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Register a new userHigher-form symmetries and 3-group in axion electrodynamics
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We study higher-form symmetries in a low-energy effective theory of a massless axion coupled with a photon in $(3+1)$ dimensions. It is shown that the higher-form symmetries of this system are accompanied by a semistrict 3-group (2-crossed module) structure, which can be found by the correlation functions of symmetry generators of the higher-form symmetries. We argue that the Witten effect and anomalous Hall effect in the axion electrodynamics can be described in terms of 3-group transformations.
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We investigate a higher-group structure of massless axion electrodynamics in $(3+1)$ dimensions. By using the background gauging method, we show that the higher-form symmetries necessarily have a global semistrict 3-group (2-crossed module) structure, and exhibit t Hooft anomalies of the 3-group. In particular, we find a cubic mixed t Hooft anomaly between 0-form and 1-form symmetries, which is specific to the higher-group structure.
We study higher-form symmetries and a higher group in $(3+1)$-dimensional axion electrodynamics where the axion and photon are massive. A topological field theory describing topological excitations with the axion-photon coupling is obtained in the low energy limit, in which higher-form symmetries are specified. By using intersections of the symmetry generators, we find that the worldvolume of an axionic domain wall is topologically ordered. We further specify the underlying mathematical structure elegantly describing all salient features of the theory to be a 4-group.
We study higher-form global symmetries and a higher-group structure of a low-energy limit of $(3+1)$-dimensional axion electrodynamics in a gapped phase described by a topological action. We argue that the higher-form symmetries should have a semi-strict 4-group (3-crossed module) structure by consistency conditions of couplings of the topological action to background gauge fields for the higher-form symmetries. We find possible t Hooft anomalies for the 4-group global symmetry, and discuss physical consequences.
We study higher-form symmetries in 5d quantum field theories, whose charged operators include extended operators such as Wilson line and t Hooft operators. We outline criteria for the existence of higher-form symmetries both from a field theory point of view as well as from the geometric realization in M-theory on non-compact Calabi-Yau threefolds. A geometric criterion for determining the higher-form symmetry from the intersection data of the Calabi-Yau is provided, and we test it in a multitude of examples, including toric geometries. We further check that the higher-form symmetry is consistent with dualities and is invariant under flop transitions, which relate theories with the same UV-fixed point. We explore extensions to higher-form symmetries in other compactifications of M-theory, such as $G_2$-holonomy manifolds, which give rise to 4d $mathcal{N}=1$ theories.
We study the Casimir effect in axion electrodynamics. A finite $theta$-term affects the energy dispersion relation of photon if $theta$ is time and/or space dependent. We focus on a special case with linearly inhomogeneous $theta$ along the $z$-axis. Then we demonstrate that the Casimir force between two parallel plates perpendicular to the $z$-axis can be either attractive or repulsive, dependent on the gradient of $theta$. We call this repulsive component in the Casimir force induced by inhomogeneous $theta$ the anomalous Casimir effect.
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