Final Report Summary - SUSY (SUPERSYMMETRY: a window to non-perturbative physics) The project has made major advances on the three main topics described in the original project proposal. The functional integrals encountered in entropy calculations for supersymmetric black holes were evaluated by means of supersymmetric localization. This approach has been used in field theory with great success, but it was applied here to a problem in quantum gravity using the formalism of off-shell supergravity. This formalism was substantially extended to accommodate the possible presence of higher-derivative supersymmetric invariants and it was proven that only a restricted class of higher-derivative couplings can possibly contribute to supersymmetric black hole entropy. This set-up also enabled a detailed analysis of a conjectured relation between black hole entropy and the partition function of the topological string, where new insights were obtained that were actually related to classical concepts in physics. The resulting expressions obtained by localization contain the full modular covariant microscopic partition function. However, they include the unwanted contributions from multi-black-hole states in the gravitational spectrum. Upon subtracting these states it turns out that one will instead be dealing with so-called mock modular forms. This phenomenon has been confirmed by explicit computations. The mirror Thermodynamic Bethe Ansatz has been further developed as a tool for solving the relevant string theory spectra and, via the gauge-string duality, for obtaining the exact spectra of the corresponding gauge theories. Within this framework the mirror model of the AdS5 × S5 superstring was used to engineer an infinite tower of coupled integral equations encoding the spectrum of the superstring at finite coupling. The corresponding equations have been solved both analytically and numerically for a broad class of composite operators in maximally supersymmetric strongly coupled Yang-Mills theories. These methods have been used extensively to obtain a wealth of new results. At present there exists no other known method for obtaining such results. For this topic an interdisciplinary approach was necessary that involved ideas and methods form string theory, supersymmetry, condensed matter physics and integrability. Important progress was made on deformed supergravity theories in various space-time dimensions. Particular examples concern ten-dimensional type IIA and IIB supergravities, the former with a so-called Romans mass term. The IIA theory has a consistent truncation to gauged supergravity in four dimensions with an ISO(7) gauge group, which has a holographic dual that takes the form of a three-dimensional ABJM theory. This established the existence of a new holographic duality. An independent open question was how to implement the massive IIA theory in the context of the novel framework of 'exceptional field theory'. The answer to this question was constructed in the form of a new deformed theory in which IIA supergravity appears as a new solution of the exceptional field theory constraints. In addition extended work was carried out to design new approaches for studying supersymmetric theories, many of which could readily be exploited in the work described above. This included the construction of conformal supergravity theories in various dimensions, the study of the embedding tensor for gauged supergravities, and the use of off-shell dimensional reduction to explore both higher-derivative couplings and the c-map.
