The initial phase of the project focused on analyzing correlation functions of operators found in quantum field theory, such as globally conserved symmetry currents. This involved integrating these techniques with existing methods to evaluate the method's viability. Our primary aim was to compare the new approach with existing ones, considering both the precision of results and the computational resources required.
The outcomes were promising, indicating the potential for further development. Incorporating conserved currents alongside other operators not only enhanced the numerical bootstrap's ability to constrain but also enabled the extraction of data inaccessible via standard scalar-based approaches.
Throughout this phase, our team developed various algorithms to efficiently tackle large-scale bootstrap problems. These algorithms were instrumental in resolving a longstanding discrepancy between experimental and simulated results regarding a specific observable related to the transition from fluid to superfluid helium. Similarly, they facilitated the rigorous demonstration of isotropic magnet instability under cubic perturbations, addressing another enduring challenge. Notably, the project achieved a breakthrough by designing an algorithm that integrates numerical properties with analytical input. This novel algorithm enabled the consideration of universal behaviors inherent in CFT within specific limits for the first time.
Additionally, CFT-MAP achieved groundbreaking precision in determining numerous observables, including critical exponents for various theories like the supersymmetric Ising model and the O(2) and O(3) models. Some of these computations would have been exceedingly difficult, if not impossible, using alternative methods.
Furthermore, the new algorithm enabled studies beyond our initial objectives. For example, we could non-perturbatively track the state spectrum of the Ising model across dimensions from 4 to 2. CFT-MAP also initiated exploration into exotic phase transitions characterized by diverse symmetry-breaking patterns.
The project also accomplished significant milestones beyond its primary objectives. This included delving into the constraints imposed by supersymmetric conformal field theories across various degrees of supersymmetry. Additionally, the project undertook a formal exploration of conformal field theories (CFT), with a focused examination on 2D CFTs.
In the project's final stages, we discovered that the techniques employed in numerical conformal bootstrap could be adapted to study scattering amplitudes in weakly coupled effective field theories. This led to investigations into phenomena like photon and pion scattering in theories resembling quantum chromodynamics, yielding bounds applicable to the real world and accurately reproducing low-lying meson resonance spectra with minimal assumptions.
The results of CFT-MAP have been disseminated through 38 publications in prestigious international scientific journals, with several more currently under review. A review on conformal bootstrap methodologies published in Reviews of Modern Physics has garnered over 600 citations since its release, with a follow-up review on numerical methods recently completed. Our team regularly presented project findings at international conferences, workshops, and local seminars worldwide.
To enhance project visibility and foster collaboration, we organized two significant events: a five-week workshop at the Galileo Galilei Institute in Florence, Italy, in October 2022, and a one-week conference at the University of Pisa, Italy, in February 2024, featuring international guests from leading universities.
