On Quantum Corrections to Spinning Strings and Bethe Equations

TL;DR

This paper investigates quantum corrections to spinning strings in AdS5xS5, confirming the agreement with Bethe equations up to fourth order and identifying new contributions at higher orders, shedding light on the three-loop discrepancy.

Contribution

It demonstrates the matching of quantum string corrections with Bethe ansatz beyond one-loop and explores the origin of the three-loop discrepancy.

Findings

Agreement with Bethe equations up to fourth order in effective coupling

Identification of new contributions at odd powers beyond fourth order

Potential explanation of the three-loop discrepancy as an order-of-limits effect

Abstract

Recently, it was demonstrated that one-loop energy shifts of spinning superstrings on AdS5xS5 agree with certain Bethe equations for quantum strings at small effective coupling. However, the string result required artificial regularization by zeta-function. Here we show that this matching is indeed correct up to fourth order in effective coupling; beyond, we find new contributions at odd powers. We show that these are reproduced by quantum corrections within the Bethe ansatz. They might also identify the "three-loop discrepancy" between string and gauge theory as an order-of-limits effect.