scholarly journals Batalin-Vilkovisky algebras and two-dimensional topological field theories

1994 ◽  
Vol 159 (2) ◽  
pp. 265-285 ◽  
Author(s):  
E. Getzler
Keyword(s):  
Topological Field Theories ◽  
Field Theories ◽  
Two Dimensional ◽  
Topological Field

scholarly journals DIFF(Σ) AND METRICS FROM HAMILTONIAN-TQFT'S IN 2+1 DIMENSIONS

1993 ◽  
Vol 08 (24) ◽  
pp. 2277-2283 ◽  
Author(s):  
ROGER BROOKS
Keyword(s):  
Topological Field Theories ◽  
Gauge Theories ◽  
Dimensional Space ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Two Dimensional ◽  
Canonical Gravity ◽  
Topological Quantum ◽  
Topological Field

The constraints of BF topological gauge theories are used to construct Hamiltonians which are anti-commutators of the BRST and anti-BRST operators. Such Hamiltonians are a signature of topological quantum field theories (TQFTs). By construction, both classes of topological field theories share the same phase spaces and constraints. We find that, for (2+1)- and (1+1)-dimensional space-times foliated as M=Σ × ℝ, a homomorphism exists between the constraint algebras of our TQFT and those of canonical gravity. The metrics on the two-dimensional hypersurfaces are also obtained.

scholarly journals Solitons in two-dimensional topological field theories

1993 ◽  
Vol 309 (3-4) ◽  
pp. 304-311 ◽  
Author(s):  
S. Penati ◽  
M. Pernici ◽  
D. Zanon
Keyword(s):  
Topological Field Theories ◽  
Field Theories ◽  
Two Dimensional ◽  
Topological Field

scholarly journals Construction of two-dimensional topological field theories with non-invertible symmetries

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Tzu-Chen Huang ◽  
Ying-Hsuan Lin ◽  
Sahand Seifnashri
Keyword(s):  
Topological Field Theories ◽  
Hilbert Spaces ◽  
Topological Defect ◽  
Field Theories ◽  
Boundary Crossing ◽  
Two Dimensional ◽  
Fusion Categories ◽  
Explicit Constructions ◽  
Crossing Symmetry ◽  
Topological Field

Abstract We construct the defining data of two-dimensional topological field theories (TFTs) enriched by non-invertible symmetries/topological defect lines. Simple formulae for the three-point functions and the lasso two-point functions are derived, and crossing symmetry is proven. The key ingredients are open-to-closed maps and a boundary crossing relation, by which we show that a diagonal basis exists in the defect Hilbert spaces. We then introduce regular TFTs, provide their explicit constructions for the Fibonacci, Ising and Haagerup ℋ3 fusion categories, and match our formulae with previous bootstrap results. We end by explaining how non-regular TFTs are obtained from regular TFTs via generalized gauging.

scholarly journals POISSON STRUCTURE INDUCED (TOPOLOGICAL) FIELD THEORIES

1994 ◽  
Vol 09 (33) ◽  
pp. 3129-3136 ◽  
Author(s):  
PETER SCHALLER ◽  
THOMAS STROBL
Keyword(s):  
Topological Field Theories ◽  
Poisson Structure ◽  
General Scheme ◽  
Hamiltonian Formulation ◽  
Field Theories ◽  
Two Dimensional ◽  
Poisson Structures ◽  
Yang Mills ◽  
Topological Field ◽  
Equations Of Motions

A class of two-dimensional field theories, based on (generically degenerate) Poisson structures and generalizing gravity-Yang–Mills systems, is presented. Locally, the solutions of the classical equations of motions are given. A general scheme for the quantization of the models in a Hamiltonian formulation is found. A BRS-formulation is outlined briefly.

scholarly journals TOPOLOGICAL FIELD THEORIES AND THE SPACE-TIME SINGULARITY

1992 ◽  
Vol 07 (02) ◽  
pp. 85-91 ◽  
Author(s):  
TOHRU EGUCHI
Keyword(s):  
Field Theory ◽  
Topological Field Theories ◽  
Space Time ◽  
Field Theories ◽  
Two Dimensional ◽  
Time Singularity ◽  
Singular Configurations ◽  
Dimensional Black Hole ◽  
Time Singularities ◽  
Topological Field

Based on a study of recently proposed solution of two-dimensional black hole we argue that the space-time singularities of general relativity may be described by topological field theories (TFTs). We also argue that in general TFT is a field theory which describes singular configurations of a reduced holonomy in its field space.

A COMMENT ON TOPOLOGICAL FIELD THEORY QUANTIZATION AND STOCHASTIC PROCESSES

1990 ◽  
Vol 05 (19) ◽  
pp. 3777-3786 ◽  
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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