One-loop quantization of rigid spinning strings in $AdS_3 \times S^3 \times T^4$ with mixed flux

Understand

We compute the one-loop correction to the classical dispersion relation of rigid closed spinning strings with two equal angular momenta in the $AdS_3 \times S^3 \times T^4$ background supported with a mixture of R-R and NS-NS three-form fluxes.

• This analysis is extended to the case of two arbitrary angular momenta in the pure NS-NS limit.
• We perform this computation by means of two different methods.
• The first method relies on the Euler-Lagrange equations for the quadratic fluctuations around the classical solution, while the second one exploits the underlying integrability of the problem through the finite-gap equations.