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  A Shortcut to the Q-Operator

Bazhanov, V., Lukowski, T., Meneghelli, C., & Staudacher, M. (2010). A Shortcut to the Q-Operator. Journal of Statistical Mechanics, 2010(11): P11002. doi:10.1088/1742-5468/2010/11/P11002.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0012-69EA-6 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0012-69EE-D
Genre: Journal Article

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Bazhanov, V.V., Author
Lukowski, T., Author
Meneghelli, Carlo1, Author              
Staudacher, Matthias2, Author              
Affiliations:
1Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, escidoc:24014              
2Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24014              

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 Abstract: Baxter's Q-operator is generally believed to be the most powerful tool for the exact diagonalization of integrable models. Curiously, it has hitherto not yet been properly constructed in the simplest such system, the compact spin-1/2 Heisenberg-Bethe XXX spin chain. Here we attempt to fill this gap and show how two linearly independent operatorial solutions to Baxter's TQ equation may be constructed as commuting transfer matrices if a twist field is present. The latter are obtained by tracing over infinitely many oscillator states living in the auxiliary channel of an associated monodromy matrix. We furthermore compare and differentiate our approach to earlier articles addressing the problem of the construction of the Q-operator for the XXX chain. Finally we speculate on the importance of Q-operators for the physical interpretation of recent proposals for the Y-system of AdS/CFT.

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 Dates: 2010-03-242010
 Publication Status: Published in print
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 Identifiers: arXiv: 1005.3261
DOI: 10.1088/1742-5468/2010/11/P11002
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Title: Journal of Statistical Mechanics
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Pages: - Volume / Issue: 2010 (11) Sequence Number: P11002 Start / End Page: - Identifier: -