Spherical Deconstruction

TL;DR

The work investigates how a four-dimensional ${\mathcal N}=1^{*}$ gauge theory in the Higgs vacuum can realize a six-dimensional gauge theory via deconstruction on a fuzzy two-sphere. By mapping N×N matrices to functions on $S^2$ with fuzzy spherical harmonics, the authors derive the full classical fermion mass spectrum and show that, as $N\to\infty$, it matches the Kaluza-Klein spectrum of Maldacena-Nunez's twisted ${\mathcal N}=(1,1)$ compactification on $S^2$, with a radius set by $R \sim M^{-1}$ and a UV cutoff $L_{UV} \sim R/N$. For finite $N$, the spectrum is a controlled truncation at mass $N^2$, plus $2N+1$ extra chiral multiplets at that mass, illustrating how higher-dimensional physics emerges from a four-dimensional theory. These results support deconstruction as a concrete framework to access higher-dimensional, non-perturbative gauge dynamics and its spectral structure, with potential links to Little String Theory via the MN construction.

Abstract

We present evidence that N=1* SUSY Yang-Mills provides a deconstruction of a six-dimensional gauge theory compactified on a two-sphere. The six-dimensional theory is a twisted compactification of N=(1,1) SUSY Yang-Mills theory of the type considered by Maldacena and Nunez (MN). In particular, we calculate the full classical spectrum of the N=1* theory with gauge group U(N) in its Higgs vacuum. In the limit N goes to infinity, we find an exact agreement with the Kaluza-Klein spectrum of the MN compactification.