MS Seminar (Mathematics - String Theory)

Speaker: Antal Jevicki (Brown university)
Title: Classical AdS String : Solutions and Dynamics of Moduli
Date: Tue, May 18, 2010, 13:15 - 14:45
Place: Seminar Room A
Abstract: In the first introductury part of the talk we describe some simple closed string solutions in AdS space-time and explain their role in the AdS/CFT correspondence of the N=4 Super Yang-Mills theory. These solutions correspond to simple folded and rotating AdS string and the n-spike generalization associated with higher twist operators of gauge theory. Identification of spikes with field theory solitons is also described.

In the second part we present a detailed construction of a general set of dynamical time dependent classical string solutions in AdS3. For this we have formulated an inverse scattering method employing strategy of reducing the string sigma model to integrable scalar field theory systems (Pokhlmeyer reduction).
The resulting integrable equations are of Hitchin and Toda type. For AdS3 this leads to a sinh-Gordon theory which possesses both regular and singular solutions. We present the construction of general (spiky) string solutions associated with the most general N-soliton configurations on an infinite line.

Based on this construction we are led to a picture where singularities of the field theory configuration translate through a direct map into spikes of the AdS string. Solitons in field theory are described in general by their moduli (collective coordinates) representing their locations and momenta. An identical particle-like interpretation turns out to hold for singularities . In our string theory representation the singular soliton coordinates map directly into coordinates associated with spike configurations. This mapping then provides a complete dynamical description of moduli associated with the general string solutions. For the simpler case of strings moving on R x S (magnons) the complete moduli space dynamics is presented, in terms of the N-body problem of Calogero (or Ruijsenaars-Schneider type.
Contact: Takayanagi