Quantum finite-size effects for dyonic magnons in the AdS₄ × ℂℙ³

We compute quantum corrections to finite-size effects for various dyonic giant magnons in the AdS₄ × ℂℙ³ in two different approaches. The off-shell algebraic curve method is used to quantize the classical string configurations in semi-classical way and to compute the corrections to the string energies. These results are compared with the F-term Lüscher formula based on the S-matrix of the AdS₄/CFT ₃. The fact that the two results match exactly provides another stringent test for the all-loop integrability conjecture and the exact S-matrix based on it.