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BIMSA TQFT and Higher Symmetries Seminar
String Condensation in 3+1D Topological Orders and Applications to Topological Holography
String Condensation in 3+1D Topological Orders and Applications to Topological Holography
Organizers
Speaker
Rui Wen
Time
Tuesday, November 12, 2024 9:45 AM - 11:15 AM
Venue
A3-2-301
Online
Zoom 468 248 1222
(BIMSA)
Abstract
In the traditional Landau paradigm, phase transitions are driven by symmetry charge condensation, also known as symmetry breaking. In contrast, topological phase transitions between topological orders are driven by topological defect condensations. A typical example of this is anyon condensation in 2+1D topological orders. Besides their significance in topological phase transitions, topological defect condensations are also foundational in the framework of topological holography. In this talk, I discuss string condensation in 3+1D topological orders, specifically, Dijkgraaf-Witten theories. I discuss the classification of Lagrangian algebras and their corresponding gapped boundaries. I also determine the outcome of a general string condensation in a 3+1D $G$-gauge theory, up to a gauge group and a twist. A byproduct of the analysis is the gravitational anomaly of a 2+1D anomalous topological order with a Tannakian Müger center. Additionally, I discuss various examples and applications of the results to topological holography for 2+1D phases, in particular, 2+1D gapless symmetry-protected topological phases.