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Semiclassical Quantization of Spinning Strings: Insights from Superstring Theory and Chern-Simons Models

This paper discusses the semiclassical quantization of spinning strings, drawing on collaborative research involving L.F. Alday, G. Arutyunov, and others. The work elaborates on the implications of solutions within superconformal Chern-Simons-matter theories and the corresponding fixed coupling constants in 11D supergravity. The focus covers the representation of spinning strings, non-zero Noether charges, and models’ integrability, highlighting the discrepancies in energy calculations and their resolution through modified dispersion relations.

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Semiclassical Quantization of Spinning Strings: Insights from Superstring Theory and Chern-Simons Models

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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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