This is a review article on the quantum toroidal algebras, focusing on their roles in various
solvable structures of 2d conformal field theory, supersymmetric gauge theory, and string …

We consider BPS states in a large class of d= 4, N= 2 field theories, obtained by reducing six-
dimensional (2, 0) superconformal field theories on Riemann surfaces, with defect operators …

Yang–Mills theories in four space–time dimensions possess a hidden symmetry which does
not exhibit itself as a symmetry of classical Lagrangians but is only revealed on the quantum …

We study four dimensional supersymmetric gauge theory in the Ω-background with the two
dimensional super-Poincare invariance. We explain how this gauge theory provides the …

We study N= 2 supersymmetric four-dimensional gauge theories, in a certain 525-02= 2
supergravity background, called the Ω-background. The partition function of the theory in the …

A bstract We study symmetries of quantum field theories involving topologically distinct
sectors of the field space. To exhibit these symmetries we define special gauge invariant …

N= 2 supersymmetric gauge theories in four dimensions are studied by formulating them as
the quantum field theories derived from configurations of fourbranes, fivebranes, and …

Using the recent advances in our understanding of non-perturbative aspects of type 11
strings we show how non-trivial exact results for N= 2 quantum field theories can be reduced …

We show how the Riemann surface σ of N= 2 Yang-Mills field theory arises in type II string
compactifications on Calabi-Yau threefolds. The relevant local geometry is given by …

We discuss the AdS/CFT duality from the perspective of integrable systems and establish a
direct relationship between the dimension of single trace local operators composed of two …