Topological Correlators in Landau-Ginzburg Models with Boundaries

By A. Kapustin, Yi Li. 2003

176 citations recorded by the source corpus.

We compute topological correlators in Landau-Ginzburg models on a Riemann surface with arbitrary number of handles and boundaries. The boundaries may correspond to arbitrary topological D-branes of type B. We also allow arbitrary operator insertions on the boundary and in the bulk. The answer is given by an explicit formula which can be regarded as an open-string generalization of C. Vafa’s formula for closed-string topological correlators. We discuss how to extend our results to the case of Landau-Ginzburg orbifolds. e-print archive: http://lanl.arXiv.org/abs/hep-th/0305136

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ef742020abb789376e1627034330377ff6d36486

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Citations in the corpus

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).”
Matrix factorizations and Cohomological Field Theories (2011, unknown): “ns of complexes obtained by replacing the condition d2 = 0 with d2 = w (see [14], [7]). Matrix factorizations appeared in physics in connection with open-closed topological string theories (see [27], [28], [29]). They are also related to an important invariant of 1Sometimes this theory is referred t”
Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m) (2012, methodology): “For foams this formula was discovered by Khovanov and Rozansky [39] generalizing work of the physicists Vafa [70], Kapustin, and Li [28].”
Dirichlet Branes and Mirror Symmetry (2009, methodology): “These have been proposed in [288] and later derived more carefully from the Landau-Ginzburg path-integral in [229].”
sl.N/-link homology (N 4) using foams and the Kapustin-Li formula (2007, methodology): “The Kapustin–Li formula was introduced by A Kapustin and Y Li [6] in the context of the evaluation of 2-dimensional TQFTs and extended to the case of prefoams by M Khovanov and L Rozansky in [9].”
Matrix Factorizations and Representations of Quivers I (2005, unknown): “y Db Z (A f). Lemma 3.5. There are isomorphisms as C-vector spaces Hom Db Z(A f) (M k,i,M l,j) ≃ Hom Db Z(A f) (M l,j,M k,i−1[1]) ∗, for all 1 ≤ k,l ≤ h− 1, i,j ∈ Z. (3.9) Proof. There is a trace map [KL2] Tr k : Af f 1−2 h (M k,i,M k,i)− → C, Φ → 1 h−1 Res " Str(dQ k ·Φ) ∂f ∂x # , (3.10) where”
Matrix factorizations and representations of quivers II: Type ADE case (2005, methodology): “mal Cohen-Macaulay modules. Recently, the categories of matrix factorizations are rediscovered in string theory as the categories of topological D-branes of type B in LandauGinzburg models (see [KL1],[KL2]). The category Db Z(Af) of graded matrix factorizations is then motivated by the work on the c”
Chern characters and Hirzebruch-Riemann-Roch formula for matrix factorizations (2010, methodology): “3) for the map τ Ē is almost identical to the formula for the boundary-bulk map in the corresponding Landau-Ginzburg model for open topological strings (see [13], [30]): we get an extra sign (−1)(n2) (see Corollary 3.”
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).”
Opening Mirror Symmetry on the Quintic (2006, background): “We now proceed to study the corrections Wquant. from worldsheet instantons.”
The $\mathfrak{sl}_n$ foam 2-category: a combinatorial formulation of Khovanov-Rozansky homology via categorical skew Howe duality (2014, methodology): “This approach builds on earlier work of Mackaay-Stosic-Vaz [40] in which a webs and foams approach was utilized; however, in that setup the link invariant was not shown to be purely combinatorial in nature, rather relying on the Kapustin-Li formula [19], [29] from topological Landau-Ginzburg models ”
A category of kernels for equivariant factorizations and its implications for Hodge theory (2011, background): “conﬁrmed Kontsevich’s prediction and gave a mathematically conjectural description of the Chern character map and the pairing on Hochschild homology for the category of matrix factorizations, [KL03a] [KL03b]. In mathematics, several foundational papers by Orlov soon followed: [Orl04, Orl06, Orl09]. ”
Moduli space actions on the Hochschild co-chains of a Frobenius algebra I: cell operads (2006, background): “[KR, KLi1, KLi2 ] 1. See also [KS2, Co] for related discussions of these”