## Final Report Summary - STRINGLEEFT (String compactifications, their low energy effective field theories and applications to physics)

The project "String Compactifications, their low energy effective field theories and applications to physics" (StringLEEFT) explored the fundamental nature and laws of our Universe, using the framework of String Theory. String theory is our leading candidate for a unified, quantum theory of gravity. StringLEEFT worked at the interface between string theory, particle physics and cosmology, to pursue realistic models of the Universe from string theory.

The project had two connected main directions. One was to further our theoretical understanding and description of compactifications of ten-dimensional string theory down to our four-dimensional Universe, and develop the necessary mathematical structures. The other was to use the ideas and ingredients of string compactifications to address the problems in our standard models of particle physics and cosmology, providing novel solutions to cosmological problems, and -- strikingly -- experimental predictions that can be tested in current and upcoming experiments.

The work performed during StringLEEFT met and exceeded the initial objectives. It resulted in three papers published in highly ranked journals and one preprint soon to be submitted for publication. One was awarded Honourable Mention at the 2016 Gravity Research Foundation Awards for Essays on Gravitation. The researcher has been invited to present her results in several international meetings, and the papers are already well-cited by subsequent work. She secured a permanent Lectureship position at the University of Liverpool at the end of the fellowship.

The results can be summarised as follows.

1. Quantum gravity and cosmology. String theory -- our leading candidate for a theory of quantum gravity -- can be considered as a generalisation of field theory -- our current framework for particle physics and cosmology. It is expected that not all field theory models of the Universe can be consistently embedded in quantum gravity -- those which cannot are not good models of Nature. StringLEEFT studied such consistency constraints on promising models of cosmology, showed that some classes of such models are inconsistent, and identified other, new string theory models which do satisfy the necessary properties. This work both gives deep insights into the properties of string theory itself and connects string theory to cosmological models.

2. New string theory models of the Early Universe. The Universe is believed to have undergone an extremely fast accelerated expansion in its first moments of existence. The reason for the "inflationary epoch" is unknown, but such an expansion is extremely sensitive to quantum gravity effects and is difficult to embed in string theory. StringLEEFT identified a new model of inflation, which actually exploits the quantum gravity effects to assist inflation. The model has distinctive signatures which can be tested for in upcoming cosmological observations.

3. A bound on primordial gravitational waves. Primordial gravitational waves are produced during inflation, but their amplitude is not fixed by inflation. StringLEEFT identified a strong upper bound on the amplitude of primordial gravitational waves from string theory, which will be probed by the next generation of primordial gravitational wave detectors. If primordial gravitational waves are detected in the near future, we can expect that string theory effects are also observable in the sky.

4. Mathematical structures for the description of string compactifications. A class of string compactifications, which have received a huge amount of attention in the last decade was studied. In particular, StringLEEFT developed their mathematical description at "low" energies -- relevant to particle physics and cosmology -- and showed their stability against certain -- potential dangerous -- quantum gravity effects.

In conclusion, StringLEEFT developed mathematical tools and our understanding of how string theory -- as a consistent theory of quantum gravity -- restricts the classes of possible models of particle physics and cosmology. New models for the Early Universe were developed, with distinctive signatures, and general implications for string theory on cosmological observations were worked out.

The impact of the results achieved is already being seen in the field, with around 50 citations to date and several invitations to present the work internationally. The results also have an impact beyond the field, connecting directly to experiments and observations, and driving future experimental programmes, which in turn stimulate novel technological developments. The results contribute to the long-term scientific goal of understanding how the origins of our Universe, its composition and its evolution. These are questions which every man and woman has pondered upon in some way.

The project had two connected main directions. One was to further our theoretical understanding and description of compactifications of ten-dimensional string theory down to our four-dimensional Universe, and develop the necessary mathematical structures. The other was to use the ideas and ingredients of string compactifications to address the problems in our standard models of particle physics and cosmology, providing novel solutions to cosmological problems, and -- strikingly -- experimental predictions that can be tested in current and upcoming experiments.

The work performed during StringLEEFT met and exceeded the initial objectives. It resulted in three papers published in highly ranked journals and one preprint soon to be submitted for publication. One was awarded Honourable Mention at the 2016 Gravity Research Foundation Awards for Essays on Gravitation. The researcher has been invited to present her results in several international meetings, and the papers are already well-cited by subsequent work. She secured a permanent Lectureship position at the University of Liverpool at the end of the fellowship.

The results can be summarised as follows.

1. Quantum gravity and cosmology. String theory -- our leading candidate for a theory of quantum gravity -- can be considered as a generalisation of field theory -- our current framework for particle physics and cosmology. It is expected that not all field theory models of the Universe can be consistently embedded in quantum gravity -- those which cannot are not good models of Nature. StringLEEFT studied such consistency constraints on promising models of cosmology, showed that some classes of such models are inconsistent, and identified other, new string theory models which do satisfy the necessary properties. This work both gives deep insights into the properties of string theory itself and connects string theory to cosmological models.

2. New string theory models of the Early Universe. The Universe is believed to have undergone an extremely fast accelerated expansion in its first moments of existence. The reason for the "inflationary epoch" is unknown, but such an expansion is extremely sensitive to quantum gravity effects and is difficult to embed in string theory. StringLEEFT identified a new model of inflation, which actually exploits the quantum gravity effects to assist inflation. The model has distinctive signatures which can be tested for in upcoming cosmological observations.

3. A bound on primordial gravitational waves. Primordial gravitational waves are produced during inflation, but their amplitude is not fixed by inflation. StringLEEFT identified a strong upper bound on the amplitude of primordial gravitational waves from string theory, which will be probed by the next generation of primordial gravitational wave detectors. If primordial gravitational waves are detected in the near future, we can expect that string theory effects are also observable in the sky.

4. Mathematical structures for the description of string compactifications. A class of string compactifications, which have received a huge amount of attention in the last decade was studied. In particular, StringLEEFT developed their mathematical description at "low" energies -- relevant to particle physics and cosmology -- and showed their stability against certain -- potential dangerous -- quantum gravity effects.

In conclusion, StringLEEFT developed mathematical tools and our understanding of how string theory -- as a consistent theory of quantum gravity -- restricts the classes of possible models of particle physics and cosmology. New models for the Early Universe were developed, with distinctive signatures, and general implications for string theory on cosmological observations were worked out.

The impact of the results achieved is already being seen in the field, with around 50 citations to date and several invitations to present the work internationally. The results also have an impact beyond the field, connecting directly to experiments and observations, and driving future experimental programmes, which in turn stimulate novel technological developments. The results contribute to the long-term scientific goal of understanding how the origins of our Universe, its composition and its evolution. These are questions which every man and woman has pondered upon in some way.