Opening the way to new developments in integrability for the gauge/gravity duality

By Rebecca Gillan on April 5, 2017

Recently Journal of Physics A published a special issue titled “an integrability primer for gauge-gravity duality” which grew out of a GATIS Young Researchers Integrability School held at Durham University in July 2015. The issue was made up of six topical reviews based on the lectures delivered at the summer school, aiming to provide a pedagogical introduction to integrability, particularly aspects relevant to the AdS/CFT correspondence. A group of researchers involved in organising and lecturing at the school; Alessandra Cagnazzo, Rouven Frassek, Alessandro Sfondrini, Istvan Szécsényi and Stijn van Tongeren guest edited the issue for the journal and we hope it will provide an interesting and useful introduction for students and early career researchers studying this exciting area. We spoke to one of the Guest Editors, Alessandro Sfondrini about his take on integrability and the special issue.

Cover image, an integrability primer for the gauge-gravity correspondence

What is integrability?

Most of the systems that we want to understand in physics cannot be studied exactly; in general, we have to resort to perturbation theory, clever approximation schemes, computer simulations, or all of the above. There are some very special systems that possess enough symmetries to allow us to study them exactly, and we call these “integrable”. While they are few, and quite special, they have a lot to teach us.

This seems very general. How is this related to today’s research?

Indeed this idea is old, and it dates back to concepts developed by Liouville in classical mechanics. In the past decades, integrable systems have been found in many fields of theoretical physics, from statistical mechanics to quantum field theory. A huge advance achieved in recent years is the discovery of integrable structures in the gauge/string duality, which is a very active topic of research.

Are you reviewing all this recent progress in the special issue?

This would be nearly impossible: there have been so many important results stemming from the application of integrability to the gauge/string duality. Initially, these appeared in the context of the correspondence between super-strings on the AdS₅ x S⁵ background and N=4 super-symmetric Yang-Mills theory, and later in its deformations and in lower dimensional examples; furthermore, the mathematical structures and the techniques emerging from this investigation have been studied in their own right, revealing beautiful insights. Unfortunately we would not be able to do justice to all this material in a single volume. Moreover, quite a number of good reviews already exist, covering different corners of this complex picture.

What is then the purpose of this special issue?

Precisely because of the breadth of the field, it is difficult for a newcomer to have a comprehensive view of it. Our aim is to present a primer on topics and techniques that are at the heart of this field, and to highlight the many connections between them. This is at the expense of delving into the details of each given model. While this issue contains plenty of examples, they are not necessarily the most representative of the gauge/gravity duality literature. Instead, they are chosen to be as simple as possible, avoiding unnecessary technicalities. We believe that after this introduction the readers will be able to easily grasp more complex details from the gauge/gravity duality literature, which we reference extensively.

How do you think that this special issue will contribute to the development of the field?

We are at a stage where our field has reached some maturity, and accumulated many important results. This may result in an obstacle for students and scientists from other fields who would like to enter the field. We believe that this issue may help overcome this obstacle, opening the way to new developments in integrability for the gauge/gravity duality and to the discovery of new links to other fields.

The special issue is available here. We have enjoyed working with the Guest Editors and community on the special issue and hope it helps to further research in this field

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