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We discuss the structure of 2D conformal field theories (CFT) at central charge c=0 describing critical disordered systems, polymers and percolation. We construct a novel extension of the c=0 Virasoro algebra, characterized by a number b…
The study of exactly marginal deformations of superconformal field theories is a topic that has received considerable attention due to their rich properties. We investigate the $\mathcal{N}=2$ preserving exactly marginal operators of 3d…
We initiate a systematic investigation of the space of 2+1 dimensional quiver gauge theories, emphasising a succinct "forward algorithm". Few "order parametres" are introduced such as the number of terms in the superpotential and the number…
The use of the AdS/CFT correspondence to arrive at quiver gauge field theories is dicussed, focusing on the orbifolded case without supersymmetry. An abelian orbifold with the finite group $Z_{p}$ can give rise to a $G = SU(N)^p$ gauge…
We study some aspects of the recently discovered connection between dimer models and D-brane gauge theories. We argue that dimer models are also naturally related to closed string theories on non compact orbifolds of $\BC^2$ and $\BC^3$,…
We explicitly construct a family of ${\cal N}=4$ superconformal mechanics of dyonic particles, generalizing the work of Anninos et al.\,\cite{Anninos:2013nra} to an arbitrary number of particles. These mechanics are obtained from a scaling…
We present a general method for computing the central charges a and c of N=2 superconformal field theories corresponding to singular points in the moduli space of N=2 gauge theories. Our method relates a and c to the U(1)_R anomalies of the…
We develop a systematic framework for constructing (3+1)-dimensional topological orders or topological quantum field theories (TQFTs) that realize specified anomalies of finite symmetries, as encountered in gauge theories with fermions or…
Given a quiver algebra A with relations defined by a superpotential, this paper defines a set of invariants of A counting framed cyclic A-modules, analogous to rank-1 Donaldson-Thomas invariants of Calabi-Yau threefolds. For the special…
We study the four-dimensional N=2 superconformal field theories that describe D3-branes probing the recently constructed N=2 S-folds in F-theory. We introduce a novel, infinite class of superconformal field theories related to S-fold…
We study the supergravity dual of four-dimensional ${\mathcal{N}=1}$ superconformal field theories arising from wrapping M5-branes on a K\"ahler two-cycle inside a Calabi-Yau threefold. We derive an effective three-dimensional theory living…
We prove the rationality of the descendent partition function for stable pairs on nonsingular toric 3-folds. The method uses a geometric reduction of the 2- and 3-leg descendent vertices to the 1-leg case. As a consequence, we prove the…
We derive a geometric formulation of the 2d central charge $c_r$ from infinite families of 4d $\mathcal{N}=1$ superconformal field theories topologically twisted on constant curvature Riemann surfaces. They correspond to toric quiver gauge…
We investigate topological properties of Calabi-Yau fourfolds and consider a wide class of explicit constructions in weighted projective spaces and, more generally, toric varieties. Divisors which lead to a non-perturbative superpotential…
We study webs of 5-branes with 7-branes in Type IIB string theory from a geometric perspective. Mathematically, a web of 5-branes with 7-branes is a tropical curve in $\mathbb{R}^2$ with focus-focus singularities introduced. To any such a…
We introduce unsupervised machine learning techniques in order to identify toric phases of 4d N=1 supersymmetric gauge theories corresponding to the same toric Calabi-Yau 3-fold. These 4d N=1 supersymmetric gauge theories are worldvolume…
We apply c-extremization, whose proof we review in full detail, to study two-dimensional N=(0,2) superconformal field theories arising from the low-energy dynamics of D3-branes wrapped on Riemann surfaces and M5-branes wrapped on…
We study the relation between Donaldson-Thomas theory of Calabi-Yau threefolds and a six-dimensional topological Yang-Mills theory. Our main example is the topological U(N) gauge theory on flat space in its Coulomb branch. To evaluate its…
We study how to couple a 6D superconformal field theory (SCFT) to gravity. In F-theory, the models in question are obtained working on the supersymmetric background R^{5,1} x B where B is the base of a compact elliptically fibered…
The open string sector of the topological B-model on CY $(m+2)$-folds is described by $m$-graded quivers with superpotentials. This correspondence generalizes the connection between CY $(m+2)$-folds and gauge theories on the worldvolume of…