scholarly journals PARTICLE CONTENT IN TOPOLOGICAL FIELD THEORIES

1994 ◽  
Vol 09 (01) ◽  
pp. 29-39 ◽  
Author(s):  
ANDREW TOON
Keyword(s):  
Field Theory ◽  
Topological Field Theories ◽  
Path Integral ◽  
Degrees Of Freedom ◽  
Field Theories ◽  
Topological Field Theory ◽  
Particle Content ◽  
Integral Measure ◽  
Topological Field ◽  
Dimensionality Of Space

By demanding that the path-integral measure of the topological field theories be metric-independent, we can derive powerful constraints on the particle content of a topological field theory as well as on the dimensionality of space-time. We also relate this metric independence to the number of degrees of freedom in the theory.

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.

Path-integral measure for topological field theories

1990 ◽  
Vol 244 (2) ◽  
pp. 249-254 ◽  
Author(s):  
L.F. Cugliandolo ◽  
G. Lozano ◽  
F.A. Schaposnik
Keyword(s):  
Topological Field Theories ◽  
Path Integral ◽  
Field Theories ◽  
Integral Measure ◽  
Topological Field

scholarly journals On dualizability of braided tensor categories

2021 ◽  
Vol 157 (3) ◽  
pp. 435-483
Author(s):  
Adrien Brochier ◽  
David Jordan ◽  
Noah Snyder
Keyword(s):  
Field Theory ◽  
Quantum Group ◽  
Topological Field Theories ◽  
Characteristic Zero ◽  
Three Dimensional ◽  
Field Theories ◽  
Topological Field Theory ◽  
Tensor Categories ◽  
Fusion Categories ◽  
Topological Field

We study the question of dualizability in higher Morita categories of locally presentable tensor categories and braided tensor categories. Our main results are that the 3-category of rigid tensor categories with enough compact projectives is 2-dualizable, that the 4-category of rigid braided tensor categories with enough compact projectives is 3-dualizable, and that (in characteristic zero) the 4-category of braided multi-fusion categories is 4-dualizable. Via the cobordism hypothesis, this produces respectively two-, three- and four-dimensional framed local topological field theories. In particular, we produce a framed three-dimensional local topological field theory attached to the category of representations of a quantum group at any value of $q$ .

PHYSICAL STATES OF THE TOPOLOGICAL SCHWINGER MODEL

1992 ◽  
Vol 07 (03) ◽  
pp. 259-266 ◽  
Author(s):  
CHIGAK ITOI ◽  
HISAMITSU MUKAIDA
Keyword(s):  
Field Theory ◽  
Path Integral ◽  
Correlation Functions ◽  
Hamiltonian Formalism ◽  
Topological Field Theory ◽  
Schwinger Model ◽  
Physical Operator ◽  
Topological Field ◽  
The Relationship ◽  
Large Gauge Transformation

The Schwinger model with the strong coupling limit is studied as a topological field theory both in the path-integral and in the Hamiltonian formalism. The correlation functions between arbitrary numbers of physical operators are obtained. All the physical states in this model are completely determined in the Hamiltonian formalism. The relationship between a physical operator and the generator of a large gauge transformation is clarified. The chiral condensation is also calculated.

scholarly journals Hamiltonian Analysis for the Scalar Electrodynamics as 3BF Theory

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 620
Author(s):  
Tijana Radenković ◽  
Marko Vojinović
Keyword(s):  
Field Theory ◽  
Category Theory ◽  
Degrees Of Freedom ◽  
Canonical Quantization ◽  
Topological Field Theory ◽  
Dynamic Constraints ◽  
Specific Choice ◽  
Higher Category Theory ◽  
Topological Field ◽  
Hamiltonian Analysis

The higher category theory can be employed to generalize the B F action to the so-called 3 B F action, by passing from the notion of a gauge group to the notion of a gauge 3-group. The theory of scalar electrodynamics coupled to Einstein–Cartan gravity can be formulated as a constrained 3 B F theory for a specific choice of the gauge 3-group. The complete Hamiltonian analysis of the 3 B F action for the choice of a Lie 3-group corresponding to scalar electrodynamics is performed. This analysis is the first step towards a canonical quantization of a 3 B F theory, an important stepping stone for the quantization of the complete scalar electrodynamics coupled to Einstein–Cartan gravity formulated as a 3 B F action with suitable simplicity constraints. It is shown that the resulting dynamic constraints eliminate all propagating degrees of freedom, i.e., the 3 B F theory for this choice of a 3-group is a topological field theory, as expected.

scholarly journals Topological field theories induced by twisted R-Poisson structure in any dimension

