Giulio Bonelli

Hitchin systems, N = 2 gauge theories and W-gravity

Abstract We propose some arguments supporting an M-theory derivation of the duality recently discovered by Alday, Gaiotto and Tachikawa between two-dimensional conformal field theories and N = 2 superconformal gauge theories in four dimensions. We find that A N − 1 Toda field theory is the simplest two-dimensional conformal field theory quantizing the moduli of N M5-branes wrapped on a Riemann surface. This leads us to identify chiral operators of the N = 2 gauge theories with integrated W-algebra currents. As a check of this correspondence we study some relevant OPEs obtaining that Nekrasovs partition function satisfies W-geometry constraints.

Exploring pure spinor string theory on AdS4 ? Bbb CBbb P3

In this paper we formulate the pure spinor superstring theory on AdS4 × CP 3 . By recasting the pure spinor action as a topological A-model on the fermionic supercoset Osp(6|4)/SO(6) × Sp(4) plus a BRST exact term, we prove the exactness of the σmodel. We then give a gauged linear σ-model which reduces to the superstring in the limit of large volume and we study its branch geometry in different phases. Moreover, we discuss possible D-brane boundary conditions and the principal chiral model for the fermionic supercoset.

Wild quiver gauge theories

A bstractWe study

Gauge Theories on ALE Space and Super Liouville Correlation Functions

\mathcal{N} = {2}

Vertices, vortices & interacting surface operators

supersymmetric SU(2) gauge theories coupled to non-Lagrangian superconformal field theories induced by compactifying the six dimensional A1 (2,0) theory on Riemann surfaces with irregular punctures. These are naturally associated to Hitchin systems with wild ramification whose spectral curves provide the relevant Seiberg-Witten geometries. We propose that the prepotential of these gauge theories on the Ω-background can be obtained from the corresponding irregular conformal blocks on the Riemann surfaces via a generalization of the coherent state construction to the case of higher order singularities.

Topological branes, p-algebras and generalized Nahm equations

We present a relation between

Generalized matrix models and AGT correspondence at all genera

{\mathcal{N}=2}

N = 1 Geometries via M-theory

quiver gauge theories on the ALE space