Extending the reach of integrability in AdS/CFT as far as possible

By Phil Brown on June 16, 2017

In their recently published Emerging Talents paper in Journal of Physics A: Mathematical and Theoretical Stijn van Tongeren and Ben Hoare study Jordanian deformations of AdS₅ and supergravity. Stijn has taken the time to answer some questions from JPhys+ to tell us more about their and his research.

Dr. Ben Hoare

Dr. Stijn van Tongeren

Who are you?

After finishing his bachelor’s degree at Utrecht University College – including a semester abroad at the University of California, Irvine – Stijn van Tongeren pursued his master’s and PhD research at Utrecht University, under the supervision of Professor Gleb Arutyunov. Since the autumn of 2013, he is a postdoctoral researcher at Humboldt University, Berlin. Stijn’s PhD research focused on thermodynamic Bethe ansatz techniques applied to the spectral problem in the canonical AdS/CFT correspondence and its established deformations. During his postdoc, his research has shifted towards the development of new integrable deformations of strings, in particular their string theory and AdS/CFT interpretation.

After completing a degree in mathematics at Cambridge University, Ben studied for his doctorate under the supervision of Professor Arkady Tseytlin at Imperial College London. Subsequently he has held postdoctoral positions at Humboldt University Berlin and ETH Zurich. Ben’s research interests lie in the broad area of integrability in gauge/string dualities. During his PhD he worked on the Pohlmeyer reduction and q-deformation of the AdS₅ x S⁵ superstring. Over the following years this subject has grown, and together with related topics has developed into the active field exploring integrable deformations of superstring theories. Ben’s current research is focused in this area with a particular emphasis on the two-dimensional worldsheet models.

What prompted you to pursue this field of research?

Quantum field theories are extremely important yet notoriously complicated tools in theoretical physics, and in particular understanding their nonperturbative behavior is a central problem in many aspects of modern research. Our field studies what some might say is the harmonic oscillator of interacting quantum field theories — planar, maximally supersymmetric Yang-Mills theory in four dimensions. We are able to get remarkable insights here, by describing this theory in terms of string theory on anti-de Sitter space, through the AdS/CFT correspondence. This string theory turns out to really be quite similar to the harmonic oscillator in the sense that it is an integrable model. Integrability here means that a model has sufficient symmetries that it becomes exactly solvable. In this sense our string and the related quantum field theory are quite similar to, for instance, the hydrogen atom in quantum mechanics or the one dimensional Heisenberg spin chain in condensed matter physics. In our setting this solvability allows us to compute two point functions in planar symmetric Yang-Mills theory at arbitrary coupling. Higher point functions appear to be tractable as well, meaning that a full nonperturbative description of an interacting four dimensional quantum field theory, albeit planar, is now within reach.

What is this latest paper all about?

Since integrability has proven so incredibly powerful in the context of the AdS/CFT correspondence, we would like to extend its reach as far as possible. To do so, there are two possible routes; we can look for integrability in other, known theories, or we can try to construct manifestly integrable theories and consider their interpretation afterwards. This second route saw a lot of progress in recent years, giving rise to a large number of new integrable deformations of our anti-de Sitter string theory. However, their physical interpretation was not clear: are they related to some four dimensional field theories? and before we can even ask that, are they string theories themselves? In our paper we answered this second question for a general class of so-called jordanian deformations, showing that they ultimately do not directly define string theories. We got this result by using an interesting relation between inhomogeneous deformations — which were known not to give string theories — and various homogeneous deformations, including jordanian ones, via singular noncompact symmetry transformations. For abelian deformations this relation demonstrates how the obstacles to a string theory interpretation disappear, nicely tying together several existing observations in the literature.

What do you plan to do next?

When these integrable deformed models describe strings, the next big question associated to them is that of their field theory interpretation, in the sense of the AdS/CFT correspondence. In some of my papers, I (Stijn) already conjectured that these string theories are in general related to various noncommutative field theories. So far there is no general underlying construction for this conjecture, and many subtle points remain to be worked out, which is what we are currently actively investigating.

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Stijn van Tongeren image owned by Stijn van Tongeren used with permission, Ben Hoare image owned by Ben Hoare used with permission. Copyright IOP publishing.