| Description |
I will describe some recent work in two parts. First, I will provide counter examples to certain widely held assumptions about the relationship between phases and phase transitions and show that (a) it is possible to have multiple universality classes on a single critical surface and (b) a stable critical surface can exist within a single, trivial phase. These two phenomena, dubbed `multiversality' and `unnecessary criticality' respectively, are not fine-tuned, stable to arbitrary symmetric perturbations and demonstrate that the existence and properties of a critical surface is not determined by the surrounding phase structure. Second, I will show that we can twist the models of the first part to produce various symmetry enriched gapless Luttinger liquid phases. I will pay particular attention to one of these which is a so-called `intrinsically gapless topological phase' which has stable boundary modes only in the presence of a gapless bulk. Symmetries and anomalies will play an important role which will be tracked, along with other details, using both a microscopic spin-chain description in the UV as well as a continuum field-theoretic description in the IR.
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