BibTeX
@MISC{Ramadanovic08finitesize,
author = {Bojan Ramadanovic and Gordon W. Semenoff},
title = {Finite size giant magnon},
year = {2008}
}
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Abstract
The quantization of the giant magnon away from the infinite size limit is discussed. We argue that this quantization inevitably leads to string theory on a ZM-orbifold of S 5. This is shown explicitly and examined in detail in the near plane-wave limit. A significant amount of work on the AdS/CFT correspondence [1],[2],[3] has been inspired the idea that the planar limit of N = 4 Yang-Mills theory and its string dual might be integrable models which would be completely solvable using a Bethe Ansätz [4],[5],[6]. Computation of the conformal dimensions of composite operators in N = 4 Yang-Mills theory can be mapped onto the problem of solving an SU(2, 2|4) spin chain. It is known that the spin chain simplifies considerably in the limit of infinite length where dynamics are encoded in the scattering of magnons and integrability would imply a factorized S-matrix. Beginning with this limit, a strategy advocated by Staudacher [7], Beisert showed that a residual SU(2|2) 2 supersymmetry and integrability determine the N = 4 S-matrix up to a phase [8],[9]. More recent work constrains [10] and essentially computes this phase [11]-[15]. An important problem that the integrability program would eventually have to address is that of finite size corrections. In fact, recent four-loop 1 computations of short operators [16],[17] suggest that the most advanced form of the integrability Ansätz, due to Beisert, Eden and Staudacher [14], is likely valid only in the infinite size limit and it is spoiled by finite size effects. In the gauge theory, these effects are thought to stem from wrapping interactions [18],[19],[20]. A place where some progress has been made in studying finite size effects is the spectrum of a single magnon. The Bethe Ansätz implies that the energy spectrum of a single magnon (at least in infinite volume) has the form
Keyphrases
finite size giant magnon finite size effect single magnon yang-mills theory infinite size limit spin chain ad cft correspondence finite size correction integrability an tz integrable model spin chain simplifies infinite length advanced form important problem conformal dimension residual su giant magnon composite operator short operator bethe an near plane-wave limit recent work constrains factorized s-matrix integrability program planar limit bethe an tz implies gauge theory significant amount energy spectrum infinite volume
