Spinning strings and minimal surfaces in AdS₃ with mixed 3-form fluxes

Abstract

Motivated by the recent proposal for the S-matrix in AdS3× S 3 with mixed three form fluxes, we study classical folded string spinning in AdS 3 with both Ramond and Neveu-Schwarz three form fluxes. We solve the equations of motion of these strings and obtain their dispersion relation to the leading order in the Neveu-Schwarz flux b. We show that dispersion relation for the spinnig strings with large spin S acquires a term given by −λ√2πb2log2S in addition to the usual λ√πlogS term where λ−−√ is proportional to the square of the radius of AdS 3. Using SO(2, 2) transformations and re-parmetrizations we show that these spinning strings can be related to light like Wilson loops in AdS 3 with Neveu-Schwarz flux b. We observe that the logarithmic divergence in the area of the light like Wilson loop is also deformed by precisely the same coefficient of the b 2 log2 S term in the dispersion relation of the spinning string. This result indicates that the coefficient of b 2 log2 S has a property similar to the coefficient of the log S term, known as cusp-anomalous dimension, and can possibly be determined to all orders in the coupling λ using the recent proposal for the S-matrix.