Planar N = 4 gauge theory and the Hubbard model

By A. Rej, D. Serban, M. Staudacher. 2005

156 citations recorded by the source corpus.

Recently it was established that a certain integrable long-range spin chain describes the dilatation operator of N = 4 gauge theory in the su(2) sector to at least three-loop order, while exhibiting BMN scaling to all orders in perturbation theory. Here we identify this spin chain as an approximation to an integrable short-ranged model of strongly correlated electrons: The Hubbard model.

Subfields: Condensed Matter Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/3a0576d870b903fc2eb61bbd61beff21c865a8d9

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Citations in the corpus

The analytic Bethe ansatz for a chain with centrally extended symmetry (2006, methodology): “The Hamiltonian can be shifted and rescaled without altering its spectrum qualitatively.”
Dressing and wrapping (2007, result): “The mechanism for the breakdown of the asymptotic approximation should be similar to the one discussed from a field theory standpoint in [47], and from a lattice model point of view in [48].”
Finite-size effects from giant magnons (2006, unknown): “18) arising only at infinite J similar to what happens in the Hubbard model description of the BDS spin chain [41].”
Four-loop perturbative Konishi from strings and finite size effects for multiparticle states (2008, methodology): “the Hubbard model was used [26] but this could not be extended to the full theory with the dressing factor.”
The Zamolodchikov-Faddeev Algebra for AdS5 x S5 Superstring (2006, background): “Then the resulting Bethe ansatz is supposed to be asymptotic and might not capture finite size corrections [21, 22, 23, 24].”
Transcendentality and crossing (2006, background): “The ‘covariant’ approaches started in [49, 47, 50] may provide an answer to this question as well as recover the dressing phase from a more fundamental (and simpler) description.”
Five loop Konishi from AdS/CFT (2009, methodology): “Double poles corresponding to anomalous thresholds were identified in [29] (6)Note however the attempt to use the Hubbard model formalism for this purpose [21].”
The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations (2006, unknown): “Moreover, in the prominent minimal compact, bosonic subsector of SU(2) the conjectured gauge theory Bethe equations [15] were recently shown to arise microscopically from the well-known Hubbard model at half filling [17].”
Integrability and transcendentality (2006, background): “Very recently a proposal was made for circumventing the asymptoticity restriction for the su(2) sector by relating the dilatation operator, whose eigenvalues are the dimensions ∆, to a Hubbard Hamiltonian [22].”
The AdS 5 ×S 5 superstring worldsheet S matrix and crossing symmetry (2006, background): “One source of the discrepancy, the so called ‘wrapping interactions’ have apparently been ruled out [17, 18] so the problem remains open.”
Wrapping at four loops in N=4 SYM theory (2007, methodology): “In [15] it was assumed that wrapping might be described by the Hubbard model.”