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Non-invertible Symmetry Enforced Gaplessness
February 10, 2023 @ 10:30 am - 11:30 am
![](https://cmsa.fas.harvard.edu/media/CMSA-QMMP-02.10.23.png)
Quantum Matter Seminar
Speaker: Ho Tat Lam (MIT)
Title: Non-invertible Symmetry Enforced Gaplessness
Abstract: Quantum systems in 3+1-dimensions that are invariant under gauging a one-form symmetry enjoy novel non-invertible duality symmetries encoded by topological defects. These symmetries are renormalization group invariants which constrain infrared dynamics. We show that such non-invertible symmetries often forbid a symmetry-preserving vacuum state with a gapped spectrum, leaving only two possibilities for the infrared dynamics: a gapless state or spontaneous breaking of the non-invertible symmetries. These non-invertible symmetries are realized in lattice gauge theories, which serve to illustrate our results.