Lloyd, T. and Stefanski, B. (2014). AdS3/CFT2, finitegap equations and massless modes. Journal of High Energy Physics, 2014(4), doi: 10.1007/JHEP04(2014)179
Abstract
It is known that string theory on AdS 3 × M 7 backgrounds, where M 7 = S 3 × S 3 × S 1 or S 3 × T 4, is classically integrable. This integrability has been previously used to write down a set of integral equations, known as the finitegap equations. These equations can be solved for the closed string spectrum of the theory. However, it has been known for some time that the finitegap equations on these AdS 3 × M 7 backgrounds do not capture the dynamics of the massless modes of the closed string theory. In this paper we reexamine the derivation of the AdS 3 × M 7 finitegap system. We find that the conditions that had previously been imposed on these integral equations in order to implement the Virasoro constraints are too strict, and are in fact not required. We identify the correct implementation of the Virasoro constraints on finitegap equations and show that this new, less restrictive condition captures the complete closed string spectrum on AdS 3 × M 7.
Publication Type:  Article 

Publisher Keywords:  AdSCFT Correspondence, Integrable Equations in Physics, Penrose limit and ppwave background 
Subjects:  Q Science > QA Mathematics Q Science > QC Physics 
Departments:  School of Mathematics, Computer Science & Engineering > Mathematics 
URI:  http://openaccess.city.ac.uk/id/eprint/4786 

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