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140
Bethe Ansatz for Quantum Strings
, 2004
"... We propose Bethe equations for the diagonalization of the Hamiltonian of quantum strings on AdS5×S 5 at large string tension and restricted to certain large charge states from a closed su(2) subsector. The ansatz differs from the recently proposed allloop gauge theory asymptotic Bethe ansatz by add ..."
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Cited by 280 (15 self)
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We propose Bethe equations for the diagonalization of the Hamiltonian of quantum strings on AdS5×S 5 at large string tension and restricted to certain large charge states from a closed su(2) subsector. The ansatz differs from the recently proposed allloop gauge theory asymptotic Bethe ansatz by additional factorized scattering terms for the local excitations. We also show that our ansatz quantitatively reproduces everything that is currently known about the string spectrum of these states. Firstly, by construction, we recover the integral Bethe equations describing semiclassical spinning strings. Secondly, we explain how to derive the 1/J energy corrections of Mimpurity BMN states, provide explicit, general formulae for both distinct and confluent mode numbers, and compare to asymptotic gauge theory. In the special cases M = 2, 3 we reproduce the results of direct quantization of Callan et al. Lastly, at large string tension and relatively small charge we recover the famous 2 4 √ n 2 λ asymptotics of massive string modes at level n. Remarkably, this behavior is entirely determined by the novel scattering terms. This is qualitatively consistent with the conjecture that these terms occur due to wrapping effects in gauge theory. Our
The factorized Smatrix of CFT/AdS
 JHEP
, 2005
"... Abstract: We argue that the recently discovered integrability in the largeN CFT/AdS system is equivalent to diffractionless scattering of the corresponding hidden elementary excitations. This suggests that, perhaps, the key tool for finding the spectrum of this system is neither the gauge theory’s ..."
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Cited by 239 (7 self)
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Abstract: We argue that the recently discovered integrability in the largeN CFT/AdS system is equivalent to diffractionless scattering of the corresponding hidden elementary excitations. This suggests that, perhaps, the key tool for finding the spectrum of this system is neither the gauge theory’s dilatation operator nor the string sigma model’s quantum Hamiltonian, but instead the respective factorized Smatrix. To illustrate the idea, we focus on the closed fermionic su(11) sector of the N = 4 gauge theory. We introduce a new technique, the perturbative asymptotic Bethe ansatz, and use it to extract this sector’s threeloop Smatrix from Beisert’s involved algebraic work on the threeloop su(23) sector. We then show that the current knowledge about semiclassical and nearplanewave quantum strings in the su(2), su(11) and sl(2) sectors of AdS5 ×S 5 is fully consistent with the existence of a factorized Smatrix. Analyzing the available information, we find an intriguing relation between the three associated Smatrices. Assuming that the relation also holds in gauge theory, we derive the threeloop Smatrix of the sl(2) sector even though this sector’s dilatation operator is not yet known beyond one loop. The resulting
Quantum corrections to the string Bethe ansatz,” hepth/0603204
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Integrable Hamiltonian for classical strings on ADS5 × S 5
, 2004
"... We find the Hamiltonian for physical excitations of the classical bosonic string propagating in the AdS5 × S5 spacetime. The Hamiltonian is obtained in a socalled uniform gauge which is related to the static gauge by a 2d duality transformation. The Hamiltonian is of the Nambu type and depends on ..."
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Cited by 104 (12 self)
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We find the Hamiltonian for physical excitations of the classical bosonic string propagating in the AdS5 × S5 spacetime. The Hamiltonian is obtained in a socalled uniform gauge which is related to the static gauge by a 2d duality transformation. The Hamiltonian is of the Nambu type and depends on two parameters: a single S5 angular momentum J and the string tension λ. In the general case both parameters can be finite. The space of string states consists of short and long strings. In the sector of short strings the large J expansion with λ ′ = λ J2 fixed recovers the planewave Hamiltonian and higherorder corrections recently studied in the literature. In the strong coupling limit λ → ∞, J fixed, the energy of short strings scales as 4 √ λ while the energy of long strings scales as √ λ. We further show that the gaugefixed Hamiltonian is integrable by constructing the corresponding Lax representation. We discuss some general properties of the monodromy matrix, and verify that the asymptotic behavior of the quasimomentum perfectly agrees with the one
The SU(3) spin chain sigma model and string theory
 JHEP
, 2004
"... hep–th/0403139 ..."
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Deformations of N = 4 SYM and integrable spin chain models
 Nucl. Phys. B 702
"... Abstract: Beginning with the planar limit of N = 4 SYM theory, we study planar diagrams for field theory deformations of N = 4 which are marginal at the free field theory level. We show that the requirement of integrability of the full one loop dilatation operator in the scalar sector, places very s ..."
