{"arxiv_id":"hep-th/0412188","incoming":{"papers":136,"sentences":200,"groups":[{"kind":"extends","label":"Builds on it","papers":1,"sentences":2,"quotes":[{"arxiv_id":"0803.3999","title":"Aspects of Integrability in AdS/CFT Duality","url":"/paper/0803.3999","section":"The asymptotic states","sentence":"For $Q>1$ , this formula is a generalisation of the exact [ref] magnon dispersion relation obtained in [ref] (see also [ref] ).","intent_p":0.92,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":4,"sentences":4,"quotes":[{"arxiv_id":"1702.02154","title":"Structure constants at wrapping order","url":"/paper/1702.02154","section":"Asymptotic data","sentence":"The magnitude $z$ is fixed by the asymptotic Bethe ansatz equation [ref] e^ipLS(z, -z)|_𝔰𝔩(2) = (x^+/x^-)^L+2z-i/2/z+i/2 /σ(z, -z)^2 = 1 , where $L = L_1$ is the length of the excited state, $σ= 1+O(g^6)$ is the BES dressing phase [ref] , and $x^± = x(z±i/2)$, with $x(z) = (z+√(z^2-4g^2))/(2g) = z/g+O(g)$.","intent_p":0.83,"contests_p":null},{"arxiv_id":"0708.2272","title":"Reflecting magnons","url":"/paper/0708.2272","section":"Appendix: integrability at two loops","sentence":"This is the asymptotic Bethe ansatz discussed in [ref] .","intent_p":0.82,"contests_p":null},{"arxiv_id":"1006.3494","title":"On string integrability. A journey through the two-dimensional hidden symmetries in the AdS/CFT dualities","url":"/paper/1006.3494","section":"Introduction","sentence":"On the gauge theory side, it is the same, namely we are dealing with the internal S-matrix, adopting the expression used by Staudacher in [ref] .","intent_p":0.97,"contests_p":null},{"arxiv_id":"0707.1621","title":"Decoupling limits of N=4 super Yang-Mills on R x S^3","url":"/paper/0707.1621","section":"The $SU(1|1)$ theory as a magnetic $XX$ Heisenberg spin chain","sentence":"Following [ref] , we rewrite the $D_2$ part of the $SU(1|1)$ Hamiltonian in spin chain form by expressing it in terms of the three Pauli matrices $σ^1,σ^2, σ^3$ as [equation] In spin chain language the bosonic partons $Z$ are spin-up spinors and the fermionic partons $χ_1$ are spin-down.","intent_p":0.95,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":3,"sentences":3,"quotes":[{"arxiv_id":"0806.1786","title":"Iterative Structure of the N=4 SYM Spin Chain","url":"/paper/0806.1786","section":"S-matrix checks","sentence":"Solving for the coefficients $S$ and $c^(i)$ in the wavefunction, we find agreement with the known 2-particle S-matrix for this sector, first obtained to three-loops in [ref] , using the result of [ref] , S(p_1, p_2) -1 - 2 i g^2 (sin(p_1) - sin(p_1-p_2) - sin(p_2)) + 4 i g^4 sin(p_1/2) sin(p_2/2) (sin(p_1 - 3 p_2/2) - 7sin(p_1 - p_2/2) + sin(3 p_1 - p_2/2) + sin(3 p_1 - p_2/2) - 8 i sin(p_1/2) sin(p_2/2) sin^2( p_1 - p_2/2) ). + 𝒪(g^6).","intent_p":0.93,"contests_p":null},{"arxiv_id":"0912.1624","title":"Five-Loop Anomalous Dimension of Twist-Two Operators","url":"/paper/0912.1624","section":"The structure of the anomalous dimension","sentence":"One can check [ref] and even prove [ref] that they coincide with the corresponding results of the ABE.","intent_p":0.96,"contests_p":null},{"arxiv_id":"2312.05888","title":"Anomalous dimensions of twist-two operators in extended N=2 and N=4 super Yang-Mills theories","url":"/paper/2312.05888","section":"Four-loop anomalous dimension in $=4$ SYM","sentence":"Finally, using Eq. [ref], we obtain [equation] The planar parts of the above results coincide with those obtained with the help of integrability [ref] .","intent_p":1.0,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites it as support","papers":2,"sentences":2,"quotes":[{"arxiv_id":"0907.3468","title":"Integrability and the AdS/CFT correspondence","url":"/paper/0907.3468","section":"Asymptotic Bethe Ansatz","sentence":"On the other hand, the perturbative asymptotic integrability for the first few orders of perturbation theory have been confirmed in some subsectors of the full theory, see [ref] and [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"1002.2363","title":"Generalized Gribov-Lipatov Reciprocity and AdS/CFT","url":"/paper/1002.2363","section":"Multi-loop calculation of anomalous dimensions via integrability","sentence":"The conjectured three loop formula has been then independently confirmed in the framework of the Bethe ansatz equations [ref] as well as within a space-time approach [ref] .] predicts that at each order $n$ the solution can be entirely expressed in terms of certain combinations of generalized harmonic sums of order $2n - 1$ or in terms of products of harmonic sums $S_𝐚$ and zeta functions $ζ(b_i)$ in such a way that the sum of their transcendentalities $|𝐚|$ and $b_i$ (see Appendix A for definitions) is again equal to $2n -1$.","intent_p":0.97,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":58,"sentences":62,"quotes":[{"arxiv_id":"0710.1991","title":"Large spin expansion of the long-range Baxter equation in the sl(2) sector of N=4 SYM","url":"/paper/0710.1991","section":"Introduction","sentence":"Going beyond one loop, asymptotic all-order Bethe Ansatz equations have been proposed [ref] .","intent_p":0.85,"contests_p":null},{"arxiv_id":"0707.0668","title":"Quantum Scattering of Giant Magnons","url":"/paper/0707.0668","section":"Introduction","sentence":"Recent developments in the study of planar $N=4$ SUSY Yang-Mills (and the dual string theory on $AdS_5×S^5$) have culminated in a proposal for a set of Asymptotic Bethe Ansatz Equations (ABAE) [ref] .","intent_p":0.96,"contests_p":null},{"arxiv_id":"1010.3229","title":"Twisted Bethe equations from a twisted S-matrix","url":"/paper/1010.3229","section":"Introduction","sentence":"For the undeformed theory, the all-loop asymptotic Bethe equations [ref] have been derived [ref] from the $AdS_5/CFT_4$ $S$-matrix [ref] - [ref] .","intent_p":0.87,"contests_p":null},{"arxiv_id":"0801.0747","title":"Finite-Size Effects for Dyonic Giant Magnons","url":"/paper/0801.0747","section":"Introduction","sentence":"The wrapping problem does not occur for the system of infinite $L$ at weak coupling, and such situation has been studied under the name of asymptotic spin chain [ref] .","intent_p":0.93,"contests_p":null},{"arxiv_id":"1012.3991","title":"Review of AdS/CFT Integrability, Chapter III.2: Exact world-sheet S-matrix","url":"/paper/1012.3991","section":"Introduction","sentence":"The world-sheet and spin-chain $S$-matrix have been derived based on an $su(2|2)^2$ symmetry in [ref] - [ref] and will be reviewed here.","intent_p":0.87,"contests_p":null}]}],"unlabelled_sentences":127},"outgoing":{"papers":0,"sentences":0,"groups":[],"unlabelled_sentences":0},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. 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