On the structure of open-closed topological field theory in two-dimensions
By C. Lazaroiu. 2000
184 citations recorded by the source corpus.
Abstract I discuss the general formalism of two-dimensional topological field theories defined on open–closed oriented Riemann surfaces, starting from an extension of Segal's geometric axioms. Exploiting the topological sewing constraints allows for the identification of the algebraic structure governing such systems. I give a careful treatment of bulk-boundary and boundary-bulk correspondences, which are responsible for the relation between the closed and open sectors. The fact that these correspondences need not be injective nor surjective has interesting implications for the problem of classifying ‘boundary conditions’. In particular, I give a clear geometric derivation of the (topological) boundary state formalism and point out some of its limitations. Finally, I formulate the problem of classifying (on-shell) boundary extensions of a given closed topological field theory in purely algebraic terms and discuss reducibility of boundary extensions.
Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/fd9090cecb5806ce468830784d2fccc40fe88393
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Citations in the corpus
- TFT construction of RCFT correlators I: Partition functions (2002, background): “In this specific context, the idea has been put forward [124,125,126] that the boundary fields yield a non-commutative Frobenius algebra – the algebra of open string states – and that its center describes an algebra of bulk fields (closed string states).”
- Landau-Ginzburg Realization of Open String TFT (2003, methodology): “In [1, 2] the openclosed TFT was axiomatically formulated in terms of five sewing constraints.”
- Topological Correlators in Landau-Ginzburg Models with Boundaries (2003, background): “Kontsevich’s conjecture concerning the boundary OPE follows from the analysis of the world-sheet action for the LG model with boundaries in the presence of both branes and anti-branes.”
- Electric-Magnetic Duality And The Geometric Langlands Program (2006, background): “3, and is part of the usual axioms of open-closed topological field theory [142,143].”
- Dirichlet Branes and Mirror Symmetry (2009, background): “Lazaroiu [325, 323, 322, 324] although the emphasis in these papers is on applications to disk instanton corrections in low energy supergravity.”
- D-branes and K-theory in 2D topological field theory (2006, background): “Lazaroiu [19] although the emphasis in these papers is on applications to disk instanton corrections in low energy supergravity.”
- Geometrical interpretation of D-branes in gauged WZW models (2001, unknown): “ar X iv :h ep -t h/ 01 05 03 8v 1 3 M ay 2 00 1 hep-th/0105038 RUNHETC-2001-15 Geometrical interpretation of D-branes in gauged WZW models Juan Maldacena1,2, Gregory Moore3, Nathan Seiberg1”
- Linear Models of Supersymmetric D-Branes (2000, background): “Remark. Open topological field theory has been studied from axiomatic point of view in [53, 54 ].”
- Topological Open P-Branes (2000, unknown): “Dec. 15, 2000”
- D branes in Landau-Ginzburg models and algebraic geometry (2002, unknown): “Assuming the standard Kähler potentialK = |Φ1|2+|Φ2|2, the worldsheet action reads S = 1 2π ∫ R×[0,π] d2x { 2 ∑ α=1 ( |∂tφα|2 − |∂σφα|2 + iψᾱ−∂+ψα− + iψᾱ+∂−ψα+ ) − |mφ1|2 − |mφ2|2 −m ( ψ1+ψ 2 − + ψ 2 +ψ 1 − ) − m̄ ( ψ1̄−ψ 2̄ + + ψ 2̄ −ψ 1̄ + )} , where φα are the bosonic components of Φα, and ψ…”