Brane realization of $q$-theory and the cosmological constant problem

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 $\mathrm{2D}$ 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 $\mathrm{2D}$ brane can be generalized to a $\mathrm{4D}$ brane with gravity. For the $\mathrm{4D}$ brane, the analogue of the $\mathrm{2D}$ surface tension is the $\mathrm{4D}$ cosmological constant, which is also nullified in full equilibrium. The $\mathrm{4D}$ 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.