We identify a new class of novae characterized by the post-eruption quiescent
light curve being more than roughly a factor of ten brighter than the
pre-eruption light curve. Eight novae (V723 Cas, V1500 Cyg, V1974 Cyg, GQ Mus,
CP Pup, T Pyx, V4633 Sgr, and RW UMi) are separated out as being significantly
distinct from other novae. This group shares a suite of uncommon properties,
characterized by the post-eruption magnitude being much brighter than before
eruption, short orbital periods, long-lasting supersoft emission following the
eruption, a highly magnetized white dwarf, and secular declines during the
post-eruption quiescence. We present a basic physical picture which shows why
all five uncommon properties are causally connected. Most novae do not have
adequate accretion for continuous hydrogen burning, but some can achieve this
if the companion star is nearby (with short orbital period) and a magnetic
field channels the matter onto a small area on the white dwarf so as to produce
a locally high accretion rate. The resultant supersoft flux irradiates the
companion star and drives a higher accretion rate (with a brighter
post-eruption phase), which serves to keep the hydrogen burning and the
supersoft flux going. The feedback loop cannot be perfectly self-sustaining, so
the supersoft flux will decline over time, forcing a decline in the accretion
rate and the system brightness. We name this new group after the prototype,
V1500 Cyg. V1500 Cyg stars are definitely not progenitors of Type Ia
supernovae. The V1500 Cyg stars have similar physical mechanisms and
appearances as predicted for nova by the hibernation model, but with this group
accounting for only 14% of novae.Comment: Astronomical Journal, in press, 39 pages, 10 figure