Project description
An innovative approach to studying the elusive S-duality symmetry
String theory has inspired spectacular progress in modern mathematics by uncovering profound symmetries at the heart of fundamental physics and mathematical theories. One such symmetry is the S-duality but this remains poorly understood owing to its complexity. In 2006, Kapustin and Witten proposed that S-duality links two types of boundary conditions, BBB and BAA branes. With the support of the Marie Skłodowska-Curie Actions programme, the hyper-mirrors project aims to prove this connection and uncover the underlying geometry. Using cutting-edge tools from algebraic geometry, the study will focus on constructing equivalences between BBB and BAA branes, developing a twistor-based approach to the geometric Langlands programme as well as applying wall-crossing to study branes with rich geometry.
Objective
"A flow of ideas from string theory has inspired spectacular progress in modern mathematical research. This intersectional phenomenon arises from the pursuit of symmetries exhibited by fundamental theories in physics and mathematics. One of these symmetries is S-duality, whose complex behaviour has remained inaccessible to our current mathematical techniques.
A theoretical breakthrough came in 2006. Kapustin and Witten conjectured that S-duality gives rise to an equivalence between two types of boundary conditions - branes of type ""BBB"" and ""BAA"", conditions that come from a hyperkähler geometric structure. Their conjecture sets out a clear route to a new mathematical understanding of S-duality: construct the proposed equivalence and shine light on the underlying geometry.
The action addresses this challenge using modern tools from algebraic geometry. New methods are developed within three vast fields of research: mirror symmetry, the geometric Langlands program, and wall-crossing. This broad range of ideas will be harnessed to seek powerful and novel insights into branes and their dualities.
Specifically, the research objectives are:
(1) Construct a categorical equivalence between BBB and BAA-branes in special cases (i.e. prove hyperkähler enhancements of homological mirror symmetry).
(2) Develop a twistor theoretic approach to the geometric Langlands program, designed to encode the hyperkähler geometry of BBB and BAA-branes.
(3) Apply wall-crossing to construct a class of branes with a particularly rich geometry and study their behaviour under S-duality.
The implementation brings together my PhD research, wall-crossing techniques developed by the supervisor Dr. Feyzbakhsh, and spectacular recent progress on the geometric Langlands program by Gaitsgory et al. In doing so, new frontiers are sought in rapidly developing fields of research, from which myself and the academic community will benefit in the years to come."
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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-2024-PF-01
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SW7 2AZ London
United Kingdom
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