Jan Plefka
Max Planck Institute for Gravitational Physics
Am Mühlenberg 1, 14476 Potsdam, Germanyhttp://www.aei.mpg.de/~plefka/
In this introductory review we discuss dynamical tests of the string/
Super Yang-Mills duality. After a brief introduction to AdS/CFT, we argue that semiclassical
string energies yield information on the quantum spectrum of the string in the limit of large
angular momenta on the
. The energies of the folded and circular spinning string solutions
rotating on a
within the
are derived, which yield all-loop predictions for the dual
gauge theory scaling dimensions. These follow from the eigenvalues of the dilatation operator
of
Super Yang-Mills in a minimal SU(2) subsector, and we display its reformulation
in terms of a Heisenberg
spin chain along with the coordinate Bethe ansatz for its
explicit diagonalization. In order to make contact to the spinning string energies, we then study
the thermodynamic limit of the one-loop gauge theory Bethe equations and demonstrate the
matching with the folded and closed string result at this loop order. Finally, the known gauge
theory results at higher-loop orders are reviewed and the associated long-range spin chain Bethe
ansatz is introduced, leading to an asymptotic all-loop conjecture for the gauge theory Bethe
equations. This uncovers discrepancies at the three-loop order between gauge theory scaling
dimensions and string theory energies and the implications of this are discussed. Along the
way, we comment on further developments and generalizations of the subject and point to the
relevant literature.
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http://www.livingreviews.org/lrr-2005-9 |
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