BF system - encyclopedic entry
The notion of the BF (topological) gauge field theory is defined.
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arXiv subjects
Boguslaw Broda
Publications and source records attributed to Boguslaw Broda.
3-dimensional scalar-vector dual of topological sigma-model
A 3-dimensional model dual to the Rozansky-Witten topological sigma-model with a hyper-Kaehler target space is considered. It is demonstrated that a Feynman diagram calculation of the classical part of its partition function yields the Milnor linking number.
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Abelian duality in three dimensions
Abelian duality on the closed three-dimensional Riemannian manifold M is discussed. Partition functions for the ordinary U(1) gauge theory and a circle-valued scalar field theory on M are explicitly calculated and compared. It is shown that the both theories are mutually dual.
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Non-Abelian Stokes theorem in action
In this short review main issues related to the non-Abelian Stokes theorem have been addressed. The two principal approaches to the non-Abelian Stokes theorem, operator and two variants (coherent-state and holomorphic) of the path-integral one, have been formulated in their simplest possible forms. A recent generalization for a knotted loop as well as a suggestion concerning higher-degree forms have been also included. Non-perturbative applications of the non-Abelian Stokes theorem, to (semi-)topological gauge theories, have been presented.
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The partition function of a 3-dimensional topological scalar-vector model
A study of the partition function of a 3-dimensional scalar-vector model formally related via duality to the Rozansky-Witten topological sigma-model is presented. The partition function is shown to consist of such topological quantities of a 3-dimensional manifold M like a lattice sum, the Reidemeister-Ray-Singer torsion and the Massey product.
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3-dimensional low-energy topological invariants
A description of the one-loop approximation formula for the partition function of a three-dimensional abelian version of the Donaldson-Witten theory is proposed. The one-loop expression is shown to contain such topological invariants of a three-dimensional manifold M like the Reidemeister-Ray-Singer torsion and Betti numbers.
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Three-dimensional topological quantum field theory of Witten type
Description of two three-dimensional topological quantum field theories of Witten type as twisted supersymmetric theories is presented. Low-energy effective action and a corresponding topological invariant of three-dimensional manifolds are considered.
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Topology of 3-dimensional Seiberg-Witten theory
A dual description of 3-dimensional topological Seiberg-Witten theory in terms of the Alexander invariant on manifolds obtained via surgery on a knot is proposed. The description directly follows from a low-energy analysis of the corresponding SUSY theory, in full analogy to the 4-dimensional case.
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Topological contents of 3D Seiberg-Witten theory
Using physical arguments (Higgs mechanism, superconductivity, infrared regime, duality) and a geometric-topological construction (scalar curvature distribution compatible with surgery), we propose a topological interpretation of 3D SW theory in terms of the abelian Casson invariant. Further algebraic reasoning shows equivalence of that invariant to the Alexander ``polynomial''. Our starting point is a 3D version of the original SW theory. Observing that the scalar curvature $R$ plays the role of a mass-squared parameter for the monopole field we can use that observation to control the theory in low-energy limit.
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Path integrals and low-dimensional topology
A path-integral approach to non-perturbative topological invariants of knots, links and manifolds of dimension three and four using topological quantum field theory of Schwarz (Chern-Simons) type is presented.
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Non-Abelian Stokes Theorem
The paper is a chapter of the above-mentioned book. It aims to give an expository presentation of author's version of the non-Abelian Stokes theorem in the framework of path-integral formalism.
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A gauge-field approach to 3- and 4-manifold invariants
The paper contains a talk given by the author at the Banach Center in Spring 1995. It recapitulates author's approach to construction of topological invariants of the Reshetikhin-Turaev-Witten type of 3- and 4-dimensional manifolds in the framework of SU(2) Chern-Simons gauge theory and its hidden (quantum) gauge symmetry.
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TQFT versus RCFT: 3-d topological invariants
A straightforward relationship between the two approaches to 3-dimensional topological invariants, one of them put forward by Witten in the framework of topological quantum field theory, and the second one proposed by Kohno in terms of rational conformal field theory, is established.
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Chern-Simons approach to three-manifold invariants
A new, formal, non-combinatorial approach to invariants of three-dimensional manifolds of Reshetikhin, Turaev and Witten in the framework of non-perturbative topological quantum Chern-Simons theory, corresponding to an arbitrary compact simple Lie group, is presented. A direct implementation of surgery instructions in the context of quantum field theory is proposed. An explicit form of the specialization of the invariant to the group SU(2) is derived.
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A note on the four-dimensional Kirby calculus
An explicit derivation of the elements of the representation ring of SU(2) needed to implement the four-dimensional Kirby calculus is sketched.
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Chern-Simons theory on an arbitrary manifold via surgery
A general formula for physical observables in Chern-Simons theory with an arbitrary compact Lie group $G$, on an arbitrary closed oriented three-dimensional manifold $\cM$ is derived in terms of vacuum expectation values of Wilson loops in ${\cal S}^3$. Surgery presentation of $\cM$ and the Kirby moves are implemented as the main ingredients of the approach. The case of $G={\rm SU}(n)$ is explicitly calculated.
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Chern-Simons approach to three-manifold invariants
% A new, formal, non-combinatorial approach to invariants of % three-dimensional manifolds of Reshetikhin, Turaev and % Witten in the framework of non-perturbative topological % quantum Chern-Simons theory, corresponding to an arbitrary % compact simple Lie group, is presented. A direct % implementation of surgery instructions in the context of % quantum field theory is proposed. An explicit form of the % specialization of the invariant to the group SU(2) is % derived, and shown to agree with the result of Lickorish. % % AMS subject classifications (1991): 57M25, 57N10, 57R65, 81T13.
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SU(2) and the Kauffman bracket
A direct relationship between the (non-quantum) group SU(2) and the Kauffman bracket in the framework of Chern-Simons theory is explicitly shown.
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