Correlation Functions ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Partition Functions ◽  
Exact Results ◽  
Strongly Coupled ◽  
Seifert Manifolds ◽  
Recent Developments ◽  
Supersymmetric Gauge ◽  
Chern Simons

We give a pedagogical introduction to the study of supersymmetric partition functions of 3D [Formula: see text] supersymmetric Chern–Simons-matter theories (with an [Formula: see text]-symmetry) on half-BPS closed three-manifolds — including [Formula: see text], [Formula: see text], and any Seifert three-manifold. Three-dimensional gauge theories can flow to nontrivial fixed points in the infrared. In the presence of 3D [Formula: see text] supersymmetry, many exact results are known about the strongly-coupled infrared, due in good part to powerful localization techniques. We review some of these techniques and emphasize some more recent developments, which provide a simple and comprehensive formalism for the exact computation of half-BPS observables on closed three-manifolds (partition functions and correlation functions of line operators). Along the way, we also review simple examples of 3D infrared dualities. The computation of supersymmetric partition functions provides exceedingly precise tests of these dualities.

scholarly journals AdS3 GRAVITATIONAL INSTANTONS FROM CONFORMAL FIELD THEORY

1999 ◽  
Vol 14 (28) ◽  
pp. 1961-1981 ◽  
Author(s):  
SHUHEI MANO
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Bound States ◽  
Three Dimensional ◽  
Partition Functions ◽  
De Sitter ◽  
Btz Black Hole ◽  
Gravitational Instantons ◽  
Conformal Field ◽  
Horizon Geometry

A conformal field theory on the boundary of three-dimensional asymptotic anti-de Sitter spaces which appear as near horizon geometry of D-brane bound states is discussed. It is shown that partition functions of gravitational instantons appear as high and low temperature limits of the partition function of the conformal field theory. The result reproduces phase transition between the anti-de Sitter space and the BTZ black hole in the bulk gravity.

The gonihedric paradigm extension of the Ising model

2015 ◽  
Vol 29 (32) ◽  
pp. 1550203 ◽  
Author(s):  
George Savvidy
Keyword(s):  
Ising Model ◽  
Spin System ◽  
Three Dimensional ◽  
Spin Systems ◽  
Three Dimensions ◽  
Partition Functions ◽  
Random Surfaces ◽  
Four Dimensions ◽  
Vacuum States ◽  
Binary Information

In this paper we review a recently suggested generalization of the Feynman path integral to an integral over random surfaces. The proposed action is proportional to the linear size of the random surfaces and is called gonihedric. The convergence and the properties of the partition function are analyzed. The model can also be formulated as a spin system with identical partition functions. The spin system represents a generalization of the Ising model with ferromagnetic, antiferromagnetic and quartic interactions. Higher symmetry of the model allows to construct dual spin systems in three and four dimensions. In three dimensions the transfer matrix describes the propagation of closed loops and we found its exact spectrum. It is a unique exact solution of the three-dimensional statistical spin system. In three and four dimensions, the system exhibits the second-order phase transitions. The gonihedric spin systems have exponentially degenerated vacuum states separated by the potential barriers and can be used as a storage of binary information.

scholarly journals Connecting mirror symmetry in 3D and 2D via localization

2014 ◽  
Vol 29 (32) ◽  
pp. 1530004 ◽  
Author(s):  
Heng-Yu Chen ◽  
Hsiao-Yi Chen ◽  
Jun-Kai Ho
Keyword(s):  
Mirror Symmetry ◽  
Gauge Theories ◽  
Three Dimensional ◽  
High Energy ◽  
Partition Functions ◽  
Two Dimensional ◽  
Abelian Gauge ◽  
Fusion Procedure ◽  
Mirror Pair ◽  
Simple Limit

We explicitly apply localization results to study the interpolation between three- and two-dimensional mirror symmetries for Abelian gauge theories with four supercharges. We first use the ellipsoid [Formula: see text] partition functions to verify the mirror symmetry between a pair of general three-dimensional 𝒩 = 2 Abelian Chern–Simons quiver gauge theories. These expressions readily factorize into holomorphic blocks and their antiholomorphic copies, so we can also obtain the partition functions on S1×S2 via fusion procedure. We then demonstrate S1×S2 partition functions for the three-dimensional Abelian gauge theories can be dimensionally reduced to the S2 partition functions of 𝒩 = (2, 2) GLSM and Landau–Ginzburg model for the corresponding two-dimensional mirror pair, as anticipated previously in M. Aganagic et al., J. High Energy Phys.0107, 022 (2001). We also comment on the analogous interpolation for the non-Abelian gauge theories and compute the K-theory vortex partition function for a simple limit to verify the prediction from holomorphic block.

scholarly journals The adsorption of non-polar gases on alkali halide crystals

1939 ◽  
Vol 173 (954) ◽  
pp. 349-367 ◽  
Keyword(s):  
Gas Phase ◽  
Three Dimensional ◽  
Adsorbed Layer ◽  
Partition Functions ◽  
Configurational Energy ◽  
Adsorbed Gas ◽  
The Difference ◽  
Gas Layer ◽  
Alkali Halide Crystals ◽  
Made In

In recent years many important theoretical advances have been made in the application of quantum statistics to adsorption problems. Fowler (1935), adopting the Langmuir picture of a monomolecular adsorbed gas layer, derived from purely statistical considerations the equation p = ( θ /1- θ ) ((2 πm ) 3/2 ( kT ) 5/2 )/ h 3 ( b g ( T )/ v s ( T ) e -x/kT , in which the undetermined constants of Langmuir’s original equation (1918) are given explicitly in terms of the partition functions, b g ( T ) and v s ( T ) belonging to atoms in the gas phase and in the adsorbed layer respectively and x , which is the difference in energy of an atom in the gas phase and in the lowest adsorption level on the surface. In subsequent developments the change in the energy of adsorption as a function of θ (the fraction of the surface covered) has been introduced in the above equation using ( a ) the Bragg and Williams approximations (Fowler 1936 a ) and ( b ) the Bethe method (Peierls 1936) to determine the configurational energy. Further applications and extensions of these methods to special adsorption problems have been carried through by Roberts (1937) and by Wang (1937), and Rushbrooke (1938) has examined the validity of the assumption, which is implicit in all this work, namely, that v s ( T ) is independent of the configuration. In addition, an approach to the solution of the statistical configuration problem when molecules condense in two layers simultaneously has recently been made by Cernuschi (1938) and developed by Dube (1938). In order to evaluate correctly the summations v s ( T ) occurring in equation (1), the Schrödinger equation for an atom moving in the three-dimensional potential field of the substrate should be solved, but this has so far proved prohibitively difficult. In the past it has been customary, and for practical purposes it is possibly generally sufficient, to substitute classical partition functions for these summations.

CHANGE OF DIMENSIONS IN CANONICAL PURE GRAVITY VIA NON-UNITARITY

1991 ◽  
Vol 06 (28) ◽  
pp. 2569-2578 ◽  
Author(s):  
YOAV PELEG
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Pure Gravity ◽  
Dynamical Change

Examining Wheeler's superspace, [Formula: see text], for manifolds Σ(3)=Σ(2)×S1, we see that the hypersurface of geometries for which the radius of the S1 submanifold tends to zero includes all the geometries of [Formula: see text]. By identifying the Σ(2)-geometries we connect the two superspaces and allow a dynamical change of dimensions. This change of dimensions results in non-conservation of information, and thus non-unitarity. Starting from a vacuum of two-dimensional universes it may be possible to end with a number of three-dimensional universes. A simple example of minisuperspace for Σ(2)=T2, is studied.

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