These lecture notes concern the semi-holomorphic 4D Chern–Simons theory and its
applications to classical integrable field theories in 2D and in particular integrable sigma …

This review is dedicated to two-dimensional sigma models with flag manifold target spaces,
which are generalizations of the familiar CP n− 1 and Grassmannian models. They naturally …

Starting with a four-dimensional gauge theory approach to rational, elliptic, and
trigonometric solutions of the Yang-Baxter equation, we determine the corresponding …

We study two-dimensional integrable field theories from the viewpoint of the four-
dimensional Chern-Simons-type gauge theory introduced recently. The integrable field …

We study the holomorphic twist of 3d N= 2 gauge theories in the presence of boundaries,
and the algebraic structure of bulk and boundary local operators. In the holomorphic twist …

We consider holomorphic Poisson-BF theory on twistor space. Classically, this describes
self-dual Einstein gravity on space-time, but at the quantum level it is plagued by an …

A bstract We find a new infinite class of infinite-dimensional algebras acting on BPS states
for non-compact toric Calabi-Yau threefolds. In Type IIA superstring compactification on a …

In this note, we study a simplified variant of the familiar holographic duality between
supergravity on AdS _3 * S^ 3 * T^ 4 AdS 3× S 3× T 4 and the SCFT (on the moduli space of) …

In these lecture notes we aim for a pedagogical introduction to both classical and quantum
integrability. Starting from Liouville integrability and passing through Lax pair and r-matrix …

The 4-dimensional semi-holomorphic Chern-Simons theory of Costello and Yamazaki
provides a gauge-theoretic origin for the Lax connection of 2-dimensional integrable field …