  We suggest that the solution to the cosmological vacuum energy puzzle is
linked to the infrared sector of the effective theory of gravity interacting
with standard model fields. We propose a specific solvable two dimensional
model where our proposal can be explicitly tested. We analyse the 2d Schwinger
model on a 2-torus and in curved 2d space, mostly exploiting the properties of
its topological susceptibility, its links with the non-trivial topology or
deviations from spacetime flatness, and its relations to the real 4d world. The
Kogut-Susskind ghost (which is a direct analogue of the Veneziano ghost in 4d)
on a 2-torus and in curved 2d space plays a crucial role in the computation of
the vacuum energy. The departure from Minkowski flatness, which is defined as
the cosmological constant in our framework, is found to scale as 1/L, where L
is the linear size of the torus. Therefore, in spite of the fact that the
physical sector of 2d QED is represented by a single massive scalar particle,
the deviation from Minkowski space is linear in L rather than exponentially
suppressed as one could naively expect.
