We compute the partition function of five-dimensional abelian gauge theory on
a five-torus T5 with a general flat metric using the Dirac method of quantizing
with constraints. We compare this with the partition function of a single
fivebrane compactified on S1 times T5, which is obtained from the six-torus
calculation of Dolan and Nappi. The radius R1 of the circle S1 is set to the
dimensionful gauge coupling constant g^2= 4\pi^2 R1. We find the two partition
functions are equal only in the limit where R1 is small relative to T5, a limit
which removes the Kaluza-Klein modes from the 6d sum. This suggests the 6d
N=(2,0) tensor theory on a circle is an ultraviolet completion of the 5d gauge
theory, rather than an exact quantum equivalence.Comment: v4, 37 pages, published versio
