Sommerfeld Theory Colloquium, The upshot of extensive studies of �uctuations in condensed matter systems is that

their qualitative importance is typically con#ned to isolated critical points of

continuous transitions between phases of matter. This conventional wisdom also

predicts the number of low energy Goldstone modes based on the so-called “G/H”

pattern of symmetry breaking. I will discuss a class of systems, some quite wellknown,

that violate this standard paradigm. Namely, they exhibit a fewer than “G/H”

number of low-energy modes due to an emergent Higgs mechanism. Even more

spectacularly, such systems exhibit “critical” ordered phases, with universal power-law

properties reminiscent of a critical point, but requiring no #ne-tuning and extending

throughout the ordered phase. One exciting recently discovered state is the heliconical

nematic that in addition to above phenomena also exhibits spontaneous chiral

symmetry breaking.