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Higgsing Transitions from Topological Field Theory & Non-Invertible Symmetry in Chern-Simons Matter Theories
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Higgsing Transitions from Topological Field Theory & Non-Invertible Symmetry in Chern-Simons Matter Theories
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Non-invertible one-form symmetries are naturally realized in (2+1)d topological quantum field theories. In this work, we consider the potential realization of such symmetries in (2+1)d conformal field theories, investigating whether gapless systems can exhibit similar symmetry structures. To that end, we discuss transitions between topological field theories in (2+1)d which are driven by the Higgs mechanism in Chern-Simons matter theories. Such transitions can be modeled mesoscopically by filling spacetime with a lattice-shaped domain wall network separating the two topological phases. Along the domain walls are coset conformal field theories describing gapless chiral modes trapped by a locally vanishing scalar mass. In this presentation, the one-form symmetries of the transition point can be deduced by using anyon condensation to track lines through the domain wall network. Using this framework, we discuss a variety of concrete examples of non-invertible one-form symmetry in fixed-point theories. For instance, $SU(k)_{2}$ Chern-Simons theory coupled to a scalar in the symmetric tensor representation produces a transition from an $SU(k)_{2}$ phase to an $SO(k)_{4}$ phase and has non-invertible one-form symmetry $PSU(2)_{-k}$ at the fixed point. We also discuss theories with $Spin(2N)$ and $E_{7}$ gauge groups manifesting other patterns of non-invertible one-form symmetry. In many of our examples, the non-invertible one-form symmetry is not a modular invariant TQFT on its own and thus is an intrinsic part of the fixed-point dynamics.
Forward citations
Cited by 7 Pith papers
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A general 2+1d transition theory out of a topological phase, driven by one Abelian anyon, is constructed and shown to depend on a single integer parameter, with p=0 giving gauging.
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Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries
Gapped phases dual to massless RG flows in 2D CFTs exhibit unusual ordering via spontaneous breaking of non-group-like symmetries and are characterized using smeared boundary CFTs applied to smeared Ishibashi states.
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Constructs Z_N extended fusion rings and modular partition functions for nonanomalous subgroups, extending to multicomponent systems and orbifoldings in CFTs.
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An algebraic RG formalism for topological orders uses ideals in fusion rings to encode noninvertible symmetries and condensation rules between anyons.
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Framework using smeared boundary CFTs classifies gapped phases dual to massless RG flows, showing they often spontaneously break non-group-like symmetries via unusual module structures outside standard boundary critic...
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