Three-dimensional N=4 theories admit a rich moduli space of vacua, with two distinct hyper-Kähler (HK) subspaces. While the Higgs branch is long understood as a HK quotient (1980s), the Coulomb branch (CB) has proven a much tougher nut to crack (2010s). It turns out it is a new HK construction in its own right.Understanding CBs is still an active area of research, and we will review the...
Generalized symmetries, such as higher-form and higher-group symmetries, will be discussed in Quantum Field Theories constructed in geometric engineering. The talk will provide an overview of recent, very lively, developments on this topic.
In string theory, a spacetime with an anti-de Sitter (AdS) factor is related to a conformal field theory (CFT) by a famous correspondence. Many such spacetimes are obtained by considering D-branes on conical Calabi–Yau singularities, which can in turn be obtained by K-stability techniques. The corresponding CFT is often, but not always, suggested by matrix factorization techniques.
Fix a Calabi-Yau 3-fold X satisfying the Bogomolov-Gieseker conjecture of Bayer-Macr`i-Toda, such as the quintic 3-fold. After a brief introduction of weak Bridgeland stability conditions, I will describe work with Richard Thomas which expresses Joyce’s generalised DT invariants counting Gieseker semistable sheaves of any rank r on X in terms of those counting sheaves of rank 1. By the MNOP...
