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of spinning strings in

Semiclassical quantization. of spinning strings in. DMITRI BYKOV. Trinity College Dublin Steklov Mathematical Institute Moscow. Based on joint work arXiv:080 7 . 440 0 with L.F.ALDAY, G.ARUTYUNOV. AHARONY, BERGMANN, JAFFERIS, MALDACENA 06’’08’. superconformal Chern-Simons-matter theories.

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of spinning strings in

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  1. Semiclassical quantization of spinning strings in DMITRI BYKOV Trinity College Dublin Steklov Mathematical Institute Moscow Based on joint work arXiv:0807.4400 with L.F.ALDAY, G.ARUTYUNOV

  2. AHARONY, BERGMANN, JAFFERIS, MALDACENA 06’’08’ superconformal Chern-Simons-matter theories Discrete values of the coupling constant solution of 11D supergravity ‘t Hooft limit fixed and real IIA superstring theory on [1/11]

  3. ARUTYUNOV, FROLOV 06’’08’ String theory on as a sigma model on the coset maximally symmetric space Maximal bosonic subgroup 24 real supercharges -symmetry fixing 16 real supercharges = # of physical bosonic d.o.f. [2/11]

  4. There exists a -grading of the Lie algebra Let Define a left-invariant -valued 1-form Its decomposition under the grading gives - vielbein (zehnbein) - spin connection - fermionic components The Lagrangian by -symmetry [3/11]

  5. Coset parameterization fermionic elements Global symmetry group acts from the left whereas local -symmetry acts from the right constrained ARUTYUNOV, FROLOV 06’’08’ represents some submanifold in the coset, on which group multiplication can be defined Fermions are neutral under [4/11]

  6. GUBSER, KLEBANOV, POLYAKOV 04’’02’ FROLOV, TSEYTLIN 04’’02’ The spinning string Two non-zero Noether conserved charges with zero Poisson bracket (Cartan) - the spin in - the spin in A classical solution representing a string rotating in with its baricenter moving along a circle in The limit fixed [5/11]

  7. The spinning string describes movement in and, as such, coincides with the solution found by FROLOV, TSEYTLIN 04’’02’ Coset element for this solution The long string approximation [6/11]

  8. Expand the action up to quadratic order in fermionic and bosonic fluctuations Obtain the frequencies Fermionic Bosonic 4 x 4 x 2 x [7/11]

  9. The result ALDAY, ARUTYUNOV, DB 07’’08’ where A limit [8/11]

  10. Integrability of the superstring in • Classically integrable sigma model • Two-loop dilatation operator known • (in the scalar sector) and is integrable MINAHAN, ZAREMBO 06’’08’ • models not integrable at the quantum level ABDALLA, FORGER, GOMES 82’ [9/11]

  11. The discrepancy ? GROMOV, VIEIRA 07’’08’ Can be resolved by tuning the dispersion relation [10/11]

  12. Conclusions • obtained 1-loop correction to the energy of the spinning string • in the long-string approximation and • discrepancy between our result and the prediction • of the asymptotic Bethe ansatz • discrepancy is removed if one modifies the dispersion relation • of the giant magnon [11/11]

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