Quantum Strings and the AdS4/CFT3 Interpolating Function

TL;DR

Abbott, Aniceto, and Bombardelli investigate the AdS$_{4}$/CFT$_{3}$ ABJM interpolating function $h(\lambda)$ by computing one-loop corrections to giant magnons with the algebraic curve. They demonstrate that three natural regularization prescriptions (old, new, and alternative new) yield the same qualitative pattern in the CP$^{3}$ sector, but the constant term $c$ in $h(\lambda)=\sqrt{\lambda/2}+c+\cdots$ depends on the prescription, taking values $c=-\frac{\log 2}{2\pi}$ for the old sum and $c=0$ for the new sums. The analysis uses the off-shell algebraic-curve method to derive fluctuation frequencies, compares leading and subleading energy corrections to Lüscher F-terms, and finds a mismatch for the alternative new sum, highlighting a scheme-dependence in extracting $h(\lambda)$. Finite-$J$ effects and dyonic magnons are explored to test the consistency with all-loop S-matrix expectations, underscoring the need for a unified regularization in matching string results to gauge-theory data. Overall, the work clarifies how regularization choices affect the CP$^{3}$ giant-magnon spectrum and the extraction of the interpolating function, informing future checks with Bethe ansatz/TBA frameworks.

Abstract

The existence of a nontrivial interpolating function h(λ) is one of the novel features of the new AdS4/CFT3 correspondence involving ABJM theory. At strong coupling, most of the investigation of semiclassical effects so far has been for strings in the AdS4 sector. Several cutoff prescriptions have been proposed, leading to different predictions for the constant term in the expansion h(λ)=\sqrt{λ/2} + c + ... . We calculate quantum corrections for giant magnons, using the algebraic curve, and show by comparing to the dispersion relation that the same prescriptions lead to the same values of c in this CP3 sector. We then turn to finite-J effects, where a comparison with the Luescher F-term correction shows a mismatch for one of the three sum prescriptions. We also compute some dyonic and higher F-terms for future comparisons.

Figures (1)

• Figure 1: Integration contours in the complex $n$ and $x$ planes, showing finite cutoffs $\left|n\right|\leq N$ and $\left|x\right|>1+\epsilon$. (We do not attempt show the distinction between heavy and light modes for the old and new old sums.) The first contour in the $x$ plane is unwrapped to give the second, containing $\mathbb{U}(\epsilon)$, after reversing its orientation.