Finite-Size Effects for Multi-Magnon States

Understand

We propose the generalized Luscher formula for multi-magnon states by which one can compute the finite-size correction to the energy of multi giant magnons at classical and one-loop levels.

• It is shown that the F-term of our formula is consistent with the exact finite-size spectrum of the sinh-Gordon model, and the mu-term agrees with the finite-size energy of magnon boundstate of the asymptotic Bethe Ansatz in the su(2) sector at strong coupling.
• In an appendix, we evaluate our formula at weak coupling under some approximations, and find that the transcendental terms arise from a sum over an infinite tower of BPS boundstates.