AdS4/CFT3 at One Loop

TL;DR

This work analyzes the AdS4/CFT3 (ABJM) correspondence by studying semi-classical Type IIA strings rotating in $AdS_4\times\mathbb{CP}^3$ and computing the one-loop sigma-model correction to a spinning-string solution. The author derives the scaling form $E-S=f(\lambda)\ln S$ with $f(\lambda)=\sqrt{2\lambda}-\frac{5\ln 2}{2\pi}+\mathcal{O}(1/\sqrt{\lambda})$, where the coefficient originates from bosonic and fermionic fluctuations; the logarithmic structure matches gauge theory expectations, but the numerical coefficient disagrees with the ABJM integrability result $f_{CS}(\lambda)=\sqrt{2\lambda}-\frac{3\ln 2}{2\pi}+\mathcal{O}(1/\sqrt{\lambda})$. The paper analyzes the fluctuation spectrum, finding two massless and six massive fermions, and shows that the mismatch persists even after symmetry and finiteness constraints are considered, suggesting deeper tensions between Bethe-ansatz predictions and worldsheet quantization. Overall, the results reinforce the expected $\ln S$ scaling but highlight a nontrivial discrepancy in the strong-coupling coefficient, inviting further investigation into the ABJM Bethe ansatz versus string-theory computations.

Abstract

I consider semi-classical type IIA strings rotating in the AdS4 part of AdS4 X CP3. The one loop sigma model corrections to this classical solution are used to compute the energy shift, and the result is found to be E-S=f(lambda) ln S with f(lambda)= sqrt{2 lambda} - 5 ln 2 /2 pi + O (1/sqrt{lambda}). Even though the functional forms match, the actual numerical value of this one loop string result differs from the result obtained on the integrable N=6 Chern-Simons (ABJM) theory side.