It seems the following remarks in M. Kapranov's paper http://arxiv.org/abs/alg-geom/9604018 page 64 bottom, has not been mentioned so far

According to the point of view going back to Y.I. Manin and B. Mazur, one should visualize any 1-dimensional arithmetic scheme X as a kind of 3-manifold and closed points x ∈ X as oriented circles in this 3-manifold. Thus the Frobenius element (which is only a conjugacy class in the fundamental group) is visualized as the monodromy around the circle (which, as an element of the fundamental group, is also defined only up to conjugacy since no base point is chosen on the circle), Legendre symbols as linking numbers and so on. From this point of view, it is natural to think of the operators (algebra elements) af,x,d for fixed f and varying x, d as forming a free boson field Af on the “3-manifold” X; more precisely, for ±d > 0, the operator a ± f,x,d is the dth Fourier component of Af along the “circle” Spec(Fq(x)). The bosons a ± f,x,d and their sums over x ∈ X (i.e., the Taylor components of log Φ ± f (t)) will be used in a subsequent paper to construct representations of U in the spirit of [FJ].

It might be that recent paper by Kapranov and coauthors: http://arxiv.org/abs/1202.4073 The spherical Hall algebra of Spec(Z)

is somehow developing ideas quoted above.

The question which I heard from V. Golyshev and others many years ago is the following: if Spec (Z) is analogous to 3-fold, what should be arithmetic analog of Chern-Simons theory ?