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Athanasios Chatzistavrakidis
Keyword(s):  
Field Theory ◽  
Poisson Structure ◽  
Sigma Model ◽  
Three Dimensions ◽  
Target Space ◽  
Field Theories ◽  
Topological Field Theory ◽  
Covariant Formulation ◽  
Topological Field ◽  
Poisson Sigma Model

Abstract We construct a class of topological field theories with Wess-Zumino term in spacetime dimensions ≥ 2 whose target space has a geometrical structure that suitably generalizes Poisson or twisted Poisson manifolds. Assuming a field content comprising a set of scalar fields accompanied by gauge fields of degree (1, p − 1, p) we determine a generic Wess-Zumino topological field theory in p + 1 dimensions with background data consisting of a Poisson 2-vector, a (p + 1)-vector R and a (p + 2)-form H satisfying a specific geometrical condition that defines a H-twisted R-Poisson structure of order p + 1. For this class of theories we demonstrate how a target space covariant formulation can be found by means of an auxiliary connection without torsion. Furthermore, we study admissible deformations of the generic class in special spacetime dimensions and find that they exist in dimensions 2, 3 and 4. The two-dimensional deformed field theory includes the twisted Poisson sigma model, whereas in three dimensions we find a more general structure that we call bi-twisted R-Poisson. This extends the twisted R-Poisson structure of order 3 by a non-closed 3-form and gives rise to a topological field theory whose covariant formulation requires a connection with torsion and includes a twisted Poisson sigma model in three dimensions as a special case. The relation of the corresponding structures to differential graded Q-manifolds based on the degree shifted cotangent bundle T*[p]T*[1]M is discussed, as well as the obstruction to them being QP-manifolds due to the Wess-Zumino term.

scholarly journals THE HIERARCHY OF ASSOCIATIVITY EQUATIONS FOR n=3 CASE WITH AN METRIC ƞ11≠0

2020 ◽  
Vol 69 (1) ◽  
pp. 199-205
Author(s):  
A.A. Zhadyranova ◽  
◽  
Zh.R. Myrzakul ◽  
K.R. Myrzakulov ◽  
Keyword(s):  
Field Theory ◽  
Nonlinear Partial Differential Equations ◽  
Topological String ◽  
Homogeneous System ◽  
Field Theories ◽  
Topological Field Theory ◽  
Topological String Theory ◽  
System Of Hydrodynamic Type ◽  
Associativity Equations ◽  
Topological Field

This paper describes the hierarchy for N = 2 and n=3 case with an metric ƞ11≠0 when V0 = 0 of associativity equations. The equation of associativity arose from the 2D topological field theory. 2D topological field theory represent the matter sector of topological string theory. These theories covariant before coupling to gravity due to the presence of a nilpotent symmetry and are therefore often referred to as cohomological field theories. We give a description of nonlinear partial differential equations of associativity in 2D topological field theories as integrable nondiagonalizable weakly nonlinear homogeneous system of hydrodynamic type. The article discusses nonlinear equations of the third order for a function f = f(x,t)) of two independent variables x, t. In this work we consider the associativity equation for n=3 case with an a metric 0 11   . The solution of some cases of hierarchy when N = 2 and V0 = 0 equations of associativity illustrated

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.

scholarly journals MULTIMATRIX MODELS: INTEGRABILITY PROPERTIES AND TOPOLOGICAL CONTENT

1996 ◽  
Vol 11 (10) ◽  
pp. 1797-1830
Author(s):  
L. BONORA ◽  
F. NESTI ◽  
E. VINTELER
Keyword(s):  
Topological Field Theories ◽  
Toda Lattice ◽  
Weak Form ◽  
Field Theories ◽  
Topological Field Theory ◽  
Discrete States ◽  
Topological Field ◽  
Structure Constants ◽  
Q Matrix ◽  
Toda Lattice Hierarchy

In this article, we analyze multimatrix chain models. They can be considered as multicomponent Toda lattice hierarchies subject to suitable coupling conditions. The extension of such models to include extra discrete states requires a weak form of integrability. The discrete states of the q-matrix model are organized in representations of sl q. We solve exactly the Gaussian type models, of which we compute several all-genus correlators. Among the latter models one can classify also the discretized c=1 string theory, which we revisit using Toda lattice hierarchy methods. Finally, we analyze the topological field theory content of the 2q-matrix models: we define primary fields (which are ∞q), metrics and structure constants, and prove that they satisfy the axioms of topological field theories. We outline a possible method for extracting interesting topological field theories with a finite number of primaries.

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