Stringing Spins and Spinning Strings

By N. Beisert, J. Minahan, M. Staudacher, K. Zarembo. 2003

353 citations recorded by the source corpus.

We apply recently developed integrable spin chain and dilatation operator techniques in order to compute the planar one-loop anomalous dimensions for certain operators containing a large number of scalar fields in N = 4 Super Yang-Mills. The first set of operators, belonging to the SO(6) representations [J,L 2J,J], interpolate smoothly between the BMN case of two impurities (J = 2) and the extreme case where the number of impurities equals half the total number of fields (J = L/2). The result for this particular [J,0,J] operator is smaller than the anomalous dimension derived by Frolov and Tseytlin [hep-th/0304255] for a semiclassical string configuration which is the dual of a gauge invariant operator in the same representation. We then identify a second set of operators which also belong to [J,L 2J,J] representations, but which do not have a BMN limit. In this case the anomalous dimension of the [J,0,J] operator does match the Frolov-Tseytlin prediction. We also show that the fluctuation spectra for this [J,0,J] operator is consistent with the string prediction.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/d5cb905a0903986d95ad9eb745778069775d6d0d

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Citations in the corpus

The N=4 SYM Integrable Super Spin Chain (2003, background): “This power was very recently illustrated in a study of scalar operators belonging to the so(6) representations [J2, J1 − J2, J2] with ∆0 = J1 + J2 in the limit where both charges J1, J2 become large [14].”
The SU(3) spin chain sigma model and string theory (2004, methodology): “Anomalous dimensions of Yang-Mills operators carrying large charges can then be calculated by solving the thermodynamic Bethe ansatz, and successfully compared to the energy of string solitons [8, 9].”
Long-range psu(2,2|4) Bethe Ansatze for gauge theory and strings (2005, background): “The immense usefulness of the Bethe ansatz in the study of these proposals was demonstrated in [2] and [26].”
Large spin limit of AdS5×S5 string theory and low energy expansion of ferromagnetic spin chains (2004, methodology): “As a consequence, one can directly relate the target space spinning string configurations to configurations of 1-d spins [21], a non-trivial connection which emerged also in the Bethe ansatz approach [11, 17].”
One-point functions in defect CFT and integrability (2015, background): “This operator is characterized by its M ∼ O(L) Bethe roots being distributed on two arches placed symmetrically around zero [58, 59] and belongs to the class of operators which have a non-vanishing overlap with the defect operators, cf.”
Classical/quantum integrability in non-compact sector of AdS/CFT (2004, methodology): “The Bethe ansatz solution of this model and related spin systems was extremely useful in comparing anomalous dimensions of local operators in SYM [16, 17, 18] to the energies of classical string solitons in AdS5 × S5 [19, 20, 21, 22].”
SPINNING STRINGS AND AdS/CFT DUALITY (2003, methodology): “This was indeed verified on specific examples in [16, 17, 18, 19, 21].”
Deformations of N = 4 SYM and integrable spin chain models (2004, background): “Also, semiclassical string configurations have been studied in a lot of detail, and dual candidate states have been identified in terms of the spin chain model via the thermodynamic Bethe ansatz, see [16, 17] and references therein.”
The Algebraic Curve of Classical Superstrings on AdS5×S5 (2005, background): “Likewise, the involved group manifolds are considered to be universal coverings.”
Yang-Mills duals for semiclassical strings on AdS5 × S5 (2003, background): “a ﬁnite amount [6]. More recently, a program has begun comparing the spectrum of semiclassical string conﬁgurations [7,8,9,10,11,12, 13,14,15] with anomalous dimensions for a wider class of operators [16,17,18,19,20,21,22]. These operators also have large charges, but are not necesserily close to BP”
Hidden Symmetries of the AdS_5 x S^5 Superstring (2003, background): “On the gauge side, Minahan and Zarembo [24] have shown that the calculation of oneloop anomalous dimensions for general scalar operators can be recast in terms of an integrable field theory (see further work [25]).”
Classical/quantum integrability in AdS/CFT (2004, methodology): “The classical chain naturally corresponds to the long wave-length limit of the quantum chain [36, 37], which is precisely what was considered in [32, 33, 24].”
A Crossing-Symmetric Phase for AdS5 x S5 Strings (2006, neutral): “They also serve as the quantum constituents for the Frolov-Tseytlin spinning string solutions [24], see [40].”
The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability (2004, methodology): “As an application, we shall derive the one-loop anomalous dimension of a state dual to a macroscopic spinning string in AdS5 × S(5) and find a remarkable agreement [60, 66].”
Planar N = 4 gauge theory and the Hubbard model (2005, background): “This was later independently rediscovered and extended in the N = 4 context in [1, 11].”
Foundations of the AdS5 × S5 superstring: I (2009, methodology): “Further progress in determination of the dressing phase relied on comparison of the energies of spinning strings at the classical and the one-loop level [24, 25], [114]-[120] with those obtained by solving the asymptotic Bethe ansatz equations [121]-[129].”
On one-loop correction to energy of spinning strings in S**5 (2004, methodology): “amiltonian of the Heisenberg ferromagnet [9]. Still, this suggests that some analytic continuation may apply. Related aspect of this problem is that the spin chain states found using the Bethe ansatz [10] are exact quantum states, while on the string theory side we are considering semiclassical stat”
Precision spectroscopy of AdS / CFT (2003, methodology): “8) was first derived [17] by assuming that J2/J < 0 and then analytically continued to J2/J > 0! For further details see Appendix C, where we also review the solution and present some further results that were not included in the paper [17].”