Let G ⊂ S O (4 ) d e n o te a fi n ite su b g ro u p c o n ta in in g th e H e ise n b e rg g ro u p . In th e se n o te s w e c la ssify a ll th e se g ro u p s, w e fi n d th e d im e n sio n o f th e sp a c e s o f Gin v a ria n t p o ly n o m ia ls a n d w e g iv e e q u a tio n s fo r th e g e n e ra to rs w h e n e v e r th e sp a c e h a s d im e n sio n tw o . Th e n w e c o m p le te t...

According to the AdS/CFT dictionary, perturbing the large N boundary theory by a relevant double-trace deformation of the form fO2 corresponds in the bulk to imposing “mixed” boundary conditions for the field dual to O. In this note we address various aspects of this correspondence. The change cUV − cIR of the central charge between the UV ad IR fixed points is known from explicit calculations ...

For two graphs $mathrm{G}$ and $mathrm{H}$ with $n$ and $m$ vertices, the corona $mathrm{G}circmathrm{H}$ of $mathrm{G}$ and $mathrm{H}$ is the graph obtained by taking one copy of $mathrm{G}$ and $n$ copies of $mathrm{H}$ and then joining the $i^{th}$ vertex of $mathrm{G}$ to every vertex in the $i^{th}$ copy of $mathrm{H}$. The neighborhood corona $mathrm{G}starmathrm{H}$ of $mathrm{G}$ and $...