Project description
Approaches to solving conformal field theories using bootstrap techniques
A conformal field theory is a quantum field theory that is invariant under conformal transformations. It is widely used to describe critical points of classical and quantum systems. The EU-funded FUNBOOTS project plans to develop a groundbreaking set of tools – analytic extremal functionals – to deepen understanding of such theories. Researchers will use the conformal bootstrap programme, which is a new approach to constructing and classifying conformal field theories non-perturbatively. It exploits basic consistency conditions that are encoded into a formidable set of bootstrap equations to map out and determine the space of conformal field theories. The proposed tools will extract information from the bootstrap equations.
Objective
Conformal Field Theories (CFTs) have a wide range of experimental and theoretical applications: describing classical and
quantum critical phenomena, where they determine critical exponents; as low (or high) energy limits of ordinary quantum
field theories; and as theories of quantum gravity in disguise via the AdS/CFT correspondence.
Unfortunately, most interesting CFTs are strongly interacting and difficult to analyse. On the one hand, perturbative and
renormalization group methods usually involve approximations that are hard to control and which require difficult
resummations. On the other hand, numerical simulations of the underlying systems are difficult near the critical point and can
access only a limited set of observables.
The conformal bootstrap program is a new approach. It exploits basic consistency conditions which are encoded into a
formidable set of bootstrap equations, to map out and determine the space of CFTs. A longstanding conjecture states that
these equations actually provide a fully non-perturbative definition of CFTs. In this project we will develop a groundbreaking
set of tools ? analytic extremal functionals ? to extract information from the bootstrap equations. This Functional Bootstrap
has the potential to greatly deepen our understanding of CFTs as well as to determine incredibly precise bounds on the
space of theories. Our main goals are A) to fully develop the functional bootstrap for the simpler and mostly unexplored one-
dimensional setting, relevant for critical systems such as spin models with long-range interactions and line defects in
conformal gauge theories, leading to analytic insights and effective numerical solutions of these systems; and B) to establish
functionals as the default technique for higher dimensional applications by developing the formalism, obtaining general
analytic bounds and integrating into existing numerical workflows to obtain highly accurate determinations of critical
exponents
Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.1 - European Research Council (ERC)
MAIN PROGRAMME
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Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
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.
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.
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Call for proposal
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2021-COG
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
75794 PARIS
France
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.