Matching Higher Conserved Charges for Strings and Spins
By G. Arutyunov, M. Staudacher. 2003
216 citations recorded by the source corpus.
We demonstrate that the recently found agreement between one-loop scaling dimensions of large dimension operators in N = 4 gauge theory and energies of spinning strings on AdS5 × S 5 extends to the eigenvalues of an infinite number of hidden higher commuting charges. This dynamical agreement is of a mathematically highly intricate and non-trivial nature. In particular, on the gauge side the generating function for the commuting charges is obtained by integrable quantum spin chain techniques from the thermodynamic density distribution function of Bethe roots. On the string side the generating function, containing information to arbitrary loop order, is constructed by solving exactly the Backlund equations of the integrable classical string sigma model. Our finding should be an important step towards matching the integrable structures on the string and gauge side of the AdS/CFT correspondence.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/d32183e6c13eb09cfed6da9fcfb74ffdcbe601ff
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In Nuclear and High Energy Physics
Citations in the corpus
- Finite-size effects from giant magnons (2006, background): “However, the insights coming from gauge theory [11– 14] from semi-classical string quantisation [11,15–20] as well as from the analysis of classical strings [21–26] lead to a conjecture for the form of the dispersion relation and the corresponding S-matrix [27,28].”
- Integrable Hamiltonian for Classical Strings on AdS5 x S5 (2004, methodology): “Alternatively, the local integrals of motion for the string sigma model can be found by means of the Bäcklund transform [16].”
- The su(2|3) dynamic spin chain (2003, methodology): “The analysis of semiclassical strings showed that indeed one can find an infinite tower of commuting charges [14] and indeed they agree, at one-loop, with the spin chain charges [ 14 ].”
- Planar N=4 Gauge Theory and the Inozemtsev Long Range Spin Chain (2004, methodology): “with the by now standard trick [18, 19, 21] of analytic continuation to (formally) negative J , resulting in a negative filling fraction α = J2/J < 0 (this flips the complex cuts onto the real axis).”
- Classical/quantum integrability in AdS/CFT (2004, methodology): “12) is the generating function of local charges in the scaling limit [46, 24].”
- Pulsating strings on Ads(5) x S(5) (2004, background): “ through the point u = 1/2πm, as expected. Now define the resolvent W(u′) ≡ Z C du σ(u) u′ −u . (2.9) By deforming the contour and picking up residues at u = 0, u = u′ and u = ∞, the resolvent becomes [31, 63] −αW(u′) = 1 u′ h 1− p (1− 2πmu′)2 − 2α(4πmu′) i +πm. (2.10) The square root denotes the bra”
- The factorized S-matrix of CFT/AdS (2004, background): “rable classical mechanics systems of Neumann type [7]. The reduction may be undone by the B¨acklund transformation, and the infinite tower of commuting charges of the original sigma model is recovered [8]. Subsequently, in an important paper by Kazakov, Marshakov, Minahan and Zarembo, it was demonstr”
- Spinning strings in AdS(5) x S**5: New integrable system relations (2003, methodology): “While recent papers [9, 10 , 11, 25] shed some light on how the integrability of the AdS5 ×S 5 string theory is related to that of the planar”
- Algebraic Curve for the SO(6) Sector of AdS/CFT (2004, background): “This is an interesting model, because (classically) it is a consistent truncation of the superstring on AdS5 × S5.”