We will have one day workshop at NCTS PHY in Hsinchu on algebraic and geometric structure in QFT.
Matthew Young (CUHK)
Jia-Ming (Frank) Liou (NCKU)
Chih-Chung Liu (NCKU)
Hung-Yu Yeh (Academia Sinica)
10:00-10:30 Registration/ Coffee
10:30-12:00 Matthew Young : Unoriented topological field theory and Real 2-representation theory
12:00-13:00 Lunch break
13:00-14:00 Jia-Ming (Frank) Liou : Recent Progress on Mean field equations on hyperelliptic curves
14:00-15:00 Chih-Chung Liu : Gromov Limit for Vortices and Compactification
15:00-15:30 Coffee break
15:30-16:30 Hung-Yu Yeh : Effective action from M-theory on twisted connected sum G2-manifolds
Abstract: I will describe a higher geometric approach to understand and prove some results about two dimensional unoriented TFT. A key tool is a twisted version of loop transgression, allowing one to easily produce cocycles on the unoriented loop space of a Real manifold. One interesting feature of this approach is the natural appearance of a categorification of the Real representation theory of a finite group.
Abstract: In this talk, I will report my recent work on the solvabilities of mean field equations on hyperelliptic curves.
Abstract: We introduce the construction of certain limit to solutions of certain gauge theoretic equations (vortex equations). Moreover, we attempt to include these limits and form a compactification of the original moduli space.
Abstract: (joint work with Thaisa Guio, Hans Jockers, and Albrecht Klemm)
We study the four-dimensional low energy effective N=1 supergravity theory of the dimensional reduction of M-theory on G2-manifolds, which are constructed by Kovalev’s twisted connected sum gluing suitable pairs of asymptotically cylindrical Calabi–Yau threefolds XL/R augmented with a circle S1 . In the Kovalev limit the Ricci-flat G2-metrics are approximated by the Ricci-flat metrics on XL/R and we identify the universal modulus — the Kovalevton — that parametrizes this limit. We observe that the low energy effective theory exhibits in this limit gauge theory sectors with extended supersymmetry. We determine the universal (semi-classical) Kahler potential of the effective N=1 supergravity action as a function of the Kovalevton and the volume modulus of the G2-manifold. This Kahler potential fulfills the noscale inequality such that no anti-de-Sitter vacua are admitted. We describe geometric degenerations in XL/R, which lead to non-Abelian gauge symmetries enhancements with various matter content. Studying the resulting gauge theory branches, we argue that they lead to transitions compatible with the gluing construction and provide many new explicit examples of G2-manifolds.
Nan-Kuo Ho (NTHU), Siye Wu (NTHU)
National Center for Theoretical Sciences, Physics Division