One-Loop Corrections to Type IIA String Theory in AdS4 x CP3

TL;DR

This paper compares methods for calculating one-loop energy corrections in type IIA string theory on AdS4 x CP3, proposing a new summation prescription that yields consistent finite results across different approaches.

Contribution

It introduces a novel summation prescription for one-loop corrections that resolves divergences and provides a unified prediction in type IIA string theory in AdS4 x CP3.

Findings

The world-sheet spectrum yields convergent one-loop corrections with standard prescriptions.

The algebraic curve spectrum initially diverges but becomes finite with the new summation method.

All three approaches agree in the large-j limit, leading to a unique correction prediction.

Abstract

We study various methods for computing the one-loop correction to the energy of classical solutions to type IIA string theory in AdS4 x CP3. This involves computing the spectrum of fluctuations and then adding up the fluctuation frequencies. We focus on two classical solutions with support in CP3: a rotating point-particle and a circular spinning string with two angular momenta equal to J. For each of these solutions, we compute the spectrum of fluctuations using two techniques, known as the algebraic curve approach and the world-sheet approach. If we use the same prescription for adding fluctuation frequencies that was used for type IIB string theory in AdS5 x S5, then we find that the world-sheet spectrum gives convergent one-loop corrections but the algebraic curve spectrum gives divergent ones. On the other hand, we find a new summation prescription which gives finite results when applied to both the algebraic curve and world-sheet spectra. Naively, this gives three predictions for the one-loop correction to the spinning string energy (one from the algebraic curve and two from the world-sheet), however we find that in the large-j limit (where j=J/sqrt(2pi^2 lambda)), the j^(-2n) terms in all three cases agree. We therefore obtain a unique prediction for the one-loop correction to the spinning string energy.