Powered by Indico
v3.2.7
It is well known that symmetry provides useful guidance to organize quantum phases of matter and leads to many important physical implications such as conservation laws and constraining low-energy dynamics of a quantum field theory. Recently, remarkable progress has been made in generalizing the concept of symmetry and elucidating its connection to topological defects. In this talk, I will discuss a recent progress on a holographic principle for generalized global symmetry, dubbed as topological holography, which describes the generalized symmetry of a quantum system in terms of a topological order in one higher dimension. This framework separates the topological data from the local dynamics of a theory and provides a unified description of the symmetry and duality in gapped and gapless phases of matter. In particular, I will focus on various exotic quantum critical points and gapless phases in (1+1)d such as phase transitions between symmetry protected topological (SPT) phases, symmetry enriched quantum critical points, deconfined quantum critical points and intrinsically gapless SPT phases. I will also discuss a topological holographic picture for conformal boundary states of (1+1)d rational conformal field theories, and uncovers the correspondence between the nature of the (1+1)d gapped phases and the boundary states.