I will describe the results of a series of works in which we have found systems for which Spontaneous Symmetry Breaking(SSB) persists to very high temperatures. The systems involve Conformal Field Theories of scalars in fractional dimensions 3<d<3 and for Gauge Theories in d=4. The systems are studied in the limit of various large numbers of species. In the process, we have found...

Extra spacetime dimensions give rise to KK fields, whose masses should be large and in particular much larger than the cosmological constant. While this can happen naturally in an effective low-energy theory, it is not the case for most known vacuum solutions of ten-or eleven-dimensional supergravity. We review efforts to find vacua that resolve this tension and recent general bounds on KK masses.

Mathematicians formulate fully extended d-dimensional TQFTs in terms of functors between a higher category of bordism and suitable target categories. Furthermore, the cobordism hypothesis identifies the basic building blocks of such TQFTs. In this talk, I will discuss Rozansky Witten models with affine targets, also known as 3-dimensional topologically twisted N=4 theories of free...