  We introduce a model of an optical cavity based on the one-dimensional
Lugiato-Lefever (LL) equation, which includes the pump represented by a
symmetric pair of tightly localized "hot spots" (HSs) with phase shift $\chi $
between them, and self-focusing or defocusing cubic nonlinearity. Families of
bound states, pinned to the double HS, are found in the system's parameter
space. They feature the effect of the symmetry breaking (SB) between peaks
pinned to individual HSs, provided that the phase shift takes values $0<\chi
<\pi $, and the LL equation includes the loss term. The SB, which is explained
analytically, takes place in the full LL model and its linearized version
alike. The same phenomenology is also explored in the framework of the LL
equation with the double HS and quintic self-focusing. In that case, there are
stable symmetric and asymmetric bound states, in spite of the presence of the
background instability driven by the critical collapse.
