Exact expressions for quantum corrections to spinning strings

TL;DR

This work derives exact one-loop quantum corrections to spinning strings in $AdS_5 \times S^5$ by an explicit $λ' = λ/J^2$ expansion, revealing analytic, non-analytic, and exponential contributions. A contour-integral approach is used to sum fluctuation frequencies, separating analytic and non-analytic pieces through distinct contour components, clarifying their origins. The authors show that analytic terms come from $S^3$ fluctuations while non-analytic and exponential terms originate from fluctuations in the full supersymmetric sigma-model, explaining limitations of the quantum string Bethe ansatz; they also obtain results for the $AdS_3 \times S^1$ sector. The findings highlight the Bethe ansatz's incompleteness and provide exact expressions for all contributions, including exponentially suppressed terms, with implications for integrability-based approaches to AdS/CFT.

Abstract

The one-loop worldsheet quantum corrections to the energy of spinning strings on R x S^3 within AdS_5 x 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 x S^5. We also comment on the case of spinning string in AdS_3 x S^1.

Figures (1)

• Figure 1: Change of integration contours. The branch-cuts are depicted by the yellow zig-zag lines.