Non-invertible duality defects and lattice symmetries in 2d CFTs

Generalized symmetries have become a powerful tool for understanding quantum field theory. In particular, two-dimensional conformal field theories provide an ideal setting for exploring these ideas, thanks to their solvability and rich defect algebras. This thesis precisely investigates non-invertible duality symmetries in compact boson models. After reviewing the c=1 theory and the construction of duality symmetries via discrete gauging, we analyze their action on Dp-branes through their definition in terms of Ishibashi states. We then turn to the c=2 compact boson, whose moduli space and O(2,2;Z) duality group exhibit a significantly richer structure. The central result of this work is the introduction of a systematic method for constructing non-invertible duality symmetries at rational points by exploiting the crystallographic symmetries of the underlying lattice to the compactification torus. This approach reveals a clear geometric origin for these defects. Finally, we analyze the action of duality symmetries on Dp-branes, showing that, unlike in the c=1 case, they can induce genuinely non-trivial transformations on boundary conditions.