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eXceptional Solutions and U-folds in quantum GRAvity

Periodic Reporting for period 1 - X-SUGRA (eXceptional Solutions and U-folds in quantum GRAvity)

Okres sprawozdawczy: 2020-01-13 do 2022-01-12

Our understanding of nature at a fundamental level is based on the frameworks of quantum field theory – describing electromagnetism and (sub)nuclear interactions – and of general relativity, describing the gravitational interaction. Such theoretical understanding of nature hides in plain sight in our day-to-day lives, shaping our perception of the universe and having determined countless technological advances in the last century.

Unifying these two pillars of fundamental physics in a single coherent framework has proven exceedingly difficult throughout the past and current centuries. String theory is believed to provide a consistent description of gravity at the quantum level and can therefore direct us toward the sought unification of the fundamental interactions. Importantly, the detailed study of string theory models of gravity is dependent on our ability to solve its equations to study its properties. This is often done by studying supergravity models, which approximate string theory under certain assumptions.

This project focused on developing of advanced techniques to solve the equations of motion of string and supergravity theories. A peculiar property of (super)string theory is also its intricate web of “U-dualities”, relating apparently different mathematical descriptions of its dynamics.

This action also focused on the mathematical and geometrical aspects of the formulation of supergravity theories in a manner that renders such U-dualities manifest.
The two broad objectives of this action were: the development of a formal framework called “exceptional field theory” meant to capture supergravity while making manifest certain infinite-dimensional dualities (referred to as “E9”), and greatly expanding our control over solutions of supergravity and string theory by classifying certain large families of geometries with desirable mathematical properties (referred to as generalised Leibniz parallelisable spaces), which play a central role in constructing new classes of solutions.

In this action the researcher has developed a systematic understanding of the so-called exceptional generalised geometries that underpin supersymmetric backgrounds in supergravity and produced large classes of new supergravity solutions relevant for holographic, black hole and flux compactification applications. The outcomes of such efforts are published in peer-reviewed, high impact journals and have been disseminated via seminars at relevant research institutions, conferences and seminars throughout and beyond Europe.
The researcher interacted with researchers in his host institution, as well as with several international collaborators within a large network of contacts and colleagues.

The main results of this action have been published in the following articles and preprints
1. Old and new vacua of 5D maximal supergravity – G. Dall'Agata, G. Inverso, D. Partipilo, published in JHEP 04 (2021) 039, DOI: 10.1007/JHEP04(2021)039 arXiv preprint: 2101.04149 [hep-th]

2. E9 exceptional field theory II. The complete dynamics – Guillaume Bossard, Franz Ciceri, Gianluca Inverso, Axel Kleinschmidt, Henning Samtleben, published in JHEP 05 (2021) 107, DOI: 10.1007/JHEP05(2021)107 arXiv preprint: 2103.12118 [hep-th]

3. New N=1 AdS4 solutions of type IIB supergravity – David Berman, Thomas Fischbacher, Gianluca Inverso, available as arXiv preprint: 2111.03002 [hep-th] (to appear in JHEP)

4. Vacua of ω-deformed SO(8) supergravity – David Berman, Thomas Fischbacher, Gianluca Inverso, Ben Scellier, arXiv preprint 2201.04173 (submitted)

Since the beginning of the project, Dr Inverso has been co-organising the weekly online seminars titled Exceptional Geometry Seminar Series, covering topics closely related to the action and keeping in contact with the relevant research community during the COVID-19 pandemic. The researcher attended several (online) conferences/workshops, and gave presentations and lectures on the topics covered by the project.
The research side of this action is grounded in string theory and quantum gravity, as such is should be regarded as intrinsically fundamental research, with no direct societal implications in the short term but clear ones in the longest term, given the centrality of quantum mechanics and gravity in our understanding and hence control of Nature's laws.

In this action, important novel families of string theory solutions were constructed by developing and exploiting a mathematical framework known as exceptional field theory, which captures the low energy degrees of freedom of string theory in a form which makes certain special properties of the theory, called U-dualities, manifest. Some emphasis was also put into the development and use of machine-learning techniques to numerically identify such solutions (and then reproduce them analytically) exploiting for instance the auto-differentiation capabilities of Google’s TensorFlow for the search of gauged supergravity solutions. Novel classes of so-called “S-fold” solutions were discovered, which are special stringy kinds of geometries where dualities play a central role, which proved especially interesting for the AdS/CFT correspondence (i.e. an identification between quantum gravity models and certain quantum field theories).

Sometimes we can truncate string theory to some simpler models called gauged supergravities, namely a theory of general relativity (in some number of spacetime dimensions) coupled to matter fields, fermions and generalisations of electromagnetic fields, all interacting with each other. A classification was performed of such models that can be associated to certain geometries, called “generalized Leibniz parallelizable spaces”, on which ten- and eleven-dimensional supergravities can be reduced.

The construction of so-called E9 exceptional field theory – the other main objective of the action – has been completed (this is described in the summary above). The theory has been developed in two different formulations – one involves an infinite amount of extra symmetries and variables, which was not previously anticipated. This allows for the definition of gauge-covariant quantities, a basic building block of any gauge theory since electromagnetism. It makes direct contact with a special mathematical property of maximal supergravity in two dimensions, called classical integrability. A second "non-covariant" formulation allows to make contact with certain algebraic structures known as “tensor hierarchy algebras” which have played an important role in developing the most mathematical aspects of supergravity in the last decade. As side-products of this work, a covariant formulation of the infinite chain of duality relations in 2d supergravity was put forward, clarifying several aspects of previous constructions; a starting point for the covariant formulation of two-dimensional gauged supergravity was determined, including a gauge-covariant twisted self-duality equation and the main (topological) part of the pseudo-action.