We derive the a
sy
mptotic Bethe an
satz (AFS equation
s [G. Arutyunov, S. Frolov, M. Staudacher, Bethe an
satz for quantu
m string
s, JHEP 0410 (2004) 016, hep-th/0406256]) for the
string on
me="mml2">style="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6TVC-4NCSGMD-3&_mathId=mml2&_user=10&_cdi=5531&_rdoc=3&_acct=C000050221&_version=1&_userid=10&md5=e629945521c4b3cf43db4eaf84380cf8" title="Click to view the MathML source">S<sup>3sup>×R sector of
me="mml3">style="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6TVC-4NCSGMD-3&_mathId=mml3&_user=10&_cdi=5531&_rdoc=3&_acct=C000050221&_version=1&_userid=10&md5=d04bcb8264f60723d59d1580aed8e180" title="Click to view the MathML source">AdS<sub>5sub>×S<sup>5sup> fro
m the integrable nonho
mogeneou
s dyna
mical
spin chain for the
string
sig
ma
model propo
sed in [N. Gro
mov, V.
Kazakov, K. Sakai, P. Vieira, String
s a
s multi-particle
state
s of quantu
m sig
ma-
model
s, hep-th/0603043]. It i
s clear fro
m the derivation that AFS equation
s can be viewed only a
s an effective
model de
scribing a certain regi
me of a
more funda
mental inho
mogeneou
s spin chain.