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• W3103156731 abstract "In this paper and upcoming ones, we initiate a systematic study of Bethe ansatz equations for integrable models by modern computational algebraic geometry. We show that algebraic geometry provides a natural mathematical language and powerful tools for understanding the structure of solution space of Bethe ansatz equations. In particular, we find novel efficient methods to count the number of solutions of Bethe ansatz equations based on Grobner basis and quotient ring. We also develop analytical approach based on companion matrix to perform the sum of on-shell quantities over all physical solutions without solving Bethe ansatz equations explicitly. To demonstrate the power of our method, we revisit the completeness problem of Bethe ansatz of Heisenberg spin chain, and calculate the sum rules of OPE coefficients in planar $mathcal{N}=4$ super-Yang-Mills theory." @default.
• W3103156731 created "2020-11-23" @default.
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• W3103156731 date "2018-03-01" @default.
• W3103156731 modified "2023-10-17" @default.
• W3103156731 title "Algebraic geometry and Bethe ansatz. Part I. The quotient ring for BAE" @default.
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• W3103156731 doi "https://doi.org/10.1007/jhep03(2018)087" @default.
• W3103156731 hasPublicationYear "2018" @default.
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