Discrete Dirac Operators, Critical Embeddings and Ihara-Selberg Functions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10312936" target="_blank" >RIV/00216208:11320/15:10312936 - isvavai.cz</a>
Result on the web
<a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i1p10" target="_blank" >http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i1p10</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Discrete Dirac Operators, Critical Embeddings and Ihara-Selberg Functions
Original language description
Tine aim the paper is to formulate a discrete analogue of the claim made by Alvarez-Gaume et al., ([1]), realizing the partition function of the free fermion on a closed Riemann surface of genus g as a linear combination of 2^(2g) Pfaffians of Dirac operators. Let G = (V, E) be a finite graph embedded in a closed Riemann surface X of genus g, x(e) the collection of independent variables associated with each edge e of G (collected in one vector variable x) and Sigma the set of all 2^(2g) spin-structureson X. We introduce 2^(2g) rotations rot(s) and (2|E| x 2|E|) matrices Delta(s) (x), s is an element of Sigma, of the transitions between the oriented edges of G determined by rotations rot(s). We show that the generating function for the oven subsets ofedges of G, i.e., the Ising partition function, is a linear combination of the square roots of 2^(2g) Ihara-Selberg functions I(Delta(s)(x)) also called Feynman functions. By a result of Foata-Zeilberger holds I(Delta(s)(x)) = det (I - De
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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