Quantum Field Theory (QFT) is the universal framework describing the fundamental interactions of nature. It provides the theoretical foundation for both the Standard Model of particle physics and for the study of critical phenomena in condensed-matter systems.
Despite numerous achievements, our theoretical understanding of this model is mostly limited to the perturbative regime, where the interaction among fundamental particles is sufficiently weak. Many of the most intriguing aspects of nature lie instead in the strongly coupled regime, which remains largely inaccessible to conventional analytical tools.
A particularly fruitful setting to explore these challenges is offered by Conformal Field Theories (CFTs). CFTs describe physical systems at criticality and represent the fixed points of the renormalisation-group flow. Moreover, some CFTs possess a holographic dual description in terms of quantum gravity on an Anti-de Sitter (AdS) background, an idea formalised in the AdS/CFT correspondence. This duality has revolutionised our understanding of strongly coupled systems by relating them to weakly coupled gravitational theories, but it still leaves many intermediate-coupling phenomena unexplored.
Hope that the deadlock of non-perturbative physics could be finally resolved appeared almost two decades ago with the discovery of integrability in the flagship holographic models together with the revival of the conformal bootstrap program by a change of perspective compared to the unsuccessful attempts in the early days of CFTs.These methodologies are to some extent complementary in their regime of validity. Integrability allows one to compute the spectrum of scaling dimensions of operators exactly, even at finite coupling, through the Quantum Spectral Curve (QSC) formalism. The conformal bootstrap exploits the consistency of the theory and conformal symmetry to derive rigorous constraints on CFT data. Together, they offer powerful but still separate windows into non-perturbative physics.
The Bootstrability project was designed to bring these two paradigms together for the first time. Its main goal is to build an analytical and numerical framework capable of computing not only spectra but also structure constants, the quantities that encode interactions among operators and determine all correlation functions in a CFT.
This ambitious program has as its long-term final goal the solution of the prototypical holographic integrable superconformal field theories: N = 4 SYM and ABJM.
The project’s specific objectives are to merge QSC spectral data with conformal-bootstrap equations to extract the structure constants developing both analytical and numerical implementations covering the full range of coupling regimes.
In its first two years, the project has achieved significant milestones, obtaining analytical and numerical non-perturbative results for the structure constants and correlation functions of defect operators in N=4 SYM. Moreover, with the long-term goal of incorporating integrability data beyond the spectrum of local operators, a completely new method was developed to compute non-perturbative Regge trajectories that link different local operators across the spectrum. These advances mark a step forward in extending the Bootstrability program beyond existing integrability techniques. The results have been disseminated through peer-reviewed publications, invited conference presentations, and the release of open-access computational tools.
Beyond its scientific results, Bootstrability demonstrates the value of cross-disciplinary research at the interface of mathematical physics, high-energy theory, and computational science. Ultimately, the project advances toward a complete non-perturbative description of quantum field theories — a step of profound importance for our understanding of nature and for future progress in quantum gravity, particle physics, and mathematical modelling.
