My research

I am interested in unifying General Relativity (gravity) with the other forces of nature and quantum mechanics. As such, I work on string and M-theory, our best candidates for such a theory of quantum gravity. Moreover, I am interested in using string and M-theory to better understand various aspects of quantum field theories, which describe the fundamental interactions of nature, such as electromagnetism and the strong nuclear force.

In particular, I study the interplay between geometry and physics in string and M-theory and seek to better understand string dualities. These dualities relate strings propagating in different backgrounds but which yield the same physics. The canonical example is given by a "T-duality" relating a string moving around a circle of radius R to a string winding a circle of radius l2/R, where l is the string length. As evidenced in this example, string dualities rely on the extended nature of strings and are thus a key property differentiating string theory from theories of point-particles. Therefore, studying string dualities is pivotal to gaining a better understanding of string theory.

A key tool in my research are the recently-formulated Exceptional Generalised Geometry (EGG), Double Field Theory (DFT) and Exceptional Field Theory (ExFT), which I have helped develop. These powerful formalisms are particularly useful for studying the geometry of string backgrounds including "fluxes", a higher-dimensional generalisation of electromagnetic fields that play an important role in various aspects of string theory. Moreover, EGG, DFT and ExFT make string dualities manifest to various degrees, making them ideal for studying this interesting feature of string theory.

Below you can find some colloquium-style talks on my research.

Supersymmetric flux vacua of string theory

Source: Wikimedia Commons.
Source: Wikimedia Commons.

One of my main interests are string backgrounds containing higher-dimensional generalisations of electromagnetic fields called "fluxes". These backgrounds play a key role in many aspects of string theory. For example, fluxes provide one of the best-understood mechanisms for generating realistic string models for our universe. More concretely, fluxes are an important ingredient in "moduli stabilisation", i.e. they give masses to scalar fields which would otherwise generate unobserved "fifth forces" in the universe.

Despite their importance, many properties of generic flux vacua, for example the spectrum of particles that they would generate in a string model of the universe, are poorly understood. My research focuses on improving our understanding of the physics of generic flux vacua, by studying their geometries properties.

Geometry of supersymmetric Anti-de Sitter vacua

Another interest of mine is the AdS/CFT correspondence, also called holography: this states that strings moving in Anti-de Sitter backgrounds (AdS), which can roughly be thought of as a box, are equivalent to quantum field theories living on the boundary of the AdS space. One feature that makes this correspondence especially exciting is that weakly-interacting strings in AdS are related to strongly-coupled quantum field theories on the boundary, and vice-versa. Since we are lacking the tools to study strongly-coupled theories directly, holography provides us with a unique opportunity to probe them.

Many interesting properties of the dual quantum field theories are encoded in the geometry of the AdS vacua of string theory. Despite many years of study, our understanding of generic properties of AdS backgrounds is still limited. I have developed new tools that allow us to study generic properties of AdS vacua of string theory in order to gain new insights into strongly-coupled quantum field theories. For example, I have been able classify which of the simplified models often employed to study the AdS vacua are valid approximations and which have no relation to string theory.

Non-geometric backgrounds in string theory

An example of a non-geometric background patched by a T-duality, which maps the radius, R, to l2/R, with l the string length.
An example of a non-geometric background patched by a T-duality, which maps the radius, R, to ls2/R, with ls the string length.

One of the intriguing features of string theory is that the extended nature of strings means that string propagating on seemingly very different spaces can lead to the same physics. Such spaces are related by "string dualities". As a result, string theory can also be defined on spaces where different regions are glued by such string dualities. While the resulting "non-geometric background" cannot be described using conventional geometry — it is ill-defined from a point-particle perspective —, it is a perfectly good space in string theory. Non-geometric backgrounds are more than a mathematical curiosity: they have many interesting phenomenological properties which make them appealing for constructing realistic string models of our universe and particle physics.

Another interesting property of non-geometric backgrounds is that strings moving in such backgrounds seem to lead to a theory of non-commutative, or even non-associative gravity. Such theories have many interesting properties, for example they contain a minimal spacetime area or volume. I was the first to develop the description of new non-geometric backgrounds in strongly-interacting string theory and conjecture their relation to non-associative gravity.

Colloquium-style talks on my research