# Research

Our research group investigates the geometry of string theory solutions, in order to gain insight into string theory's ability to provide realistic models of nature ("string phenomenology") and to better understand quantum field theories at strong coupling via holography.

One interesting feature of string theory is that it is only consistent 10 spacetime dimensions. Therefore, to learn about physics in lower dimensions, we consider string compactifications, 10-dimensional spacetimes consisting of a D-dimensional "macroscopic" part and a (10-D)-dimensional compact part. Most of the interesting compactifications in both string phenomenology and holography have non-vanishing fluxes, higher-dimensional analogues of electromagnetic fields that arise in string theory. We are still lacking a systematic understanding of these "flux compactifications", which is a major obstacle in relating string theory to the real world or quantum field theories via holography. Our research group seeks to better understand these flux compactifications and their role in string phenomenology and holography. In particular, we want to understand

- if and to what extent flux compactifications allow string theory to give realistic models of nature and whether we can obtain testable predictions,
- general properties, such as the spectra and marginal deformations, of strongly-coupled quantum field theories, especially those with minimal amounts of supersymmetry.

This research sits at the intersection of physics and mathematics and combines various topics from string theory, supergravity and mathematical physics. A key tool in our research are the recently-formulated Exceptional Generalised Geometry (EGG), Double Field Theory (DFT) and Exceptional Field Theory (ExFT). These powerful formalisms unify the gravitational and flux degrees of freedom of string theory, thus providing a natural language for studying the geometry flux compactifications. Moreover, EGG, DFT and ExFT make "string dualities" manifest to various degrees, making them ideal for studying this interesting feature of string theory.

### Flux vacua in string phenomenology

Our group studies string compactifications 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 of 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.

In string theory, these phenomenological properties are encoded in the geometry of the flux compactification. For example, the moduli space of the flux compactification (i.e. deformations of the compactification that still solve the equations of motion) determines the number of massless scalar fields that would be observed in 4 dimensions, and the dimension of the moduli space is encoded in topological data of the compactification. Similarly, other important phenomenological properties, such as the gauge groups that would arise, are encoded in the geometry of the compactification.

There are well-developed methods for extracting this data and analysing the phenomenology of the compactification when no fluxes are present (e.g. Calabi-Yau manifolds). On the other hand, little is known about flux compactifications, especially with large backreaction on the geometry. Our research group aims to remedy this situation by developing tools that allow us to analyse the phenomenology of generic flux compactifications.

### Flux vacua in holography

Our group also studies the AdS/CFT correspondence, or "holography". This states that strings moving in D-dimensional Anti-de Sitter backgrounds (AdS), which can roughly be thought of as a box, times a (10-D)-dimensional compactification, are equivalent to quantum field theories in (D-1) dimensions, 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 compactification of string theory. In all known cases, these compactifications contain non-vanishing fluxes. Despite many years of study, our understanding of generic properties of these compactifications is still very limited, especially when we consider little or no supersymmetry. We are developing 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.

An example of our research is covered here.

### Non-geometric backgrounds in string theory

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. Non-geometric backgrounds might also provide new examples of holographic dualities.