We discuss the cosmological constant problem using the properties of a
freely-suspended two-dimensional condensed-matter film, i.e., an explicit
realization of a 2D brane. The large contributions of vacuum fluctuations to
the surface tension of this film are cancelled in equilibrium by the
thermodynamic potential arising from the conservation law for particle number.
In short, the surface tension of the film vanishes in equilibrium due to a
thermodynamic identity. This 2D brane can be generalized to a 4D brane with
gravity. For the 4D brane, the analogue of the 2D surface tension is the 4D
cosmological constant, which is also nullified in full equilibrium. The 4D
brane theory provides an alternative description of the phenomenological
q-theory of the quantum vacuum. As for other realizations of the vacuum
variable q, such as the 4-form field-strength realization, the main
ingredient is the conservation law for the variable q, which makes the vacuum
a self-sustained system. For a vacuum within this class, the nullification of
the cosmological constant takes place automatically in equilibrium. Out of
equilibrium, the cosmological constant can be as large as suggested by naive
estimates based on the summation of zero-point energies. In this brane
description, q-theory also corresponds to a generalization of unimodular
gravity.Comment: 5 pages, v3: final versio
