We introduce a definition and framework for internal topological symmetries in quantum field
theory, including “noninvertible symmetries” and “categorical symmetries”. We outline a …

Starting with a gentle approach to the Alday–Gaiotto–Tachikawa (AGT) correspondence
from its 6d origin, these notes provide a wide (albeit shallow) survey of the literature on …

The statistical model of crystal melting represents BPS configurations of D-branes on a toric
Calabi–Yau three-fold. Recently it has been noticed that an infinite-dimensional algebra, the …

A bstract We initiate the study of how the insertion of magnetically charged states in 4d self-
dual gauge theories impacts the 2d chiral algebras supported on the celestial sphere at …

A bstract We study half-BPS line operators in 3d\(\mathcal {N}\)= 4 gauge theories, focusing
in particular on the algebras of local operators at their junctions. It is known that there are …

A bstract We develop new techniques for computing exact correlation functions of a class of
local operators, including certain monopole operators, in three-dimensional\(\mathcal {N} …

A bstract The quiver Yangian, an infinite-dimensional algebra introduced recently in [1], is
the algebra underlying BPS state counting problems for toric Calabi-Yau three-folds. We …

The supersymmetric cigar (half-) index or cigar partition function of 3d $\mathcal {N}= 2$
gauge theories contains a wealth of information. Physically, it captures the spectrum of BPS …

The product of local operators in a topological quantum field theory in dimension greater
than one is commutative, as is more generally the product of extended operators of …

We introduce the shifted quantum affine algebras. They map homomorphically into the
quantized K-theoretic Coulomb branches of 3 d N= 4 3 d {\mathcal N= 4 SUSY quiver gauge …