Matrix Riemann-Hilbert Problems Related to Branched Coverings of ℂℙ1

Korotkin, Dmitry

doi:10.1007/978-3-0348-8003-9_2

Cited by 11 publications

(25 citation statements)

References 32 publications

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“…In physics terms, the hyperelliptic tau-function coincides with the chiral partition function of the Ashkin-Teller model [43], and is defined to be det∂ on the hyperelliptic curve (see also [27] for discussion).…”

Section: (B4)mentioning

confidence: 99%

Spectral Determinants on Mandelstam Diagrams

Hillairet

Kalvin

Kokotov

2015

Commun. Math. Phys.

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We study the regularized determinant of the Laplacian as a functional on the space of Mandelstam diagrams (noncompact translation surfaces glued from finite and semi-infinite cylinders). A Mandelstam diagram can be considered as a compact Riemann surface equipped with a conformal flat singular metric |ω| 2 , where ω is a meromorphic one-form with simple poles such that all its periods are pure imaginary and all its residues are real. The main result is an explicit formula for the determinant of the Laplacian in terms of the basic objects on the underlying Riemann surface (the prime form, theta-functions, the canonical meromorphic bidifferential) and the divisor of the meromorphic form ω. As an important intermediate result we prove a decomposition formula of the type of Burghelea-Friedlander-Kappeler for the determinant of the Laplacian for flat surfaces with cylindrical ends and conical singularities.

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Section: (B4)mentioning

confidence: 99%

Spectral Determinants on Mandelstam Diagrams

Hillairet

Kalvin

Kokotov

2015

Commun. Math. Phys.

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“…Closely related formulae for the isomonodromic tau-function of the class of Riemann-Hilbert problems solved in [10] were first found in [8] without reference to any associated Frobenius manifold. The connections between the formulae in [8] and Frobenius manifolds were conjectured in [11] and finally established in [9].…”

Section: The Isomonodromic Tau-functionmentioning

confidence: 99%

On the isomonodromic tau-function for the Hurwitz spaces of branched coverings of genus zero and one

Kokotov

Strachan

2005

Mathematical Research Letters

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The isomonodromic tau-function for the Hurwitz spaces of branched coverings of genus zero and one are constructed explicitly. Such spaces may be equipped with the structure of a Frobenius manifold and this introduces a flat coordinate system on the manifold. The isomonodromic taufunction, and in particular the associated G-function, are rewritten in these coordinates and an interpretation in terms of the caustics (where the multiplication is not semisimple) is given.

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“…In the papers of Bershadsky & Radul (1987) and Nakayashiki (1997), they were generalized to the case of Z N curves and applied by Bershadsky & Radul (1987) and Knizhnik (1989) for the calculation of correlation functions in the conformal field theory. In the works of Kitaev & Korotkin (1998), Korotkin (2000), Enolskii & Grava (2004) and Kokotov & Korotkin (2004) the Thomae formulae are used to construct the t-function of the Schlesinger equation associated with hyperelliptic and more general curves. Recently, Thomae-type formulae for trigonal curve were implemented by Braden & Enolski (2006, 2007 to describe charge 3 monopole solution to Bogomolny equation.…”

Section: Introductionmentioning

confidence: 99%