IAS CMP/QFT Group Meeting

Abstract: This talk explores the connection between global symmetries and the theory of classical and quantum error-correcting codes. When the symmetry is Abelian, we show that classical isotropic (self-orthogonal) codes emerge naturally as non-anomalous subgroups of the global symmetry. Gauging this symmetry, equivalently, the Abelian anyon condensation in the associated SymTFT, is then described in the language of quantum stabilizer codes. The code-based picture highlights the role of modular invariance in the SymTFT framework, providing an efficient way to count all Lagrangian subgroups and, in 2d, establishing a direct connection with the modular bootstrap program.

In the second part of the talk, I present ongoing work extending the connection to codes beyond the Abelian setting. I will formulate a conjecture that the Lagrangian algebra objects can be defined as modular invariants at asymptotically high genus, and use it to count the Lagrangian algebra objects in tensor powers of the Ising modular tensor category.