Classical / quantum integrability in non - compact sector of AdS / CFT
نویسندگان
چکیده
We discuss non-compact SL(2, R) sectors in N=4 SYM and in AdS string theory and compare their integrable structures. We formulate and solve the Riemann-Hilbert problem for the finite gap solutions of the classical sigma model and show that at one loop it is identical to the classical limit of Bethe equations of the spin (-1/2) chain for the dilatation operator of SYM.
منابع مشابه
Review of AdS/CFT Integrability, Chapter VI.2: Yangian Algebra
We review the study of Hopf algebras, classical and quantum R-matrices, infinite-dimensional Yangian symmetries and their representations in the context of integrability for the N = 4 vs AdS5×S correspondence. Mathematics Subject Classification (2010): 81T60, 81T30, 81U15, 16T05, 17B65
متن کاملQuantum string integrability and AdS/CFT
Recent explorations of the AdS/CFT correspondence have unveiled integrable structures underlying both planar N = 4 super-Yang-Mills theory and type IIB string theory on AdS5 × S. Integrability in the gauge theory emerges from the fact that the dilatation generator can be identified with the Hamiltonian of an integrable quantum spin chain, and the classical string theory has been shown to contai...
متن کاملOn the Integrability of String Theory in AdS 5 × S 5 Ian Swanson
Integrability occupies an increasingly important role in direct tests of the AdS/CFT correspondence. Integrable structures have appeared in both planar N = 4 super YangMills theory and type IIB superstring theory on AdS5 × S. A generalized statement of the AdS/CFT conjecture has therefore emerged in which, in addition to string energies corresponding to gauge theory anomalous dimensions, an inf...
متن کاملReview of AdS/CFT Integrability, Chapter III.1: Bethe Ansätze and the R-Matrix Formalism
The one-dimensional Heisenberg XXX spin chain appears in a special limit of the AdS/CFT integrable system. We review various ways of proving its integrability, and discuss the associated methods of solution. In particular, we outline the coordinate and the algebraic Bethe ansatz, giving reference to literature suitable for learning these techniques. Finally, we speculate which of the methods mi...
متن کاملIntegrability and non-perturbative effects in the AdS/CFT correspondence
We present a non-perturbative resummation of the asymptotic strong-coupling expansion for the dressing phase factor of the AdS5 × S string S-matrix. The non-perturbative resummation provides a general form for the coefficients in the weak-coupling expansion, in agreement with crossing symmetry and transcendentality. The ambiguities of the non-perturbative prescription are discussed together wit...
متن کامل