Built on

W. Ji, S.-H. Shao and X.-G. Wen, Topological Transition on the Conformal Manifold , Phys. Rev. Res. 2
Original
1909
Earlier work this paper cites.
R. Thorngren and Y. Wang, Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases , 1912.02817
Original
1912
Earlier work this paper cites.
E. P. Verlinde, Fusion Rules and Modular Transformations in 2D Conformal Field Theory , Nucl. Phys. B 300
1988
Earlier work this paper cites.
E. Witten, On S duality in Abelian gauge theory , Selecta Math. 1
1995
Earlier work this paper cites.
V. Petkova and J. Zuber, Generalized twisted partition functions , Phys. Lett. B 504
2001
Earlier work this paper cites.
J. Fuchs, I. Runkel and C. Schweigert, TFT construction of RCFT correlators 1. Partition functions , Nucl. Phys. B 646
2002
Earlier work this paper cites.
J. Frohlich, J. Fuchs, I. Runkel and C. Schweigert, Kramers-Wannier duality from conformal defects , Phys. Rev. Lett. 93
2004
Earlier work this paper cites.
J. Frohlich, J. Fuchs, I. Runkel and C. Schweigert, Duality and defects in rational conformal field theory , Nucl. Phys. B 763
2007
Earlier work this paper cites.

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2022

Exploring Non-Invertible Symmetries in Free Theories

Niro, Pierluigi, Roumpedakis, Konstantinos, Sela, Orr

Understand

Symmetries corresponding to local transformations of the fundamental fields that leave the action invariant give rise to (invertible) topological defects, which obey group-like fusion rules.

One can construct more general (codimension-one) topological defects by specifying a map between gauge-invariant operators from one side of the defect and such operators on the other side.
In this work, we apply such construction to Maxwell theory in four dimensions and to the free compact scalar theory in two dimensions.
In the case of Maxwell theory, we show that a topological defect that mixes the field strength $F$ and its Hodge dual $\star F$ can be at most an $SO(2)$ rotation.

Built on

W. Ji, S.-H. Shao and X.-G. Wen, Topological Transition on the Conformal Manifold , Phys. Rev. Res. 2
Original
1909
Earlier work this paper cites.
R. Thorngren and Y. Wang, Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases , 1912.02817
Original
1912
Earlier work this paper cites.
E. P. Verlinde, Fusion Rules and Modular Transformations in 2D Conformal Field Theory , Nucl. Phys. B 300
1988
Earlier work this paper cites.
E. Witten, On S duality in Abelian gauge theory , Selecta Math. 1
1995
Earlier work this paper cites.
V. Petkova and J. Zuber, Generalized twisted partition functions , Phys. Lett. B 504
2001
Earlier work this paper cites.
J. Fuchs, I. Runkel and C. Schweigert, TFT construction of RCFT correlators 1. Partition functions , Nucl. Phys. B 646
2002
Earlier work this paper cites.
J. Frohlich, J. Fuchs, I. Runkel and C. Schweigert, Kramers-Wannier duality from conformal defects , Phys. Rev. Lett. 93
2004
Earlier work this paper cites.
J. Frohlich, J. Fuchs, I. Runkel and C. Schweigert, Duality and defects in rational conformal field theory , Nucl. Phys. B 763
2007
Earlier work this paper cites.