  We investigate partition-function zeros of the many-body interacting
spherical spin glass, the so-called $p$-spin spherical model, with respect to
the complex temperature in the thermodynamic limit. We use the replica method
and extend the procedure of the replica symmetry breaking ansatz to be
applicable in the complex-parameter case. We derive the phase diagrams in the
complex-temperature plane and calculate the density of zeros in each phase.
Near the imaginary axis away from the origin, there is a replica symmetric
phase having a large density. On the other hand, we observe no density in the
spin-glass phases, irrespective of the replica symmetry breaking. We speculate
that this suggests the absence of the temperature chaos. To confirm this, we
investigate the multiple many-body interacting case which is known to exhibit
the chaos effect. The result shows that the density of zeros actually takes
finite values in the spin-glass phase, even on the real axis. These
observations indicate that the density of zeros is more closely connected to
the chaos effect than the replica symmetry breaking.
