Event One: Noninvertible symmetry protected topological phases on lattice
Speaker: Weiguang Cao
Time: Dec 23 (Tue), 3:00 – 4:30PM
Location:R1710, SIMIS
Zoom Meeting ID: 869 8806 6346 Passcode: SIMIS
Abstract:
The recent discovery of noninvertible symmetries—a radical extension of conventional symmetry—has challenged long-standing paradigms in condensed matter physics and quantum information and opened new territory in both theory and technology. Unlike ordinary symmetries, which can be inverted, these symmetries behave like projections (one-way operations) yet still strongly constrain quantum dynamics and enable new classes of phases and phase transitions. However, their role in organizing and stabilizing novel quantum phases remains poorly understood. One important example is a symmetry protected topological (SPT) phase, characterized by nontrivial edge modes and potential applications in quantum information. In this talk, I will discuss the classification of noninvertible symmetry-protected topological (NISPT) phases in both closed and open quantum systems using a duality-based method, and present concrete lattice realizations. These lattice models provide controlled playgrounds in which the physics of noninvertible symmetry can be explored numerically and, potentially, experimentally.
Event Two: Condensation of string-like topological defects in (3+1)d gapped bulk theory
Speaker: Hao Xu
Time: Dec 24 (Wed), 2:00 – 3:30PM
Location:R1710, SIMIS
Zoom Meeting ID: 813 8371 1820 Passcode: SIMIS
Abstract:
Given a finite symmetry group $G$ with anomaly $\pi \in \mathrm{H}^4(G,U(1))$, the 4D Dijkgraaf–Witten model provides an exactly solvable gauge theory with applications in high-energy physics and topological phases of matter. The topological defects in these models form a braided fusion 2-category $\mathscr{Z}(\mathbf{2Vect}^\pi_G)$, the Drinfeld center of $\pi$-twisted $G$-crossed finite semisimple linear categories.
Extending the theory of anyon condensation in 3D, my work (in collaboration with Décoppet) develops a higher-dimensional framework using étale algebras and their local modules in braided fusion 2-categories. In particular, I classify connected étale algebras in $\mathscr{Z}(\mathbf{2Vect}^\pi_G)$, which correspond to twisted $G$-crossed braided multifusion categories.
Additionally, Décoppet has shown that the Drinfeld center of any fusion 2-category is either a 4D Dijkgraaf–Witten model or a fermionic analogue. Time permitting, I will also discuss classification results for fusion 2-categories via the study of Lagrangian algebras.
Event Three: Gauge theory and skein modules
Speaker: Du Pei
Time: Dec 25 (Thur), 2:00 – 3:30PM
Location:R1610, SIMIS
Zoom Meeting ID: 813 8371 1820 Passcode: SIMIS
Abstract:
We study 3-manifold skein modules by embedding them into the Hilbert spaces of 4d N=4 super-Yang-Mills theories. Using a deformation, we give an explicit algorithm to determine the dimensions as well as the list of generators with general gauge groups when the three-manifold has reduced holonomy. We find that the dimensions are often not the same for Langlands-dual pairs beyond the A-series, for which we give a physics explanation involving chiral symmetry breaking. This approach helps to clarify the relation between the Betti version of the geometric Langlands program with the gauge-theoretic approach of Kapustin and Witten and explains why the dimensions of skein modules do not have a TQFT-like behavior.
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