The authors compute the leading finite-size corrections to thermal observables of the large-N critical O(N) model on S^1 x S^2 using a perturbative expansion in beta/r.
Vacuum energy on orbifold factors of spheres
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abstract
The vacuum energy is calculated for a free, conformally-coupled scalar field on the orbifold space-time \R$\times \S^2/\Gamma$ where $\Gamma$ is a finite subgroup of O(3) acting with fixed points. The energy vanishes when $\Gamma$ is composed of pure rotations but not otherwise. It is shown on general grounds that the same conclusion holds for all even-dimensional factored spheres and the vacuum energies are given as generalised Bernoulli functions (i.e. Todd polynomials). The relevant $\zeta$- functions are analysed in some detail and several identities are incidentally derived. The general discussion is presented in terms of finite reflection groups.
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The large $N$ vector model on $S^1\times S^2$
The authors compute the leading finite-size corrections to thermal observables of the large-N critical O(N) model on S^1 x S^2 using a perturbative expansion in beta/r.