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BIMSA TQFT and Higher Symmetries Seminar
Extracting symmetry fractionalisation data from microscopics
Extracting symmetry fractionalisation data from microscopics
演讲者
Siddharth Vadnerkar
时间
2024年10月29日 09:40 至 11:40
地点
A3-2-301
线上
Zoom 468 248 1222
(BIMSA)
摘要
Based on "An operator algebraic approach to symmetry defects and fractionalisation", (arxiv:2411.XXXX). Joint work with Kyle Kawagoe and Daniel Wallick.
Symmetry has always played an important role in physics, and in the last 2 decades, the notion of topological order has taken the centre stage in many sub-disciplines of physics. A Symmetry Enriched Topological (SET) order is when one marries the concept of topological order and symmetry and considers sysems that have a global symmetry, as well as topological order. It is well known that gapped topological order in 2+1 dimensions is mathematically described by Unitary Modular Tensor Categories, and houses long-range quasi-particle excitations called anyons. It is natural to study the consequences of imposing a symmetry on such a system. The landmark paper by BBCW (arxiv:1410.4540) worked out the algebraic theory of such a resulting system, with the conclusion that such a theory must be a
In this talk, we take an entirely different approach. Starting from the algebra of local observables of any lattice system in 2+1D, we propose a "selection criterion" to extract global data of such system. We then work out the resultant theory of such data and it turns out to be a
Symmetry has always played an important role in physics, and in the last 2 decades, the notion of topological order has taken the centre stage in many sub-disciplines of physics. A Symmetry Enriched Topological (SET) order is when one marries the concept of topological order and symmetry and considers sysems that have a global symmetry, as well as topological order. It is well known that gapped topological order in 2+1 dimensions is mathematically described by Unitary Modular Tensor Categories, and houses long-range quasi-particle excitations called anyons. It is natural to study the consequences of imposing a symmetry on such a system. The landmark paper by BBCW (arxiv:1410.4540) worked out the algebraic theory of such a resulting system, with the conclusion that such a theory must be a
In this talk, we take an entirely different approach. Starting from the algebra of local observables of any lattice system in 2+1D, we propose a "selection criterion" to extract global data of such system. We then work out the resultant theory of such data and it turns out to be a