Non-invertible symmetries in Non-Linear Sigma Models

By this point it is fairly well known that symmetries can be generalised in many ways, including the case where the topological operator that generates the symmetry does not have an inverse. A family of constructions of such type of defects are intimately related to dualities, with examples ranging from high-low temperature duality in the Ising model to S-duality in N=4 SYM.  In this talk I will discuss the construction of non-invertible defects based on T-duality in 2 dimensions, generalising the well known defect of the free compact boson to (almost) arbitrary Non-Linear Sigma Models with Wess-Zumino term. Our approach highlights the microscopic origin of the topological terms that are responsible for the non-invertibility of the defect, and it also circumvents some limitations that are usually present when topological lines are discussed in a more categorical language: for example, the CFT doesn’t need to be rational, nor there is a need for the target space to include cycles so as to have winding charges.

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