Search for: All records

A bstract We propose a unified perspective on two sets of objects that usually arise in the study of bipartite field theories. Each of the sets consists of a polytope, or equivalently a toric Calabi-Yau, and a quiver theory. We refer to the two sets of objects as original and twin. In the simplest cases, the two sides of the correspondence are connected by the graph operation known as untwisting. The democratic treatment that we advocate raises new questions regarding the connections between these objects, some of which we explore. With this motivation in mind, we establish a correspondence between the mutations of the original polytope and the twin quiver. This leads us to propose that non-toric twin quivers are naturally associated to generalized toric polygons (GTPs) and we explore various aspects of this idea. Supporting evidence includes global symmetries, the ability of twin quivers to encode the generalized s -rule, and the connection between the mutations of polytopes and of configurations of webs of 5-branes suspended from 7-branes. We introduce three methods for constructing twin quivers for GTPs. We also investigate the connection between twin quivers obtained using different toric phases. Twin quivers provide a powerful new perspective on GTPs. The ideas presented in this paper may represent a step towards the generalization of brane tilings to GTPs. 

We give a summary of recent progress on the signed area enumeration of 9 closed walks on planar lattices. Several connections are made with quantum mechanics 10 and statistical mechanics. Explicit combinatorial formulae are proposed which rely on 11 sums labelled by the multicompositions of the length of the walks. 

We give a summary of recent progress on the signed area enumeration of 9 closed walks on planar lattices. Several connections are made with quantum mechanics 10 and statistical mechanics. Explicit combinatorial formulae are proposed which rely on 11 sums labelled by the multicompositions of the length of the walks. 

A bstract The 2 d (0 , 2) supersymmetric gauge theories corresponding to the classes of Y p,k (ℂℙ 1 × ℂℙ 1 ) and Y p,k (ℂℙ 2 ) manifolds are identified. The complex cones over these Sasaki-Einstein 7-manifolds are non-compact toric Calabi-Yau 4-folds. These infinite families of geometries are the largest ones for Sasaki-Einstein 7-manifolds whose metrics, toric diagrams, and volume functions are known explicitly. This work therefore presents the largest list of 2 d (0 , 2) supersymmetric gauge theories corresponding to Calabi-Yau 4-folds with known metrics. 

Abstract We calculate the number of open walks of fixed length and algebraic area on a square planar lattice by an extension of the operator method used for the enumeration of closed walks. The open walk area is defined by closing the walks with a straight line across their endpoints and can assume half-integer values in lattice cell units. We also derive the length and area counting of walks with endpoints on specific straight lines and outline an approach for dealing with walks with fully fixed endpoints. 

In this talk I discuss some features of the entanglement entropy for fuzzy geometry, focusing on its dependence on the background fields and the spin connection of the emergent continuous manifold in a large N limit. Using the Landau-Hall paradigm for fuzzy geometry, this is argued to be given by a generalized Chern-Simons form, making a point of connection with the thermodynamic view of gravity. Matter-gravity couplings are also considered in the same framework; they naturally lead to certain specific nonminimal couplings involving powers of the curvature. 

A bstract Recently, the first instance of a model of D-branes at Calabi-Yau singularities where supersymmetry is broken dynamically into stable vacua has been proposed. This construction was based on a system of N regular and M = 1 fractional branes placed at the tip of the so-called (orientifolded) Octagon singularity. In this paper we show that this model admits a large M generalization, having the same low energy effective dynamics. This opens up the possibility that the effect on geometry is smooth, and amenable to describing the gauge theory all along the RG flow, including the deep IR, in terms of a weakly coupled gravity dual background. The relevance of this result in the wider context of the string landscape and the Swampland program is also discussed.