# 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.

Below you can find some colloquium-style talks given by our group on our research.

### 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, such as 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.

### 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.

# Research highlights

## Stability of non-supersymmetric solutions of string theory

One of string theory's most prominent predictions is that our universe has extra spatial dimensions that we do not observe directly. Instead, these extra dimensions are curled up into a small compact space. In order to yield any meaningful physics, these "compactifications" must be stable, much like a ball in a valley of a hill is stable since if it is pushed slightly to the side, it will roll-back to its initial position. By contrast, if the ball is at the top of a hill, a small push to the side will cause the ball to roll down the hill and far away from its original unstable position. Similarly, in an unstable compactification, a small deformation of the shape of the extra dimensions of string theory will cause the extra dimensions to rapidly expand to large size or even to collapse and form a rip in space. Typically, string compactifications are unstable, unless they possess supersymmetry, an elegant symmetry arising in string theory but which is not observed in the real world.

Adolfo Guarino (University of Oviedo), Emanuel Malek (Humboldt-Universität zu Berlin) and Henning Samtleben (École Normale Supérieure de Lyon) proved the stability of 7 non-supersymmetric solutions of string theory, consisting of a 4-dimensional negatively curved spacetime, called anti-de Sitter space, and 6 curled up dimensions making up a spherical shape. These form the first examples of stable string theory solutions containing anti-de Sitter space. While these solutions cannot be used to directly model our universe, they could provide the first models for 3-dimensional non-supersymmetric condensed matter systems via the "holographic principle". Moreover, this class of solutions are a stepping stone towards better understanding non-supersymmetric solutions of string theory in general.

Stable Nonsupersymmetric Anti‐de Sitter Vacua of Massive IIA Supergravity, Adolfo Guarino, Emanuel Malek, Henning Samtleben, Phys. Rev. Lett. 126 (2021), 061601

Stable Nonsupersymmetric Anti‐de Sitter Vacua of Massive IIA Supergravity,

Adolfo Guarino, Emanuel Malek, Henning Samtleben,

Phys. Rev. Lett. 126 (2021), 061601

## Listening to the shape of string theory universes

One of string theory's most prominent predictions is that our universe has extra spatial dimensions that we do not observe directly. Nonetheless, just as the shape of an instrument, such as a trumpet, determines the sound of musical notes played, so too the shape of string theory's extra dimensions determines the physics, in particular the masses of particles, that would be observed in our 4-dimensional universe. Computing the masses of these particles has been a longstanding technical challenge, especially for the complicated shapes of extra dimensions that underlie most efforts to connect string theory to real-world physics. Emanuel Malek (Max Planck Institute for Gravitational Physics, Potsdam) and Henning Samtleben (École Normale Supérieure de Lyon) have developed a powerful new method, that for the first time allows us to compute the masses arising from the shapes of extra dimensions in important string theory models. The researchers exploited the fact that many interesting shapes for the extra dimensions can be squashed, stretched and bent into much simpler and highly symmetric ones, such as round spheres, for which the masses can be computed straightforwardly. Their new method allows us to track for the first time how this squashing, stretching and bending of the extra dimensions affects the masses of particles, thus allowing us to determine the masses due to complicated shapes. This will lead to a better understanding of what shape the extra dimensions of string theory must have to realistically model our universe, as well as progress in learning about fundamental interactions via the "holographic principle".

Kaluza-Klein Spectroscopy for Supergravity, Emanuel Malek, Henning Samtleben, Phys. Rev. Lett. 124 (2020), 101601

Kaluza-Klein Spectroscopy for Supergravity,

Emanuel Malek, Henning Samtleben,

Phys. Rev. Lett. 124 (2020), 101601

# Colloquium-style talks by our group

- Exceptional Field Theory and applications to the AdS/CFT correspondence, QFT Colloquium (general QFT audience), Humboldt-Universität zu Berlin
- Listening to the shape of string theory's extra dimensions, IRIS Colloquium (general physics audience), Humboldt-Universität zu Berlin