scholarly journals Solitonic sectors, conformal boundary conditions and three-dimensional topological field theory

2000 ◽  
Author(s):  
Christoph Schweigert ◽  
J. Fuchs
Keyword(s):  
Field Theory ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Topological Field Theory ◽  
Conformal Boundary ◽  
Topological Field

scholarly journals Conformal Boundary Conditions and Three-Dimensional Topological Field Theory

2000 ◽  
Vol 84 (8) ◽  
pp. 1659-1662 ◽  
Author(s):  
Giovanni Felder ◽  
Jürg Fröhlich ◽  
Jürgen Fuchs ◽  
Christoph Schweigert
Keyword(s):  
Field Theory ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Topological Field Theory ◽  
Conformal Boundary ◽  
Topological Field

scholarly journals THREE-DIMENSIONAL FIELD THEORIES FROM INFINITE-DIMENSIONAL LIE ALGEBRAS

1994 ◽  
Vol 09 (23) ◽  
pp. 4063-4076
Author(s):  
R. E. C. PERRET
Keyword(s):  
Field Theory ◽  
Lie Algebras ◽  
Three Dimensional ◽  
Virasoro Algebra ◽  
Simons Theory ◽  
Topological Field Theory ◽  
Induced Gravity ◽  
Infinite Dimensional ◽  
Topological Field ◽  
Chern Simons

A procedure for constructing topological actions from centrally extended Lie algebras is introduced. For a Kac–Moody algebra, this produces the three-dimensional Chern–Simons theory, while for the Virasoro algebra, the result is a new three-dimensional topological field theory whose physical states satisfy the Virasoro Ward identity. This topological field theory is shown to be a first order formulation of two-dimensional induced gravity in the chiral gauge. The extension to W3 gravity is discussed.

scholarly journals Three-dimensional topological field theory and symplectic algebraic geometry I

2009 ◽  
Vol 816 (3) ◽  
pp. 295-355 ◽  
Author(s):  
Anton Kapustin ◽  
Lev Rozansky ◽  
Natalia Saulina
Keyword(s):  
Field Theory ◽  
Algebraic Geometry ◽  
Three Dimensional ◽  
Topological Field Theory ◽  
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 $q$ .

scholarly journals ON A CLASS OF TOPOLOGICAL QUANTUM FIELD THEORIES IN THREE DIMENSIONS

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.

scholarly journals Boundary conditions in topological AdS4/CFT3

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Pietro Benetti Genolini ◽  
Matan Grinberg ◽  
Paul Richmond
Keyword(s):  
Field Theory ◽  
Free Energy ◽  
Boundary Conditions ◽  
Smooth Solution ◽  
Three Dimensional ◽  
Field Theories ◽  
Legendre Transformation ◽  
Generating Functional ◽  
Holographic Duals

Abstract We revisit the construction in four-dimensional gauged Spin(4) supergravity of the holographic duals to topologically twisted three-dimensional $$ \mathcal{N} $$ N = 4 field theories. Our focus in this paper is to highlight some subtleties related to preserving supersymmetry in AdS/CFT, namely the inclusion of finite counterterms and the necessity of a Legendre transformation to find the dual to the field theory generating functional. Studying the geometry of these supergravity solutions, we conclude that the gravitational free energy is indeed independent from the metric of the boundary, and it vanishes for any smooth solution.

scholarly journals Bootstrapping boundary-localized interactions

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Connor Behan ◽  
Lorenzo Di Pietro ◽  
Edoardo Lauria ◽  
Balt C. van Rees
Keyword(s):  
Boundary Condition ◽  
Scalar Field ◽  
Boundary Conditions ◽  
Parameter Space ◽  
Three Dimensional ◽  
Conformal Boundary ◽  
Dimensional Boundary ◽  
Dirichlet And Neumann Conditions ◽  
Boundary Fields ◽  
Boundary Dynamics

Abstract We study conformal boundary conditions for the theory of a single real scalar to investigate whether the known Dirichlet and Neumann conditions are the only possibilities. For this free bulk theory there are strong restrictions on the possible boundary dynamics. In particular, we find that the bulk-to-boundary operator expansion of the bulk field involves at most a ‘shadow pair’ of boundary fields, irrespective of the conformal boundary condition. We numerically analyze the four-point crossing equations for this shadow pair in the case of a three-dimensional boundary (so a four-dimensional scalar field) and find that large ranges of parameter space are excluded. However a ‘kink’ in the numerical bounds obeys all our consistency checks and might be an indication of a new conformal boundary condition.

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