On Bethe equations of 2d conformal field theory
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68378271%3A_____%2F24%3A00598833" target="_blank" >RIV/68378271:_____/24:00598833 - isvavai.cz</a>
Result on the web
<a href="https://hdl.handle.net/11104/0364683" target="_blank" >https://hdl.handle.net/11104/0364683</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/JHEP09(2024)115" target="_blank" >10.1007/JHEP09(2024)115</a>
Alternative languages
Result language
angličtina
Original language name
On Bethe equations of 2d conformal field theory
Original language description
We study the higher spin algebras of two-dimensional conformal field theory from the perspective of quantum integrability. Starting from Maulik-Okounkov instanton R-matrix and applying the procedure of algebraic Bethe ansatz, we obtain infinite commuting families of Hamiltonians of quantum ILW hierarchy parametrized by the shape of the auxiliary torus. We calculate explicitly the first five of these Hamiltonians. Then, we numerically verify that their joint spectrum can be parametriezed by solutions of Litvinov’s Bethe ansatz equations and we conjecture a general formula for the joint spectrum of all ILW Hamiltonians, based on results of Feigin, Jimbo, Miwa and Mukhin.There are two interesting degeneration limits, the infinitely thick and the infinitely thin auxiliary torus. In one of these limits, the ILW hierarchy degenerates to Yangian or Benjamin-Ono hiearchy and the Bethe equations can be easily solved. The other limit is singular but we can nevertheless extract local Hamiltonians corresponding to quantum KdV or KP hierarchy. Litvinov’s Bethe equations in this local limit provide an alternative to Bethe ansatz equations of Bazhanov, Lukyanov and Zamolodchikov, but are more transparent, work at any rank and are manifestly symmetric under triality symmetry of W1+∞W1+∞. Finally, we illustrate analytic properties of the solutions of Bethe equations in minimal models, in particular for Lee-Yang CFT. The analytic structure of Bethe roots is very rich as it captures the representation theory of W_N minimal models.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10303 - Particles and field physics
Result continuities
Project
<a href="/en/project/GX20-25775X" target="_blank" >GX20-25775X: Applied String Field Theory</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of High Energy Physics
ISSN
1029-8479
e-ISSN
1029-8479
Volume of the periodical
2024
Issue of the periodical within the volume
9
Country of publishing house
DE - GERMANY
Number of pages
105
Pages from-to
115
UT code for WoS article
001316967400002
EID of the result in the Scopus database
2-s2.0-85204484855