[HTML][HTML] The elliptic dilogarithm for the sunset graph

S Bloch, P Vanhove - Journal of Number Theory, 2015 - Elsevier
We study the sunset graph defined as the scalar two-point self-energy at two-loop order. We
evaluated the sunset integral for all identical internal masses in two dimensions. We give …

A Feynman integral via higher normal functions

S Bloch, M Kerr, P Vanhove - Compositio Mathematica, 2015 - cambridge.org
We study the Feynman integral for the three-banana graph defined as the scalar two-point
self-energy at three-loop order. The Feynman integral is evaluated for all identical internal …

Local mirror symmetry and the sunset Feynman integral

S Bloch, M Kerr, P Vanhove - arXiv preprint arXiv:1601.08181, 2016 - arxiv.org
We study the sunset Feynman integral defined as the scalar two-point self-energy at two-
loop order in a two dimensional space-time. We firstly compute the Feynman integral, for …

Spectral theory and mirror curves of higher genus

S Codesido, A Grassi, M Marino - Annales Henri Poincaré, 2017 - Springer
Recently, a correspondence has been proposed between spectral theory and topological
strings on toric Calabi–Yau manifolds. In this paper, we develop in detail this …

Period integrals from wall structures via tropical cycles, canonical coordinates in mirror symmetry and analyticity of toric degenerations

H Ruddat, B Siebert - Publications mathématiques de l'IHÉS, 2020 - Springer
We give a simple expression for the integral of the canonical holomorphic volume form in
degenerating families of varieties constructed from wall structures and with central fiber a …

Feynman integrals, toric geometry and mirror symmetry

P Vanhove - Elliptic Integrals, Elliptic Functions and Modular Forms …, 2019 - Springer
This expository text is about using toric geometry and mirror symmetry for evaluating
Feynman integrals. We show that the maximal cut of a Feynman integral is a GKZ …

On the remodeling conjecture for toric Calabi-Yau 3-orbifolds

B Fang, CC Liu, Z Zong - Journal of the American Mathematical Society, 2020 - ams.org
The Remodeling Conjecture proposed by Bouchard-Klemm-Mariño-Pasquetti (BKMP)
relates the A-model open and closed topological string amplitudes (the all genus open and …

Spectral theory and mirror symmetry

M Marino - Proc. Symp. Pure Math, 2018 - books.google.com
Recent developments in string theory have revealed a surprising connection between
spectral theory and local mirror symmetry: it has been found that the quantization of mirror …

Matrix models from operators and topological strings

M Marino, S Zakany - Annales Henri Poincaré, 2016 - Springer
We propose a new family of matrix models whose 1/N expansion captures the all-genus
topological string on toric Calabi–Yau threefolds. These matrix models are constructed from …

Operators and higher genus mirror curves

S Codesido, J Gu, M Mariño - Journal of High Energy Physics, 2017 - Springer
A bstract We perform further tests of the correspondence between spectral theory and
topological strings, focusing on mirror curves of genus greater than one with nontrivial mass …