On D=5 super Yang-Mills theory and (2,0) theory

TL;DR

This work investigates whether the six-dimensional (2,0) theory can be defined or effectively captured by circle-compactified five-dimensional maximally supersymmetric Yang-Mills theory, leveraging the key relation $g_5^2 = R_6$ to connect 5D dynamics with the 6D UV completion. It argues that if a UV cutoff $\Lambda$ arises from the (2,0) theory, KK modes at scale $1/R_6$ provide the necessary high-energy content, potentially constraining perturbative finiteness and shaping the 4D reduction on $T^2$ via S-duality. The paper analyzes one-loop compactification to D=4, obtaining finite, duality-respecting corrections such as $C_8 L^4 \mathrm{tr}\,F^4$ with $C_8 = \zeta(4) E(\tau,2)$, and studies the structure of D=5 UV divergences projected into D=4 operators, including possible $\log g_4$ terms. The conclusions emphasize that the 5D divergences can be interpreted through the (2,0) UV completion and duality constraints, but a definitive statement on finiteness awaits explicit higher-loop calculations; a distinctive signature would be log-divergent coefficients in certain higher-dimension operators.

Abstract

We discuss how D=5 maximally supersymmetric Yang-Mills theory (MSYM) might be used to study or even to define the (2,0) theory in six dimensions. It is known that the compactification of (2,0) theory on a circle leads to D=5 MSYM. A variety of arguments suggest that the relation can be reversed, and that all of the degrees of freedom of (2,0) theory are already present in D=5 MSYM. If so, this relation should have consequences for D=5 SYM perturbation theory. We explore whether it might imply all orders finiteness, or else an unusual relation between the cutoff and the gauge coupling. S-duality of the reduction to D=4 may provide nonperturbative constraints or tests of these options.