Exact expressions for quantum corrections to spinning strings

Abstract

Abstract The one-loop worldsheet quantum corrections to the energy of spinning strings on R × S 3 within AdS 5 × S 5 are reexamined. The explicit expansion in the effective 't Hooft coupling λ ′ = λ / J 2 is rigorously derived. The expansion contains both analytic and non-analytic terms in λ ′ , as well as exponential corrections. Furthermore, we pin down the origin of the terms that are not captured by the quantum string Bethe ansatz, which only produces analytic terms in λ ′ . It is shown that the analytic terms arise from string fluctuations within the S 3 , whereas the non-analytic and exponential terms, which are not captured by the Bethe ansatz, originate from the fluctuations in all directions within the supersymmetric sigma model on AdS 5 × S 5 . We also comment on the case of spinning string in AdS 3 × S 1 .