Abstract: Duality connects seemingly different theories and their phases, and when a theory remains unchanged under duality, it is self-dual. Self-duality is a valuable tool for studying quantum critical points, as it constrains the theory to the phase boundary. In this talk, I will first explore the self-duality in 2+1d deconfined quantum criticality described by $N_f=2$ QED3 and its application in investigating the multicritical points. In the second part, I will talk about the mathematical structure of the self-duality in 1+1d. As an interesting example, I will discuss the self-duality in 1+1d conformal field theory and the self-duality under gauging the non-invertible self-duality symmetry. The talk is mainly based on arXiv:2104.05147 and arXiv:2310.19867.
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