Twisty itsy bitsy topological field theory

We extend the topological field theory (itsy bitsy topological field theory) of our previous work from mod 2 to twisted coefficients. This topological field theory is derived from sutured Floer homology (SFH) but described purely in terms of surfaces with signed points on their boundary (occupied surfaces) and curves on those surfaces respecting signs (sutures). It has information-theoretic (itsy) and quantum-field-theoretic (bitsy) aspects. In the process we extend some results of SFH, consider associated ribbon graph structures, and construct explicit admissible Heegaard decompositions.

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Floer Homology, A∞-categories and Topological Field Theory

Geometry and physics ◽

10.1201/9781003072393-2 ◽

2021 ◽

pp. 9-32

Author(s):

Kenji Fukaya ◽

Paul Seidel

Keyword(s):

Field Theory ◽

Floer Homology ◽

Topological Field Theory ◽

Topological Field

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Equivalence between stochastic quantization of a two-dimensional BF-type topological field theory and three-dimensional topological quantum field theory for a magnetic monopole

Journal of Physics G Nuclear and Particle Physics ◽

10.1088/0954-3899/20/6/004 ◽

1994 ◽

Vol 20 (6) ◽

pp. 891-894

Author(s):

W F Chen ◽

Z Y Zhu

Keyword(s):

Field Theory ◽

Magnetic Monopole ◽

Three Dimensional ◽

Topological Quantum Field Theory ◽

Topological Field Theory ◽

Quantum Field ◽

Two Dimensional ◽

Stochastic Quantization ◽

Topological Quantum ◽

Topological Field

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ON A CLASS OF TOPOLOGICAL QUANTUM FIELD THEORIES IN THREE DIMENSIONS

International Journal of Modern Physics A ◽

10.1142/s0217751x96002121 ◽

1996 ◽

Vol 11 (25) ◽

pp. 4577-4596

Author(s):

MASAKO ASANO

Keyword(s):

Field Theory ◽

Three Dimensional ◽

Space Structure ◽

Three Dimensions ◽

Topological Field Theory ◽

Quantum Field Theories ◽

Quantum Field ◽

Manifolds With Boundary ◽

Topological Quantum ◽

Topological Field

We investigate the Chung–Fukuma–Shapere theory, or Kuperberg theory, of three-dimensional lattice topological field theory. We construct a functor which satisfies Atiyah’s axioms of topological quantum field theory by reformulating the theory as a Turaev–Viro type state sum theory on a triangulated manifold. This corresponds to giving the Hilbert space structure to the original theory. The theory can be extended to give a topological invariant of manifolds with boundary.

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A COMMENT ON TOPOLOGICAL FIELD THEORY QUANTIZATION AND STOCHASTIC PROCESSES

International Journal of Modern Physics A ◽

10.1142/s0217751x90001604 ◽

1990 ◽

Vol 05 (19) ◽

pp. 3777-3786 ◽

Cited By ~ 2

Author(s):

L.F. CUGLIANDOLO ◽

G. LOZANO ◽

H. MONTANI ◽

F.A. SCHAPOSNIK

Keyword(s):

Field Theory ◽

Equilibrium State ◽

Stochastic Processes ◽

Topological Field Theories ◽

Topological Charge ◽

Field Theories ◽

Langevin Equations ◽

Topological Field Theory ◽

Topological Field

We discuss the relation between different quantization approaches to topological field theories by deriving a connection between Bogomol’nyi and Langevin equations for stochastic processes which evolve towards an equilibrium state governed by the topological charge.

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Towards effective topological field theory for knots

Nuclear Physics B ◽

10.1016/j.nuclphysb.2015.08.005 ◽

2015 ◽

Vol 899 ◽

pp. 395-413 ◽

Cited By ~ 32

Author(s):

A. Mironov ◽

A. Morozov

Keyword(s):

Field Theory ◽

Topological Field Theory ◽

Topological Field

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TETRAHEDRA AND POLYNOMIAL EQUATIONS IN TOPOLOGICAL FIELD THEORY

International Journal of Modern Physics A ◽

10.1142/s0217751x91001738 ◽

1991 ◽

Vol 06 (20) ◽

pp. 3571-3598 ◽

Cited By ~ 1

Author(s):

NOUREDDINE CHAIR ◽

CHUAN-JIE ZHU

Keyword(s):

Field Theory ◽

Topological Field Theory ◽

Fundamental Representation ◽

Conformal Blocks ◽

Conformal Field ◽

Witten Theory ◽

Topological Field ◽

General Program ◽

The One ◽

Chern Simons

Some tetrahedra in SUk(2) Chern-Simons-Witten theory are computed. The results can be used to compute an arbitrary tetrahedron inductively by fusing with the fundamental representation. The results obtained are in agreement with those of quantum groups. By associating a (finite) topological field theory (FTFT) to every rational conformal field theory (RCFT), we show that the pentagon and hexagon equations in RCFT follow directly from some skein relations in FTFT. By generalizing the operation of surgery on links in FTFT, we also derive an explicit expression for the modular transformation matrix S(k) of the one-point conformal blocks on a torus in RCFT and the equations satisfied by S(k), in agreement with those required in RCFT. The implication of our results on the general program of classifying RCFT is also discussed.

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