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

F. R. Klinkhamer^{+}, G. E. Volovik^{*× 1)}

^{+}Institute for Theoretical Physics, Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe, Germany

^{*}Low Temperature Laboratory, Aalto University, FI-00076 Aalto, Finland

^{×}Landau Institute for Theoretical Physics RAS, 119334 Moscow, Russia

**Abstract**

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.