Nontrivial bundles and defect operators in n-form gauge theories

Abstract

Abstract In (d + 1)-dimensional 1-form nonabelian gauge theories, we classify nontrivial 0-form bundles in ℝ d , which yield configurations of D(d − 2j)-branes wrapping (d − 2j)-cycles c d−2j in Dd-branes. We construct the related defect operators U (2j−1)(c d−2j ), which are disorder operators carrying the D(d – 2j) charge. We compute the commutation relations between the defect operators and Chern-Simons operators on odd-dimensional closed manifolds, and derive the generalized Witten effect for U (2j−1)(c d−2j ). When c d−2j is not exact, U (2j−1)(c d−2j ) and U (2j−1)(– c d−2j ) can also combine into an electric (2j – 1)-form global symmetry operator, where the (2j – 1)-form is the Chern-Simons form. The dual magnetic (d – 2j)-form global symmetry is generated by the D(d – 2j) charge. We also study nontrivial 1-form bundles in (d + 1)-dimensional 2-form nonabelian gauge theories, where the defect operators are U 2 j c d − 2 j − 1 $$ {\mathcal{U}}^{(2j)}\left({c}_{d-2j-1}\right) $$ . With the field strength of the 1-form taken as the flat connection of the 2-form, we classify the topological sectors in 2-form theories.

Keywords

• Gauge Symmetry
• Global Symmetries
• Solitons Monopoles and Instantons
• Wilson
• ’t Hooft and Polyakov loops