Note on a duality of topological branes

2014/01/31 by Taro Kimura
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Brane cosmology #Combinatorics #Duality (order theory) #Fourier transform #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Partition function (quantum field theory) #Physics #Polynomial #Pure mathematics #Quantum mechanics #Topology (electrical circuits) #Transformation (genetics) #hep-th

paper · pdf · doi:10.1093/ptep/ptu141

published as Prog. Theor. Exp. Phys. (2014) 103B04 · 1+18 pages, 2 figures; title changed, references added; minor corrections

arxiv created 2014/09/29 · openalex publication_date 2014/10/16 · arxiv updated 2014/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We show a duality of branes in the topological B-model by inserting two kinds of non-compact branes simultaneously. We explicitly derive the integral formula for the matrix model partition function describing this situation, which correspondingly includes both the characteristic polynomial and the external source. We show that these two descriptions are dual to each other through the Fourier transformation, and the brane partition function satisfies integrable equations in one and two dimensions.

Citations

• About the x-y symmetry of the F_g algebraic invariants
• String-orthogonal polynomials, string equations, and 2-Toda symmetries
• Topological expansion of mixed correlations in the hermitian 2 Matrix Model and x-y symmetry of the F_g invariants
• Towards unified theory of 2d gravity
• Topological M-theory as unification of form theories of gravity
• Matrix models, topological strings, and supersymmetric gauge theories
• Intersection Theory, Integrable Hierarchies and Topological Field Theory