Periodic Reporting for period 2 - StringyGeometry (Stringy geometry: quantum corrections and the fate of string compactifications from spacetime and the worldsheet)
Berichtszeitraum: 2022-09-01 bis 2023-08-31
This Marie Skłodowska Curie Action (MSCA) titled "Stringy geometry: quantum corrections and the fate of string compactifications from spacetime and the worldsheet" used and developed new geometric and mathematical structures to understand quantum corrections in string theory. The MSCA was a Global Fellowship, with the outgoing phase at the University of Chicago in the USA and the return phase at Sorbonne Université in France.
The project tackled a fundamental shortcoming in our understanding: whether supergravity solutions used as starting points in phenomenology or AdS/CFT can be extended to full string theory solutions. The Fellow developed new techniques for a range of important problems in theoretical and mathematical physics, including: the removal of extra long-range forces, understanding complicated "non-Kähler" geometries, formal aspects of string phenomenology and particle physics, and the existence of solutions in string theory that look like our own expanding universe.
These topics are important for society as string theory remains the leading contender for a "theory of everything". The project made significant progress in understanding whether string theory can describe our expanding universe by developing new mathematical tools to analyze quantum corrections in string theory solutions. The tools developed during this MSCA have found wide-ranging applications in physics and mathematics, continuing the European tradition of mathematical physics.
The overall objectives include developing new kinds of mathematics to describe the shapes and spaces that naturally appear in string theory; understanding when solutions to simpler theories can be lifted to full solutions of string theory; and incorporating quantum effects into the remarkable geometries that string theory gives us. Key achievements included: proving the existence of new supergravity solutions with corrections using geometric flows, developing generalised geometry techniques for massive IIA supergravity, establishing novel connections between stringy corrections and mathematical tools like Ricci flow, and creating new methods to analyze the spectrum of worldsheet conformal field theories. The project's results have important implications for understanding fundamental aspects of string theory and its ability to describe our universe, while also advancing mathematical techniques that have applications beyond theoretical physics.
The project tackled a fundamental shortcoming in our understanding: whether supergravity solutions used as starting points in phenomenology or AdS/CFT can be extended to full string theory solutions. The Fellow developed new techniques for a range of important problems in theoretical and mathematical physics, including: the removal of extra long-range forces, understanding complicated "non-Kähler" geometries, formal aspects of string phenomenology and particle physics, and the existence of solutions in string theory that look like our own expanding universe.
These topics are important for society as string theory remains the leading contender for a "theory of everything". The project made significant progress in understanding whether string theory can describe our expanding universe by developing new mathematical tools to analyze quantum corrections in string theory solutions. The tools developed during this MSCA have found wide-ranging applications in physics and mathematics, continuing the European tradition of mathematical physics.
The overall objectives include developing new kinds of mathematics to describe the shapes and spaces that naturally appear in string theory; understanding when solutions to simpler theories can be lifted to full solutions of string theory; and incorporating quantum effects into the remarkable geometries that string theory gives us. Key achievements included: proving the existence of new supergravity solutions with corrections using geometric flows, developing generalised geometry techniques for massive IIA supergravity, establishing novel connections between stringy corrections and mathematical tools like Ricci flow, and creating new methods to analyze the spectrum of worldsheet conformal field theories. The project's results have important implications for understanding fundamental aspects of string theory and its ability to describe our universe, while also advancing mathematical techniques that have applications beyond theoretical physics.
The project advanced understanding of string theory through both mathematical analysis and computational approaches. The research focussed on two complementary areas that together provided new insights into quantum effects in string theory.
The first major area of work involved analysing string theory through geometric structures. The Fellow studied worldsheet string models in spaces with special geometric properties, known as G2 and Spin(7) structures. This investigation revealed that certain physical quantities, specifically the partition functions that count string vibrations, have a remarkable "topological" property - they remain unchanged when the underlying geometry is deformed. The Fellow also developed and expanded the mathematical framework of "generalised geometry," which proved particularly well-suited for describing the complex spaces that appear in string theory. This led to a groundbreaking proof of the existence of certain deformed string theory solutions that incorporate quantum corrections.
The second focus area involved developing new mathematical tools to understand quantum corrections. The Fellow created new frameworks that revealed how quantum effects modify string theory solutions, including the development of a "generalised holomorphic structure" approach. This work established unexpected connections between string theory and other areas of mathematics, particularly geometric flows. The research also produced first-time calculations of fundamental quantities in certain string theory models, providing concrete results in previously intractable areas.
These research achievements have been extensively shared with the scientific community through seventeen peer-reviewed papers published in leading journals. The work has been presented at major international conferences, including prestigious venues such as Strings, StringMath, and StringPheno. The Fellow organised workshops and seminars at both host institutions, delivered graduate-level lectures on the new mathematical techniques, and engaged in public outreach activities to communicate these complex ideas to broader audiences.
