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Spin chains and string theory
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Recently, an impressive agreement was found between anomalous dimensions of certain operators in N=4 SYM and rotating strings with two angular momenta in the bulk of AdS5xS5. A one-loop field theory computation, which involves solving a Heisenberg chain by means of the Bethe ansatz agrees with the large angular momentum limit of a rotating string. We point out that the Heisenberg chain can be equally well solved by using a sigma model approach. Moreover we also show that a certain limit, akin to the BMN limit, leads exactly to the same sigma model for a string rotating with large angular momentum. The agreement is then at the level of the action. As an upshot we propose that the rotating string should be identified with a coherent, semi-classical state built out of the eigenstates of the spin chain. The agreement is then complete. For example we show that the mean value of the spin <S> gives, precisely, the position of the string in the bulk. This suggests a more precise formulation of the AdS/CFT correspondence in the large-N limit and also indicates a way to obtain string theory duals of other gauge theories.
Forward citations
Cited by 5 Pith papers
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Finite scalar field theory with SU(1,1) spacetime symmetry from near-BPS limits of $\mathcal{N}=4$ SYM
A non-Lorentzian scalar QFT with SU(1,1) symmetry obtained from N=4 SYM is finite at all orders in perturbation theory.
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Spread complexity for the planar limit of holography
Spread complexity is generalized to fermionic and supercoherent states, and applied to large-charge rotating strings in AdS5 x S5, yielding Krylov paths that reduce to effective SU(2)/SL(2) coherent-state complexity.
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Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory
An explicit conformal mapping is derived between null-reduced R times S^3 and Omega-deformed Minkowski TNC geometries, giving the state-operator generator map H0 = (R^2 H + C/R^2 - J - N)/2 in SU(1,2) non-Lorentzian CFTs.
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On quantum corrections to semiclassical strings on $\mathrm{AdS}_5\times S^5/\mathbb{Z}_{L}$ orbifold backgrounds
On an orbifold AdS5×S5/ZL background, one-loop string energies for three semiclassical solutions match finite-size twisted Bethe-ansatz and Landau-Lifshitz predictions, with novel stable fractional-winding sectors.
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An Introduction to String Newton-Cartan Holography and Integrability
String Newton-Cartan holography, the non-relativistic limit of the AdS/CFT correspondence, is organized and reviewed around five consistency conditions, with its classical solutions, spectrum, and integrability structure.
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