Landau-Ginzburg Realization of Open String TFT

By I. Brunner, M. Herbst, W. Lerche, Bernhard Scheuner. 2003

166 citations recorded by the source corpus.

We investigate B-type topological Landau-Ginzburg theory with one variable, with D2brane boundary conditions. The allowed brane configurations are determined in terms of the possible factorizations of the superpotential, and compute the corresponding open string chiral rings. These are characterized by bosonic and fermionic generators that satisfy certain relations. Moreover we show that the disk correlators, being continuous functions of deformation parameters, satisfy the topological sewing constraints, thereby proving consistency of the theory. In addition we show that the open string LG model is, in its content, equivalent to a certain triangulated category introduced by Kontsevich, and thus may be viewed as a concrete physical realization of it.

Subfields: Atomic and Molecular Physics, and Optics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/e6a4378deb9faf292d271f6ad2c53f0f32adc29e

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

Homological algebra of knots and BPS states (2011, background): “y from crossings. For example, for the fundamental representation of g= sl(N) the potential is a function of a single variable, (3.1) Wsl(N), (x) = x N+1 . In physics, matrix factorizations are known [41, 42, 43, 44, 45, 46] to describe D-branes and topological defects in Landau-Ginzburg models whic”
D-branes and K-theory in 2D topological field theory (2006, background): “In this setting, we find without difficulty that the endomorphisms of the identity morphism are given, just as in the topological example above, by the Hochschild complex Ĉ = {A→ A⊗ A→ A⊗ A⊗ A→ . . . }, whose cohomology is H∗(X ; ∧∗ TX).”
Dirichlet Branes and Mirror Symmetry (2009, background): “For example, the endomorphism algebra of Mp is [70, 288] a Z2-graded algebra generated by an even element a and an odd element η with relations ηa = aη, a = 0, η(2) = −ap−2q, q = min{p,m− p}”
Phases Of N=2 Theories In 1+1 Dimensions With Boundary (2008, unknown): “If 1 ≤ n ≤ d − 1, this brane is believed to flow to the conformally invariant boundary condition in the minimal model known as the Cardy brane with L = (n − 1) (see for example [35] for Cardy branes in RCFTs, [36, 37] for D-branes in (2, 2) minimal models and [38, 39] for relation to LG branes).”
Khovanov-Rozansky Homology and Topological Strings (2004, background): “In fact, the category hmfW is a simple example of a “D-brane category”, whose objects are D-branes in N = 2 Landau-Ginzburg model with a superpotential W [27,28,29,30].”
G-flux in F-theory and algebraic cycles (2011, background): “The technology of matrix factorizations has found its incarnation in string theory, in the context of D-branes, through the works [93] and [94].”