<p>We consider codimension-one defects in the theory of <i>d</i> compact scalars on a two-dimensional worldsheet, acting linearly by mixing the scalars and their duals. By requiring that the defects are topological, we find that they correspond to a non-Abelian zero-form symmetry acting on the fields as elements of O(<i>d</i>; ℝ) × O(<i>d</i>; ℝ), and on momentum and winding charges as elements of O(<i>d, d</i>; ℝ). When the latter action is rational, we prove that it can be realized by combining gauging of non-anomalous discrete subgroups of the momentum and winding U(1) symmetries, and elements of the O(<i>d, d</i>; ℤ) duality group, such that the couplings of the theory are left invariant. Generically, these defects map local operators into non-genuine operators attached to lines, thus corresponding to a non-invertible symmetry. We confirm our results within a Lagrangian description of the non-invertible topological defects associated to the O(<i>d, d</i>; ℚ) action on charges, giving a natural explanation of the rationality conditions. Finally, we apply our findings to toroidal compactifications of bosonic string theory. In the simplest non-trivial case, we discuss the selection rules of these non-invertible symmetries, verifying explicitly that they are satisfied on a worldsheet of higher genus.</p>

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Non-invertible defects on the worldsheet

  • Sriram Bharadwaj,
  • Pierluigi Niro,
  • Konstantinos Roumpedakis

摘要

We consider codimension-one defects in the theory of d compact scalars on a two-dimensional worldsheet, acting linearly by mixing the scalars and their duals. By requiring that the defects are topological, we find that they correspond to a non-Abelian zero-form symmetry acting on the fields as elements of O(d; ℝ) × O(d; ℝ), and on momentum and winding charges as elements of O(d, d; ℝ). When the latter action is rational, we prove that it can be realized by combining gauging of non-anomalous discrete subgroups of the momentum and winding U(1) symmetries, and elements of the O(d, d; ℤ) duality group, such that the couplings of the theory are left invariant. Generically, these defects map local operators into non-genuine operators attached to lines, thus corresponding to a non-invertible symmetry. We confirm our results within a Lagrangian description of the non-invertible topological defects associated to the O(d, d; ℚ) action on charges, giving a natural explanation of the rationality conditions. Finally, we apply our findings to toroidal compactifications of bosonic string theory. In the simplest non-trivial case, we discuss the selection rules of these non-invertible symmetries, verifying explicitly that they are satisfied on a worldsheet of higher genus.