Project description
Analytic methods for the conformal bootstrap
The conformal bootstrap is a powerful method for studying conformal field theories, but its progress is limited by heavy numerical costs and slow convergence in higher dimensions. Supported by the Marie Skłodowska-Curie Actions programme, the Aah-Boots project develops an analytic framework that links optimal bootstrap bounds to the extremal solutions that saturate them. This will be used to create a hybrid analytic-numerical approach that reduces reliance on large-scale computation. The method will then be applied to key problems in quantum field theory, including the conformal window of quantum chromodynamics and supersymmetric conformal field theories in four dimensions. By moving beyond brute-force numerics, the project offers a faster and more fundamental way to obtain precision results in conformal field theory.
Objective
"The conformal bootstrap program has been spectacularly successful in producing rigorous numerical bounds on the dynamical data of conformal field theories (CFTs)—systems appearing ubiquitously in many areas of physics and experimental setups. The standard numerical bootstrap uses basic consistency principles to exclude huge regions of parameter space, often leaving small allowed ""islands"" that essentially determine low-lying CFT data, e.g. for the 3d Ising model.
Despite its success, the bootstrap is still held back by its reliance on heavy numerical algorithms. The state-of-the-art bounds for 3d Ising required the order of 10 million CPU-hours. Not only is this slow and expensive, but numerical convergence is a scientific bottleneck. Particularly in 4d CFTs, slow convergence has widely been found to be an obstacle to obtaining precision islands.
In light of these numerical limitations, it is natural to ask if the shape and position of bootstrap islands can be understood analytically. We will develop such an analytic understanding by rigorously proving the duality between optimal bounds and the extremal solutions that saturate them. A consequence is that bootstrap islands for a given system of correlators cannot shrink to zero size, answering an enduring foundational question.
As well as significantly expanding theoretical understanding of the bootstrap, we will harness this analytic information to develop a hybrid (analytic/numerical) bootstrap method. The idea is to solve directly for extremal solutions and extract optimal bounds from them. This stands to be much faster than the usual semi-definite programming numerics, opening a new avenue for precision 4d CFT bootstrap with multi-correlator systems that would otherwise be intractable. We will apply this hybrid method to bootstrap the conformal window of QCD, bounding low-lying CFT data and the conformal window in the number of flavors Nf. We will further apply it to bootstrap interesting 4d N=1 and N=2 SCFTs."
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Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
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Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA)
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Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships
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Call for proposal
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(opens in new window) HORIZON-MSCA-2025-PF
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WC2R 2LS London
United Kingdom
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