Related papers: Rational Conformal Field Theories and Complex Mult…
In Calabi-Yau fourfold compactifications of M-theory with flux, we investigate the possibility of partial supersymmetry breaking in the three-dimensional effective theory. To this end, we place the effective theory in the framework of…
Starting from the geometrical construction of special Lagrangian submanifolds of a toric variety, we identify a certain subclass of A-type D-branes in the linear sigma model for a Calabi-Yau manifold and its mirror with the A- and B-type…
We describe a simple algorithm that computes the recently discovered brane tilings for a given generic toric singular Calabi-Yau threefold. This therefore gives AdS/CFT dual quiver gauge theories for D3-branes probing the given non-compact…
T-branes are a non-abelian generalization of intersecting branes in which the matrix of normal deformations is nilpotent along some subspace. In this paper we study the geometric remnant of this open string data for six-dimensional F-theory…
Logarithmic Conformal Field Theories (LCFT) play a key role, for instance, in the description of critical geometrical problems (percolation, self avoiding walks, etc.), or of critical points in several classes of disordered systems…
6d superconformal field theories (SCFTs) are the SCFTs in the highest possible dimension. They can be geometrically engineered in F-theory by compactifying on non-compact elliptic Calabi-Yau manifolds. In this paper we focus on the class of…
We derive global constraints on the non-BPS sector of supersymmetric 2d sigma-models whose target space is a Calabi-Yau manifold. When the total Hodge number of the Calabi-Yau threefold is sufficiently large, we show that there must be…
Chiral orbifold models are defined as gauge field theories with a finite gauge group $\Gamma$. We start with a conformal current algebra A associated with a connected compact Lie group G and a negative definite integral invariant bilinear…
This review talk focusses on some of the interesting developments in the area of superstring compactification that have occurred in the last couple of years. These include the discovery that ``mirror symmetric" pairs of Calabi--Yau spaces,…
On certain M-theory backgrounds which are a circle fibration over a smooth Calabi-Yau, the quantum theory of M2 branes can be studied in terms of the K-theoretic Donaldson-Thomas theory on the threefold. We extend this relation to…
We consider the field theories on multiple stacks of D5 branes wrapped on four cycles of resolved/deformed conifold geometries fibered over a two torus. The central charges of the D5 branes are slightly misaligned when the branes are…
In type-II string theory compactifications on Calabi-Yau manifolds, topological string theory partition functions give a class of exact F-terms in the four-dimensional effective action. We point out that in the background of constant…
We formulate a conjecture on the finitude of rationality fields (i.e., Fourier coefficient fields) of newforms of bounded degree, and prove this for CM forms assuming a generalized Riemann hypothesis. Then we explicitly determine what…
Boundary conformal field theory (BCFT) is simply the study of conformal field theory (CFT) in domains with a boundary. It gains its significance because, in some ways, it is mathematically simpler: the algebraic and geometric structures of…
We revisit type II$_0$ limits in the vector multiplet moduli space of compactifications of Type IIB string theory on Calabi-Yau threefolds. These limits are special because they cannot be described using mirror symmetry. While we showed in…
Compactifications of the physical superstring to two dimensions provide a general template for realizing 2D conformal field theories coupled to worldsheet gravity, i.e. non-critical string theories. Motivated by this observation, in this…
We study the recently proposed crystal model for three dimensional superconformal field theories arising from M2-branes probing toric Calabi-Yau four-fold singularities. We explain the algorithms mapping a toric Calabi-Yau to a crystal and…
We study the quantum volume of D-branes wrapped around various cycles in Calabi-Yau manifolds, as the manifold's moduli are varied. In particular, we focus on the behaviour of these D-branes near phase transitions between distinct low…
We present the construction of the candidate conformal field theories dual to $AdS_4$ non-maximally supersymmetric compactifications of 11D supergravity. We compare the spectra of the two theories and discuss the realization of the baryonic…
The $\mathcal{N}=1$ superconformal field theories that arise in AdS-CFT from placing a stack of D3-branes at the singularity of a toric Calabi-Yau threefold can be described succinctly by dimer models. We present an efficient algorithm for…