scholarly journals 2D and 3D topological field theories for generalized complex geometry

2010 ◽  
Vol 14 (2) ◽  
pp. 695-725 ◽  
Author(s):  
Alberto S. Cattaneo ◽  
Jian Qiu ◽  
Maxim Zabzine
Keyword(s):  
Topological Field Theories ◽  
Complex Geometry ◽  
Field Theories ◽  
Generalized Complex ◽  
Topological Field ◽  
2D And 3D

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.

scholarly journals Topological field theories on manifolds with Wu structures

2017 ◽  
Vol 29 (05) ◽  
pp. 1750015 ◽  
Author(s):  
Samuel Monnier
Keyword(s):  
Topological Field Theories ◽  
Geometric Quantization ◽  
Discrete Symmetry ◽  
Local System ◽  
Field Theories ◽  
Simons Theory ◽  
General Point ◽  
Topological Field ◽  
Generalized Cohomology ◽  
Chern Simons

We construct invertible field theories generalizing abelian prequantum spin Chern–Simons theory to manifolds of dimension [Formula: see text] endowed with a Wu structure of degree [Formula: see text]. After analyzing the anomalies of a certain discrete symmetry, we gauge it, producing topological field theories whose path integral reduces to a finite sum, akin to Dijkgraaf–Witten theories. We take a general point of view where the Chern–Simons gauge group and its couplings are encoded in a local system of integral lattices. The Lagrangian of these theories has to be interpreted as a class in a generalized cohomology theory in order to obtain a gauge invariant action. We develop a computationally friendly cochain model for this generalized cohomology and use it in a detailed study of the properties of the Wu Chern–Simons action. In the 3-dimensional spin case, the latter provides a definition of the “fermionic correction” introduced recently in the literature on fermionic symmetry protected topological phases. In order to construct the state space of the gauged theories, we develop an analogue of geometric quantization for finite abelian groups endowed with a skew-symmetric pairing. The physical motivation for this work comes from the fact that in the [Formula: see text] case, the gauged 7-dimensional topological field theories constructed here are essentially the anomaly field theories of the 6-dimensional conformal field theories with [Formula: see text] supersymmetry, as will be discussed elsewhere.

scholarly journals Superconformal current algebras and topological field theories

1994 ◽  
Vol 340 (1-2) ◽  
pp. 48-56 ◽  
Author(s):  
J.M. Isidro ◽  
A.V. Ramallo
Keyword(s):  
Topological Field Theories ◽  
Field Theories ◽  
Topological Field ◽  
Current Algebras

scholarly journals Topological field theories of 2- and 3-forms in six dimensions

2017 ◽  
Vol 58 (8) ◽  
pp. 082304 ◽  
Author(s):  
Yannick Herfray ◽  
Kirill Krasnov
Keyword(s):  
Topological Field Theories ◽  
Field Theories ◽  
Topological Field ◽  
Six Dimensions

The Vilkovisky-De Witt effective action in BF-type topological field theories

1991 ◽  
Vol 269 (1-2) ◽  
pp. 116-122 ◽  
Author(s):  
Danny Birmingham ◽  
H.T. Cho ◽  
R. Kantowski ◽  
M. Rakowski
Keyword(s):  
Topological Field Theories ◽  
Effective Action ◽  
Field Theories ◽  
Topological Field

scholarly journals PERTURBATION THEORY FOR ANTISYMMETRIC TENSOR FIELDS IN FOUR DIMENSIONS

1993 ◽  
Vol 08 (05) ◽  
pp. 929-945 ◽  
Author(s):  
N. MAGGIORE ◽  
S.P. SORELLA
Keyword(s):  
Perturbation Theory ◽  
Topological Field Theories ◽  
Field Theories ◽  
Antisymmetric Tensor ◽  
Tensor Fields ◽  
Four Dimensions ◽  
Topological Field ◽  
Supersymmetric Structure

Perturbation theory for a class of topological field theories containing antisymmetric tensor fields is considered. These models are characterized by a supersymmetric structure which allows us to establish their perturbative finiteness.

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