# Tristan McLoughlin

#### Assistant Professor in Mathematics

at Trinity College Dublin

My current research is in the area of Quantum Field theory, Quantum Gravity and String theory. I am particularly interested in using symmetries to find exact results in gauge and gravity theories.

My research is currently funded by two grants:

- Marie Curie, Career Integration Grant EMSGT, March 2013-February 2017
- Science Foundation Ireland, Career Development Award EMSCS, December 2016 - November 2020

In lay terms, the goal of my research to probe the fundamental structure of nature at its smallest and largest scales. Much of the world around us – the rigidity of chair beneath us, the light we see or indeed why the stars give off that very light – is currently understood in terms of quantum field theories. These theories, which describe electricity and magnetism and the nuclear forces, the so-called weak and the strong forces, combine the rules of quantum mechanics with those of special relativity. When these forces are weak there is excellent agreement between theoretical predictions and experimental observation. However in many physically interesting scenarios the forces are very strong, for example the forces which hold together the proton and neutron at everyday energies or between electrons in superconductors, and in these cases our mathematical tools to analyse the quantum field theories are limited and many important questions remain unanswered.

The goal of my research is to develop theoretical tools to address these questions by making use of the remarkable duality between string theory and quantum field theories. Two theories are said to be dual when every object in one theory has an alternative, but equivalent, description in the other theory. The most studied example has, on one side of the duality, strings moving in ten dimensions, a time direction plus nine spatial dimensions. Moreover this space is curved in a specific fashion and has an edge or boundary, while the strings are either closed loops or have their end points on the boundary. This string theory is conjectured to be dual to a specific four dimensional quantum field theory which, although not the same as the theory that describes the strong force, shares many similar features. Most excitingly the duality relates the weakly interacting regime of one theory to the strongly coupled regime of the dual theory. it means that we can understand strongly interacting gauge theories by considering weakly interacting string theories. Furthermore, and just as interesting, it implies we can describe certain theories of quantum gravity by gauge theories.

One remarkable discovery that has led to a great deal of progress is that certain examples of this duality seem to be integrable. That is to say there is an infinite number of conserved quantities and while these conserved quantities do not have a simple description similar to, say, conservation of energy, just like conservation of energy they make calculational problems much more tractable. In fact the existence of this integrability may make it possible to actually prove the duality in certain limits. Naturally the ultimate goal is to use the insight and tools from gauge/gravity duality to study realistic problems and there has already been some progress in this direction. As an example, one can use the gauge/gravity duality to describe, at least qualitatively, the strong interactions at high temperatures and densities as seen in accelerators. There of course remains a huge amount to be done in exactly solving even the simplest examples of the duality and even more in understanding realistic systems both of which will no doubt require profound new insights into both quantum field theory and string theory.