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dc.contributor.author
Jiang, Yunfeng
dc.contributor.author
Zhang, Yang
dc.date.accessioned
2018-04-04T17:00:52Z
dc.date.available
2018-04-02T03:53:00Z
dc.date.available
2018-04-04T17:00:52Z
dc.date.issued
2018-03
dc.identifier.other
10.1007/JHEP03(2018)087
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/254391
dc.identifier.doi
10.3929/ethz-b-000254391
dc.description.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 Gröbner 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 N=4 super-Yang-Mills theory.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
Springer
en_US
dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
dc.subject
Bethe Ansatz
en_US
dc.subject
Differential and Algebraic Geometry
en_US
dc.subject
Lattice Integrable Models
en_US
dc.title
Algebraic geometry and Bethe ansatz. Part I. The quotient ring for BAE
en_US
dc.type
Journal Article
dc.rights.license
Creative Commons Attribution 4.0 International
dc.date.published
2018-03-14
ethz.journal.title
Journal of High Energy Physics
ethz.journal.volume
2018
en_US
ethz.pages.start
87
en_US
ethz.size
39 p.
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.grant
Multi-loop Scattering Amplitudes via Algebraic Geometry
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.place
Berlin
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02010 - Dep. Physik / Dep. of Physics::02511 - Institut für Theoretische Physik / Institute for Theoretical Physics::03896 - Beisert, Niklas / Beisert, Niklas
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02010 - Dep. Physik / Dep. of Physics::02511 - Institut für Theoretische Physik / Institute for Theoretical Physics::03896 - Beisert, Niklas / Beisert, Niklas
ethz.grant.agreementno
161341
ethz.grant.fundername
SNF
ethz.grant.funderDoi
10.13039/501100001711
ethz.grant.program
Ambizione
ethz.date.deposited
2018-04-02T03:53:02Z
ethz.source
SCOPUS
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2018-04-04T17:01:01Z
ethz.rosetta.lastUpdated
2019-01-02T12:41:45Z
ethz.rosetta.exportRequired
true
ethz.rosetta.versionExported
true
ethz.COinS
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