On string integrability. A journey through the two-dimensional hidden symmetries in the AdS/CFT dualities

TL;DR

This paper reviews the role of integrability in two-dimensional sigma-models within the AdS/CFT dualities, highlighting the discovery of conserved charges that advance understanding of string and gauge theory correspondences.

Contribution

It provides a comprehensive review of classical and quantum integrability in AdS/CFT, focusing on the AdS_5/CFT_4 and AdS_4/CFT_3 dualities and their associated superstring models.

Findings

Demonstrates classical and quantum integrability of superstrings on AdS backgrounds.

Highlights the significance of conserved charges in confirming dualities.

Discusses the differences between pure spinor and Green-Schwarz formulations.

Abstract

One of the main topics in the modern String Theory are the AdS/CFT dualities. Proving such conjectures is extremely difficult since the gauge and string theory perturbative regimes do not overlap. In this perspective, the discovery of infinitely many conserved charges, i.e. the integrability, in the planar AdS/CFT has allowed us to reach immense progresses in understanding and confirming the duality. We review the fundamental concepts and properties of integrability in two-dimensional sigma-models and in the AdS/CFT context. The first part is focused on the AdS_5/CFT_4 duality, especially the classical and quantum integrability of the type IIB superstring on AdS_5 x S^5 are discussed in both pure spinor and Green-Schwarz formulations. The second part is dedicated to the AdS_4/CFT_3 duality with particular attention to the type IIA superstring on AdS_4 x CP^3 and its integrability. This review is based on a shortened and revised version of the author's PhD thesis, discussed at Uppsala University in September 2009.