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.

scholarly journals GENERALIZED ABELIAN CHERN-SIMONS THEORIES AND THEIR CONNECTION TO CONFORMAL FIELD THEORIES

1992 ◽  
Vol 07 (19) ◽  
pp. 4477-4486 ◽  
Author(s):  
MARCO A.C. KNEIPP
Keyword(s):  
Three Dimensional ◽  
Magnetic Monopoles ◽  
Field Theories ◽  
Vertex Operators ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Integral Lattice ◽  
Conformal Field ◽  
Free Scalar ◽  
Chern Simons

We discuss the generalization of Abelian Chern-Simons theories when θ-angles and magnetic monopoles are included. We map these three dimensional theories into sectors of two-dimensional conformal field theories. The introduction of θ-angles allows us to establish in a consistent fashion a connection between Abelian Chern-Simons and 2-d free scalar field compactified on a noneven integral lattice. The Abelian Chern-Simons with magnetic monopoles is related to a conformal field theory in which the sum of the charges of the chiral vertex operators inside a correlator is different from zero.

scholarly journals Chern-Simons invariants from ensemble averages

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Meer Ashwinkumar ◽  
Matthew Dodelson ◽  
Abhiram Kidambi ◽  
Jacob M. Leedom ◽  
Masahito Yamazaki
Keyword(s):  
Three Dimensional ◽  
Lens Spaces ◽  
Kinetic Term ◽  
Simons Theory ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Integral Quadratic Form ◽  
Conformal Field ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We discuss ensemble averages of two-dimensional conformal field theories associated with an arbitrary indefinite lattice with integral quadratic form Q. We provide evidence that the holographic dual after the ensemble average is the three-dimensional Abelian Chern-Simons theory with kinetic term determined by Q. The resulting partition function can be written as a modular form, expressed as a sum over the partition functions of Chern-Simons theories on lens spaces. For odd lattices, the dual bulk theory is a spin Chern-Simons theory, and we identify several novel phenomena in this case. We also discuss the holographic duality prior to averaging in terms of Maxwell-Chern-Simons theories.

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 Quantum criticality in many-body parafermion chains

2021 ◽  
Vol 4 (2) ◽  
Author(s):  
Ville Lahtinen ◽  
Teresia Mansson ◽  
Eddy Ardonne
Keyword(s):  
Partition Function ◽  
Boundary Conditions ◽  
Quantum Criticality ◽  
Field Theories ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Many Body ◽  
Modular Invariant ◽  
Potts Models ◽  
Conformal Field

We construct local generalizations of 3-state Potts models with exotic critical points. We analytically show that these are described by non-diagonal modular invariant partition functions of products of Z_3Z3 parafermion or u(1)_6u(1)6 conformal field theories (CFTs). These correspond either to non-trivial permutation invariants or block diagonal invariants, that one can understand in terms of anyon condensation. In terms of lattice parafermion operators, the constructed models correspond to parafermion chains with many-body terms. Our construction is based on how the partition function of a CFT depends on symmetry sectors and boundary conditions. This enables to write the partition function corresponding to one modular invariant as a linear combination of another over different sectors and boundary conditions, which translates to a general recipe how to write down a microscopic model, tuned to criticality. We show that the scheme can also be extended to construct critical generalizations of kk-state clock type models.

scholarly journals Gravitational Dressing of Aharonov-Bohm Amplitudes

1997 ◽  
Vol 12 (06) ◽  
pp. 1043-1051 ◽  
Author(s):  
Giovanni Amelino-Camelia ◽  
Ian I. Kogan ◽  
Richard J. Szabo
Keyword(s):  
Three Dimensional ◽  
Matter Field ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Gravitational Analog ◽  
Bohm Effect ◽  
Aharonov Bohm ◽  
Chern Simons

We investigate Aharonov-Bohm scattering in a theory in which charged bosonic matter field are coupled to topologically massive electrodynamics and topologically massive gravity. We demonstrate that, at one-loop order, the transmuted spins in this theory are related to the ones of ordinary Chern-Simons gauge theory in the same way that the Knizhnik-Polyakov-Zamolodchikov formula relates the Liouville-dressed conformal weights of primary operators to the bare weights of primary operators to the bare weights in two-dimensional conformal field theories. We remark on the implications of this connection two-dimensional conformal field theories and three-dimensional gauge and gravity theories for a topological membrane reformulation of strings. We also discuss some features of the gravitational analog of the Aharonov-Bohm effect.

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 NON-ABELIAN FRACTIONAL QUANTUM HALL STATES AND CHIRAL COSET CONFORMAL FIELD THEORIES

2000 ◽  
Vol 15 (30) ◽  
pp. 4857-4870 ◽  
Author(s):  
D. C. CABRA ◽  
E. FRADKIN ◽  
G. L. ROSSINI ◽  
F. A. SCHAPOSNIK
Keyword(s):  
Quantum Hall ◽  
Field Theories ◽  
Simons Theory ◽  
Conformal Field Theories ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Conformal Field ◽  
Quantum Hall States ◽  
Effective Lagrangian ◽  
Chern Simons

We propose an effective Lagrangian for the low energy theory of the Pfaffian states of the fractional quantum Hall effect in the bulk in terms of non-Abelian Chern–Simons (CS) actions. Our approach exploits the connection between the topological Chern–Simons theory and chiral conformal field theories. This construction can be used to describe a large class of non-Abelian FQH states.

scholarly journals BOSE–FERMI EQUIVALENCE IN THREE-DIMENSIONAL NONCOMMUTATIVE SPACETIME

2008 ◽  
Vol 23 (35) ◽  
pp. 3015-3022
Author(s):  
K. M. AJITH ◽  
E. HARIKUMAR ◽  
M. SIVAKUMAR
Keyword(s):  
Partition Function ◽  
Gauge Field ◽  
Three Dimensional ◽  
Coupling Constant ◽  
Spin Factor ◽  
Noncommutative Spacetime ◽  
Chern Simons

We study the fermionisation of Seiberg–Witten mapped action (to order θ) of the λϕ4 theory coupled minimally with U(1) gauge field governed by Chern–Simons action. Starting from the corresponding partition function we derive nonperturbatively (in coupling constant) the partition function of the spin-1/2 theory following Polyakov spin factor formalism. We find that the dual interacting fermionic theory is nonlocal. This feature also persists in the limit of vanishing self-coupling. In θ → 0 limit, the commutative result is obtained.

Chiral modular bootstrap

2019 ◽  
Vol 34 (28) ◽  
pp. 1950168 ◽  
Author(s):  
M. Ashrafi
Keyword(s):  
Black Hole ◽  
Upper Bound ◽  
Three Dimensional ◽  
Conformal Weight ◽  
Two Dimensional ◽  
Btz Black Hole ◽  
Conformal Field ◽  
Dimensional Gravity ◽  
Large Spin ◽  
Dimension Ratio

Using modular bootstrap we show the lightest primary fields of a unitary compact two-dimensional conformal field theory (with [Formula: see text], [Formula: see text]) has a conformal weight [Formula: see text]. This implies that the upper bound on the dimension of the lightest primary fields depends on their spin. In particular if the set of lightest primary fields includes extremal or near extremal states whose spin to dimension ratio [Formula: see text], the corresponding dimension is [Formula: see text]. From AdS/CFT correspondence, we obtain an upper bound on the spectrum of black hole in three-dimensional gravity. Our results show that if the first primary fields have large spin, the corresponding three-dimensional gravity has extremal or near extremal BTZ black hole.

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