  We study rotating fermionic matter at finite temperature in the framework of
the Nambu-Jona-Lasinio model. In order to respect causality the rigidly
rotating system must be bound by a cylindrical boundary with appropriate
boundary conditions that confine the fermions inside the cylinder. We show the
finite geometry with the MIT boundary conditions affects strongly the phase
structure of the model leading to three distinct regions characterized by
explicitly broken (gapped), partially restored (nearly gapless) and
spontaneously broken (gapped) phases at, respectively, small, moderate and
large radius of the cylinder. The presence of the boundary leads to specific
steplike irregularities of the chiral condensate as functions of coupling
constant, temperature and angular frequency. These steplike features have the
same nature as the Shubnikov-de Haas oscillations with the crucial difference
that they occur in the absence of both external magnetic field and Fermi
surface. At finite temperature the rotation leads to restoration of
spontaneously broken chiral symmetry while the vacuum at zero temperature is
insensitive to rotation ("cold vacuum cannot rotate"). As the temperature
increases the critical angular frequency decreases and the transition becomes
softer. A phase diagram in angular frequency-temperature plane is presented. We
also show that at fixed temperature the fermion matter in the chirally restored
(gapless) phase has a higher moment of inertia compared to the one in the
chirally broken (gapped) phase.
