Classical/quantum integrability in AdS/CFT
Vladimir Kazakov,Andrei Marshakov,Andrei Marshakov,Joseph A. Minahan,Joseph A. Minahan,Konstantin Zarembo +5 more
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TLDR
In this article, a unified approach to the long wavelength Bethe equations, the classical ferromagnet and the classical string solutions in the SU(2) sector is presented, governed by complex curves endowed with meromorphic differentials with integer periods.Abstract:
We discuss the AdS/CFT duality from the perspective of integrable systems and establish a direct relationship between the dimension of single trace local operators composed of two types of scalar fields in = 4 super Yang-Mills and the energy of their dual semiclassical string states in AdS5 × S5. The anomalous dimensions can be computed using a set of Bethe equations, which for ``long'' operators reduces to a Riemann-Hilbert problem. We develop a unified approach to the long wavelength Bethe equations, the classical ferromagnet and the classical string solutions in the SU(2) sector and present a general solution, governed by complex curves endowed with meromorphic differentials with integer periods. Using this solution we compute the anomalous dimensions of these long operators up to two loops and demonstrate that they agree with string-theory predictions.read more
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Transcendentality and crossing
TL;DR: In this article, the authors discuss possible phase factors for the S-matrix of planar gauge theory, leading to modifications at four-loop order as compared to an earlier proposal, and present evidence that this choice is nonperturbatively related to a recently conjectured crossing-symmetric phase factor for perturbative string theory on AdS5? S5 once the constant is fixed to a particular value.
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The su(2|2) dynamic S-matrix
TL;DR: In this paper, the S-matrix for the su(2|3) dynamic spin chain and for planar N = 4 super Yang-Mills was derived and investigated.
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Long-range psu(2,2|4) Bethe Ansatze for gauge theory and strings
TL;DR: In this article, the authors generalize various existing higher-loop Bethe ansatze for simple sec- tors of the integrable long-range dynamic spin chain describing planar N = 4 Super Yang-Mills Theory to the full psu(2,2|4) symmetry and, asymptotically, to arbitrary loop order.
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Bethe ansatz for quantum strings
TL;DR: In this paper, 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 were proposed.
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A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills
TL;DR: In this paper, the long-range spin chain approach to planar N = 4 gauge theory at high loop order was investigated, and the corresponding all-loop asymptotic Bethe ansatz was shown to be related to a standard inhomogeneous spin chain.
References
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The Large N limit of superconformal field theories and supergravity
TL;DR: In this article, it was shown that the large-N limits of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravityon the product of anti-de Sitter spacetimes, spheres, and other compact manifolds.
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Anti De Sitter Space And Holography
TL;DR: In this article, it was shown that the Kaluza-Klein modes of Type IIB supergravity on $AdS_5\times {\bf S}^5$ match with the chiral operators of the super Yang-Mills theory in four dimensions.
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Gauge Theory Correlators from Non-Critical String Theory
TL;DR: In this paper, a boundary of the anti-deSitter space analogous to a cut-off on the Liouville coordinate of the two-dimensional string theory is introduced to obtain certain Green's functions in 3+1-dimensional N = 4 supersymmetric Yang-Mills theory with a large number of colors via non-critical string theory.
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Anti de sitter space and holography
TL;DR: In this article, a correspondence between conformal field theory observables and those of supergravity was proposed, where correlation functions in conformal fields are given by the dependence of the supergravity action on the asymptotic behavior at infinity.