Fuzzy Instantons

TL;DR

This paper introduces instanton-like solutions in a matrix model that satisfy self-duality, with actions quantized for small matrices and approaching continuous ratios as matrix size increases.

Contribution

It presents a new class of solutions in matrix models with quantized actions that interpolate to continuous values in the large matrix limit.

Findings

For small matrices, the action quantizes to integer multiples.

As matrix size grows, the ratio of action to matrix dimension approaches any real number between zero and one.

Solutions satisfy a self-duality condition in the matrix model.

Abstract

We present a series of instanton-like solutions to a matrix model which satisfy a self-duality condition and possess an action whose value is, to within a fixed constant factor, an integer l^2. For small values of the dimension n^2 of the matrix algebra the integer resembles the result of a quantization condition but as n -> \infty the ratio l/n can tend to an arbitrary real number between zero and one.