An integral arising from the chiral sl(n) Potts model
Abstract
We show that the integral
J(t)=(1/
π
3
)
∫
π
0
∫
π
0
∫
π
0
dxdydzlog(t−cosx−cosy−cosz+cosxcosycosz)
, can be expressed in terms of
5
F
4
hypergeometric functions. The integral arises in the solution by Baxter and Bazhanov of the free-energy of the
sl(n)
Potts model, which includes the term
J(2)
. Our result immediately gives the logarithmic Mahler measure of the Laurent polynomial
k−(x+1/x)−(y+1/y)−(z+1/z)+1/4(x+1/x)(y+1/y)(z+1/z)
in terms of the same hypergeometric functions.