The project has had significant impact through knowledge transfer and collaboration. The research, conducted first at the University of Chicago and then at Sorbonne Université, has created lasting partnerships between these institutions. Graduate students have been trained in these advanced mathematical techniques, ensuring the continuation of this research direction. The tools and frameworks developed during the project have found applications beyond theoretical physics, contributing to both physics and mathematics.
The comprehensive approach of the project - combining mathematical innovation, computational methods, and international collaboration - has created lasting impact in both theoretical physics and mathematics. The established partnerships between European and American institutions continue to facilitate scientific exchange, while the mathematical tools developed are being actively used by researchers around the world to advance our understanding of fundamental physics.
The first major area of work involved analysing string theory through geometric structures. The Fellow studied worldsheet string models in spaces with special geometric properties, known as G2 and Spin(7) structures. This investigation revealed that certain physical quantities, specifically the partition functions that count string vibrations, have a remarkable "topological" property - they remain unchanged when the underlying geometry is deformed. The Fellow also developed and expanded the mathematical framework of "generalised geometry," which proved particularly well-suited for describing the complex spaces that appear in string theory. This led to a groundbreaking proof of the existence of certain deformed string theory solutions that incorporate quantum corrections.
The second focus area involved developing new mathematical tools to understand quantum corrections. The Fellow created new frameworks that revealed how quantum effects modify string theory solutions, including the development of a "generalised holomorphic structure" approach. This work established unexpected connections between string theory and other areas of mathematics, particularly geometric flows. The research also produced first-time calculations of fundamental quantities in certain string theory models, providing concrete results in previously intractable areas.
These research achievements have been extensively shared with the scientific community through seventeen peer-reviewed papers published in leading journals. The work has been presented at major international conferences, including prestigious venues such as Strings, StringMath, and StringPheno. The Fellow organised workshops and seminars at both host institutions, delivered graduate-level lectures on the new mathematical techniques, and engaged in public outreach activities to communicate these complex ideas to broader audiences.
The project has had significant impact through knowledge transfer and collaboration. The research, conducted first at the University of Chicago and then at Sorbonne Université, has created lasting partnerships between these institutions. Graduate students have been trained in these advanced mathematical techniques, ensuring the continuation of this research direction. The tools and frameworks developed during the project have found applications beyond theoretical physics, contributing to both physics and mathematics.
The comprehensive approach of the project - combining mathematical innovation, computational methods, and international collaboration - has created lasting impact in both theoretical physics and mathematics. The established partnerships between European and American institutions continue to facilitate scientific exchange, while the mathematical tools developed are being actively used by researchers around the world to advance our understanding of fundamental physics.
The project has made several fundamental advances beyond the state of the art in theoretical physics and mathematics. Prior to this research, there was no unified framework for understanding deformations of supergravity solutions with flux, and calculations of basic physical quantities in these geometries were largely restricted to supersymmetric cases. The project overcame these limitations by developing a unified geometric framework for analysing flux deformations, creating new computational methods to calculate previously inaccessible physical quantities, establishing novel connections between string theory and mathematical tools like Ricci flow and anomaly flow, and pioneering the use of machine learning techniques to study geometric structures in string theory
These advances have had significant scientific impact, leading to seventeen peer-reviewed publications and establishing new research directions in both physics and mathematics. The tools developed during the project have broader applications beyond string theory, particularly the numerical and machine learning techniques that can be applied to other areas of physics and mathematics. The socio-economic impact of the research includes strengthening European leadership in theoretical and mathematical physics, training students in cutting-edge computational and mathematical techniques, and creating lasting research collaborations between European and American institutions.
The project's success in bridging physics and mathematics while developing practical computational tools shows how fundamental research can lead to broader technological and methodological advances. The establishment of new international collaborations and training of young researchers ensures these advances will continue to benefit the scientific community beyond the project's completion.
These advances have had significant scientific impact, leading to seventeen peer-reviewed publications and establishing new research directions in both physics and mathematics. The tools developed during the project have broader applications beyond string theory, particularly the numerical and machine learning techniques that can be applied to other areas of physics and mathematics. The socio-economic impact of the research includes strengthening European leadership in theoretical and mathematical physics, training students in cutting-edge computational and mathematical techniques, and creating lasting research collaborations between European and American institutions.
The project's success in bridging physics and mathematics while developing practical computational tools shows how fundamental research can lead to broader technological and methodological advances. The establishment of new international collaborations and training of young researchers ensures these advances will continue to benefit the scientific community beyond the project's completion.