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Register a new userOn D=5 super Yang-Mills theory and (2,0) theory
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Michael R. Douglas
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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.
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The connection of maximally supersymmetric Yang-Mills theory to the (2,0) theory in six dimensions has raised the possibility that it might be perturbatively ultraviolet finite in five dimensions. We test this hypothesis by computing the coefficient of the first potential ultraviolet divergence of planar (large N_c) maximally supersymmetric Yang-Mills theory in D = 5, which occurs at six loops. We show that the coefficient is nonvanishing. Furthermore, the numerical value of the divergence falls very close to an approximate exponential formula based on the coefficients of the divergences through five loops. This formula predicts the approximate values of the ultraviolet divergence at loop orders L > 6 in the critical dimension D = 4 + 6/L. To obtain the six-loop divergence we first construct the planar six-loop four-point amplitude integrand using generalized unitarity. The ultraviolet divergence follows from a set of vacuum integrals, which are obtained by expanding the integrand in the external momenta. The vacuum integrals are integrated via sector decomposition, using a modified version of the FIESTA program.
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