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Theory Center Seminar<br>
Mon., March 31, 2014<br>
1:00 p.m. (coffee at 12:45 p.m.)<br>
CEBAF Center, Room L102<br>
<br>
Vladimir Kazakov<br>
Laboratoire de Physique Théorique de l'Ecole Normale Supérieure<br>
Paris, France<br>
<br>
<b>Exact Spectrum of Anomalous Dimensions in Planar N=4 SYM Theory</b><br>
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The planar N=4 Super-Yang-Mills theory appears to be integrable via
its AdS/CFT duality to a superstring sigma-model defined on a
two-dimensional world sheet. This allows formulation of a finite
system of functional, or Riemann-Hilbert equations, exact at any YM
coupling, calculating the anomalous dimensions of,<i> a priori</i>,
any local operators, which can be efficiently analyzed in various
approximations: weak coupling (9 loops for the anomalous dimension
of Konishi operator!), strong coupling and possibly BFKL, and solved
numerically. The solution is based on a nice mathematical structure
of quantum integrability: Hirota equations, their Wronskian
solutions in terms of Baxter's Q-functions and a peculiar analytic
structure of these functions w.r.t. the spectral parameter.
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