Finite-size effects of β-deformed AdS5/CFT4 at strong coupling

We compute both classical and quantum finite-size corrections at leading order in the strong coupling limit for the (dyonic) giant magnon in the Lunin–Maldacena background. Based on the exact S-matrix conjectured for the deformed theory, we generalize the Lüscher formula to include twisted boundary conditions and show that the results match with those derived both by finite-size classical solutions of the giant magnon and by algebraic curve analysis.