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Cited by 52 (7 self)
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Abstract: Beginning with the planar limit of N = 4 SYM theory, we study planar diagrams for field theory deformations of N = 4 which are marginal at the free field theory level. We show that the requirement of integrability of the full one loop dilatation operator in the scalar sector, places very strong constraints on the field theory, so that the only soluble models correspond essentially to orbifolds of N = 4 SYM. For these, the associated spin chain model gets twisted boundary conditions that depend on the length of the chain, but which are still integrable. We also show that theories with integrable subsectors appear quite generically, and it is possible to engineer integrable subsectors to have some specific symmetry, however these do not generally lead to full integrability. We also try to construct a theory whose spin chain has quantum group symmetry SOq(6) as a deformation of the SO(6) Rsymmetry structure of N = 4 SYM. We show that it is not possible to obtain a spin chain with that symmetry from deformations of the scalar potential of N = 4 SYM. We also show that the natural context for these questions can be better phrased in terms of multimatrix quantum mechanics rather than in four dimensional field theories. Keywords: AdS/CFT, Integrable spin chains. – 1 – Contents
On spin chains and field theories
"... We point out that the existence of global symmetries in a field theory is not an essential ingredient in its relation with an integrable model. We describe an obvious construction which, given an integrable spin chain, yields a field theory whose 1loop scale transformations are generated by the spi ..."
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Cited by 47 (1 self)
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We point out that the existence of global symmetries in a field theory is not an essential ingredient in its relation with an integrable model. We describe an obvious construction which, given an integrable spin chain, yields a field theory whose 1loop scale transformations are generated by the spin chain Hamiltonian. We also identify a necessary condition for a given field theory to be related to an integrable spin chain. As an example, we describe an anisotropic and paritybreaking generalization of the XXZ Heisenberg spin chain and its associated field theory. The system has no nonabelian global symmetries and does not admit a supersymmetric extension without the introduction of more propagating bosonic fields. For the case of a 2state chain we find the spectrum and the eigenstates. For certain values of its coupling constants the field theory associated to this general type of
N = 4 SYM to Two Loops: Compact Expressions for the NonCompact Symmetry Algebra of the su(1, 12) Sector
, 2005
"... We begin a study of higherloop corrections to the dilatation generator of N = 4 SYM in noncompact sectors. In these sectors, the dilatation generator contains infinitely many interactions, and therefore one expects very complicated higherloop corrections. Remarkably, we find a short and simple ex ..."
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Cited by 34 (5 self)
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We begin a study of higherloop corrections to the dilatation generator of N = 4 SYM in noncompact sectors. In these sectors, the dilatation generator contains infinitely many interactions, and therefore one expects very complicated higherloop corrections. Remarkably, we find a short and simple expression for the twoloop dilatation generator. Our solution for the noncompact su(1,12) sector consists of nested commutators of four O(g 1) generators and one simple auxiliary generator. Moreover, the solution does not require the planar limit; we conjecture that it is valid for any gauge group. To obtain the twoloop dilatation generator, we find the complete O(g 3) symmetry algebra for this sector, which is also given by concise expressions. We check our solution using published results of direct field theory calculations. By applying the expression for the twoloop dilatation generator to compute selected anomalous dimensions and the sl(2) sector internal Smatrix, we confirm recent conjectures of the higherloop Bethe ansatz of
On the integrability of large N planewave matrix theory”, Nucl. Phys. B679
, 2004
"... We show the threeloop integrability of large N planewave matrix theory in a subsector of states comprised of two complex light scalar fields. This is done by diagonalizing the theory’s Hamiltonian in perturbation theory and taking the large N limit. At oneloop level the result is known to be equa ..."
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Cited by 33 (1 self)
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We show the threeloop integrability of large N planewave matrix theory in a subsector of states comprised of two complex light scalar fields. This is done by diagonalizing the theory’s Hamiltonian in perturbation theory and taking the large N limit. At oneloop level the result is known to be equal to the Heisenberg spin1/2 chain, which is a wellknown integrable system. Here, integrability implies the existence of hidden conserved charges and results in a degeneracy of parity pairs in the spectrum. In order to confirm integrability at higher loops, we show that this degeneracy is not lifted and that (corrected) conserved charges exist. Planewave matrix theory is intricately connected to N = 4 Super YangMills, as it arises as a consistent reduction of the gauge theory on a threesphere. We find that after appropriately renormalizing the mass parameter of the planewave matrix theory the effective Hamiltonian is identical to the dilatation operator of N = 4 Super YangMills theory in the considered subsector. Our results therefore represent a strong support for the conjectured threeloop integrability of planar N = 4 SYM and are in disagreement with a recent dual string theory finding. Finally, we study the stability of the large N integrability