Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-03-24
J. Phys. A: Math. Theor. 44 (2011) 124003
Physics
High Energy Physics
High Energy Physics - Theory
PhD thesis. Contains also unpublished previously results and introduction to the subject of integrability in terms of function
Scientific paper
10.1088/1751-8113/44/12/124003
In this thesis a general procedure to represent the integral Bethe Ansatz equations in the form of the Reimann-Hilbert problem is given. This allows us to study in simple way integrable spin chains in the thermodynamic limit. Based on the functional equations we give the procedure that allows finding the subleading orders in the solution of various integral equations solved to the leading order by the Wiener-Hopf technics. The integral equations are studied in the context of the AdS/CFT correspondence, where their solution allows verification of the integrability conjecture up to two loops of the strong coupling expansion. In the context of the two-dimensional sigma models we analyze the large-order behavior of the asymptotic perturbative expansion. Obtained experience with the functional representation of the integral equations allowed us also to solve explicitly the crossing equations that appear in the AdS/CFT spectral problem.
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