A relation between moduli space of D-branes on orbifolds and Ising model
Tomomi Muto
TL;DR
This paper explores the connection between the moduli space of D-branes on abelian orbifolds and the ground state counting problem of an antiferromagnetic Ising model on a triangular lattice derived from the McKay quiver.
Contribution
It establishes a novel relationship between the geometry of D-branes on orbifolds and statistical mechanics models, specifically linking toric geometry calculations to Ising model ground states.
Findings
The moduli space analysis is related to counting Ising model ground states.
The Ising model is defined on a triangular lattice from the McKay quiver.
A combinatorial approach connects gauge theory moduli spaces with statistical physics.
Abstract
We study D-branes transverse to an abelian orbifold C^3/Z_n Z_n. The moduli space of the gauge theory on the D-branes is analyzed by combinatorial calculation based on toric geometry. It is shown that the calculation is related to a problemto count the number of ground states of an antiferromagnetic Ising model. The lattice on which the Ising model is defined is a triangular one defined on the McKay quiver of the orbifold.
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