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Non-invertible Symmetry Enforced Gaplessness

CMSA EVENTS: CMSA QUANTUM MATTER IN MATH & PHYSICS SEMINAR

When: February 10, 2023
10:30 am - 11:30 am
Where: Virtually
Speaker: Ho Tat Lam - MIT

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.


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