Coarse-graining quivers

TL;DR

This paper introduces a block-spin-like coarse-graining transformation on supersymmetric quiver gauge theories from D-brane probes, revealing a fractal-like structure in the moduli space and connecting to matrix coarse-graining methods.

Contribution

It presents a novel coarse-graining procedure for quiver gauge theories that uncovers fractal structures and links to previous matrix coarse-graining frameworks.

Findings

Flow structures under Higgsing are characterized.

The quiver lattice deconstructs an inhomogeneous fractal dimension.

Connections established with matrix coarse-graining methods.

Abstract

We describe a block-spin-like transformation on a simplified subset of the space of supersymmetric quiver gauge theories that arise on the worldvolumes of D-brane probes of orbifold geometries, by sequentially Higgsing the gauge symmetry in these theories. This process flows to lower worldvolume energies in the regions of the orbifold moduli space where the closed string blowup modes, and therefore the expectation values of the bifundamental scalars, exhibit a hierarchy of scales. Lifting to the ``upstairs'' matrices of the image branes makes contact with the matrix coarse-graining defined in a previous paper. We describe the structure of flows we observe under this process. The quiver lattice for $\BC^2/\BZ_N$ in this region of moduli space deconstructs an inhomogeneous, fractal-like extra dimension, in terms of which our construction describes a coarse-graining of the deconstruction lattice.