Gauge invariant finite size spectrum of the giant magnon

Abstract

It is shown that the finite size corrections to the spectrum of the giant magnon solution of classical string theory, computed using the uniform light-cone gauge, are gauge invariant and have physical meaning. This is seen in two ways: from a general argument where the single magnon is made gauge invariant by putting it on an orbifold as a wrapped state obeying the level matching condition as well as all other constraints, and by an explicit calculation where it is shown that physical quantum numbers do not depend on the uniform light-cone gauge parameter. The resulting finite size effects are exponentially small in the $R$-charge and the exponent (but not the prefactor) agrees with gauge theory computations using the integrable Hubbard model.Comment: 12 pages, some clarifications, references adde

Review of AdS/CFT Integrability, Chapter III.5: Lüscher Corrections

“…Subsequently, corrections to its energy were found when the excitation was considered on a cylinder of finite size J . The resulting correction was evaluated from the deformed classical solution in [24,25] …”

Wrapping interactions at strong coupling: The giant magnon

“…The curious numerical prefactor includues e = exp(1), the base of natural logarithm. This result is even more interesting when one compares it to finite size corrections for the magnon computed within the Hubbard model approach [36] which gives [36,35] …”

“…Finally, finite size corrections were found for the giant magnon dispersion relation at strong coupling from classical string solutions [25,35]. They have the form…”

Quantum strings and the AdS4/CFT3 interpolating function

“…Here we have included the twists in q 3 (x) and q 4 (x) as used by [42,46] which amount to orbifolding the space by an angle p so as to make the giant magnon a closed string [47][48][49]. Note that these twists play no role in the leading corrections, but are important in the subleading corrections.…”