Bandres, Miguel A. and Lipstein, Arthur E.
(2010)
* One-loop corrections to type IIA string theory in AdS_4 × CP^3.*
Journal of High Energy Physics, 2010
(4).
pp. 1-45.
ISSN 1126-6708.
http://resolver.caltech.edu/CaltechAUTHORS:20100601-080301662

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## Abstract

We study various methods for computing the one-loop correction to the energy of classical solutions to type IIA string theory in AdS_4 × CP^3. This involves computing the spectrum of fluctuations and then adding up the fluctuation frequencies. We focus on two classical solutions with support in CP^3: 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 AdS_5 × S^5, 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 /√2π^2⋋),J^(-2n) terms in all three cases agree. We therefore obtain a unique prediction for the one-loop correction to the spinning string energy.

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Additional Information: | © SISSA 2010. Received: 23 January 2010. Accepted: 20 March 2010. Published online: 14 April 2010. This work was supported in part by the U.S. Department of Energy under Grant No. DE-FG02-92ER40701. We are grateful to Shinji Hirano, Tristan McLoughlin, Victor Mikhaylov, Tatsuma Nishioka, Sakura Schafer-Nameki, and John H. Schwarz for helpful discussions. In particular, we would like to thank VM for sharing his unpublished notes on the spinning string algebraic curve and its semi-classical quantization, SSN for helping us with various calculations in this paper and for providing many useful explanations, and JHS for his guidance and many useful comments. | ||||||||||||

Group: | Caltech Theory | ||||||||||||

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Subject Keywords: | AdS-CFT Correspondence; Chern-Simons Theories; Integrable Field Theories. | ||||||||||||

Record Number: | CaltechAUTHORS:20100601-080301662 | ||||||||||||

Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20100601-080301662 | ||||||||||||

Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||

ID Code: | 18500 | ||||||||||||

Collection: | CaltechAUTHORS | ||||||||||||

Deposited By: | Ruth Sustaita | ||||||||||||

Deposited On: | 02 Jun 2010 16:37 | ||||||||||||

Last Modified: | 06 Mar 2013 04:38 |

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