Deconstructing (2,0) Proposals
N. Lambert, C. Papageorgakis, M. Schmidt-Sommerfeld
TL;DR
The paper tackles how to relate the six-dimensional (2,0) theory to five-dimensional MSYM, using three complementary approaches: DLCQ, deconstruction from a four-dimensional circular quiver, and the conjectured equivalence to 5D MSYM on S^1. Through explicit discretisation and Higgsing analyses, the authors show that the 4D N=2 circular quiver deconstructs 5D MSYM on a discretised circle with lattice spacing $a$, provided the identifications $a = 1/(G v)$ and $g_{YM}^2 = G/v$ hold, which also fixes the circle radius $R_4 = N a/(2\pi)$. They further demonstrate that DLCQ of the (2,0) theory on a circle of finite radius $R_5$ agrees with the DLCQ of 5D MSYM (or the deconstructed theory) in the corresponding limits, with instanton-soliton (or caloron) moduli-space quantum mechanics capturing the finite-momentum sectors. The overall picture supports the view that 5D MSYM furnishes a nonperturbatively well-defined framework for describing the (2,0) theory on S^1 and that deconstruction and DLCQ provide consistent, UV-complete descriptions without introducing extra degrees of freedom beyond those of 5D MSYM. Together these results offer a coherent, cross-validated route to understanding the UV completion and interrelations of the (2,0) theory, 5D MSYM, and their discretised/quiver realizations.
Abstract
We examine the relationships between three proposals for the six-dimensional (2,0) theory: the DLCQ of hep-th/9707079, hep-th/9712117, the deconstruction prescription of hep-th/0110146, and the five-dimensional maximally supersymmetric Yang-Mills proposal of 1012.2880, 1012.2882. We show that hep-th/0110146 gives a deconstruction of five-dimensional maximally supersymmetric Yang-Mills. The proposal of hep-th/9707079, hep-th/9712117 uses a subset of the degrees of freedom of five-dimensional Yang-Mills and we show that compactification of it on a circle of finite radius agrees with the DLCQ arising from the proposal of 1012.2880, 1012.2882 or from the deconstruction proposal of hep-th/0110146.