In this lecture note, we give a basic introduction to the rapidly developing concepts of
generalized symmetries, from the perspectives of both high energy physics and condensed …

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We propose a graph-based approach to 5d superconformal field theories (SCFTs) based on
their realization as M-theory compactifications on singular elliptic Calabi-Yau threefolds …

A bstract In [1, 2] we proposed an approach based on graphs to characterize 5d
superconformal field theories (SCFTs), which arise as compactifications of 6d\(\mathcal …

We propose graphs, the Combined Fiber Diagrams (CFD), to characterize all 5d
superconformal field theories (SCFTs) that arise as S 1-reductions of 6d SCFTs. Transitions …

A bstract We decompose sphere partition functions and indices of three-
dimensional\(\mathcal {N}\)= 2 gauge theories into a sum of products involving a universal …

A bstract We systematically analyse 5d superconformal field theories (SCFTs) obtained by
dimensional reduction from 6d\(\mathcal {N}\)=(1, 0) SCFTs. Such theories have a …

A bstract We classify 5d\(\mathcal {N}\)= 1 gauge theories carrying a simple gauge group
that can arise by mass-deforming 5d SCFTs and 6d SCFTs (compactified on a circle …

We revisit the correspondence between Calabi-Yau (CY) threefold isolated singularities
$\mathbf {X} $ and five-dimensional superconformal field theories (SCFTs), which arise at …

A bstract We use the 5-sphere partition functions of supersymmetric Yang-Mills theories to
explore the (2, 0) superconformal theory on S 5× S 1. The 5d theories can be regarded as …