Understanding the origins of flavour in both quark and lepton sectors is one of the most challenging fundamental problems in contemporary particle physics. The Workshop will be devoted to the approach to the flavour puzzle based on modular invariance, proposed in 2017 and since then extensively studied both in a bottom-up and a top-down perspective. Modular invariance has been investigated in the context of field and superstring theories, being a key feature of several theoretical constructions such as theories with toroidal compactification of extra dimensions, superstring theories on tori or orbifolds, supergravity theories. In this context the modular group acts on the matter generation space and is broken by the vacuum expectation value of a single complex scalar field, offering an economic setup to understand the origin of flavour, including CP violation, in particle physics. Yukawa couplings are described by modular forms, extensively studied by mathematicians since the 19th century, and more recently, in particular, for their major implications on number theory. Modular invariance can be investigated both in a bottom-up and in a top-down approach, thus representing a unique opportunity for phenomenologists and string theorists to confront their ideas. Open questions that will be discussed during the Workshop include:
- Connection between bottom-up and top-down constructions.
- The problem of moduli stabilisation and supersymmetry breaking.
- Extensions of the modular group, such as symplectic or metaplectic groups.
- CP violation in the quark and lepton sectors.
- Reduction of parameters needed to describe the quark sector.
- Relation between the flavour puzzle and critical phenomena.
We encourage participation from both the more mathematical and string theory related as well as phenomenology communities, to ensure a thorough discussion connecting bottom-up and top-down approaches to this formidable and extremely challenging endeavour.
The list of participants includes:
- Gui-Jun Ding (USTC, Hefei)
- Stephen King (University of Southampton)
- Tatsuo Kobayashi (Hokkaido University)
- Xiang-Gan Liu (UC, Irvine)
- Myriam Mondragón (UNAM, Mexico)
- João Penedo (CFTP, Lisbon)
- Saul Ramos-Sanchez (UNAM, Mexico)
- Michael Ratz (UC, Irvine)
- Nicole Righi (King's College London)
- Morimitsu Tanimoto (Niigata University)