Luca V. Delacrétaz, Diego M. Hofman, Grégoire Mathys
SciPost Phys. 8, 047 (2020) ·
published 26 March 2020

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We recast superfluid hydrodynamics as the hydrodynamic theory of a system with an emergent anomalous higherform symmetry. The higherform charge counts the winding planes of the superfluid — its constitutive relation replaces the Josephson relation of conventional superfluid hydrodynamics. This formulation puts all hydrodynamic equations on equal footing. The anomalous Ward identity can be used as an alternative starting point to prove the existence of a Goldstone boson, without reference to spontaneous symmetry breaking. This provides an alternative characterization of Landau phase transitions in terms of higherform symmetries and their anomalies instead of how the symmetries are realized. This treatment is more general and, in particular, includes the case of BKT transitions. As an application of this formalism we construct the hydrodynamic theories of conventional (0form) and 1form superfluids.
Dionysios Anninos, Diego M. Hofman, Jorrit Kruthoff
SciPost Phys. 7, 054 (2019) ·
published 23 October 2019

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We consider quantum field theory near the horizon of an extreme Kerr black hole. In this limit, the dynamics is well approximated by a tower of electrically charged fields propagating in an $SL(2,\mathbb{R})$ invariant AdS$_2$ geometry endowed with a constant, symmetry preserving background electric field. At large charge the fields oscillate near the AdS$_2$ boundary and no longer admit a standard Dirichlet treatment. From the Kerr black hole perspective, this phenomenon is related to the presence of an ergosphere. We discuss a definition for the quantum field theory whereby we 'UV' complete AdS$_2$ by appending an asymptotically two dimensional Minkowski region. This allows the construction of a novel observable for the fluxcarrying modes that resembles the standard flat space Smatrix. We relate various features displayed by the highly charged particles to the principal series representations of $SL(2,\mathbb{R})$. These representations are unitary and also appear for massive quantum fields in dS$_2$. Both fermionic and bosonic fields are studied. We find that the free charged massless fermion is exactly solvable for general background, providing an interesting arena for the problem at hand.
SciPost Phys. 6, 006 (2019) ·
published 14 January 2019

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We discuss generalized global symmetries and their breaking. We extend Goldstone's theorem to higher form symmetries by showing that a perimeter law for an extended $p$dimensional defect operator charged under a continuous $p$form generalized global symmetry necessarily results in a gapless mode in the spectrum. We also show that a $p$form symmetry in a conformal theory in $2(p+1)$ dimensions has a free realization. In four dimensions this means any 1form symmetry in a $CFT_4$ can be realized by free Maxwell electrodynamics, i.e. the current can be photonized. The photonized theory has infinitely many conserved 0form charges that are constructed by integrating the symmetry currents against suitable 1forms. We study these charges by developing a twistorbased formalism that is a 4d analogue of the usual holomorphic complex analysis familiar in $CFT_2$. The charges are shown to obey an algebra with central extension, which is an analogue of the 2d Abelian KacMoody algebra for higher form symmetries.
SciPost Phys. 4, 005 (2018) ·
published 29 January 2018

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We study the holographic duals of fourdimensional field theories with 1form global symmetries, both discrete and continuous. Such higherform global symmetries are associated with antisymmetric tensor gauge fields in the bulk. Various different realizations are possible: we demonstrate that a Maxwell action for the bulk antisymmetric gauge field results in a nonconformal field theory with a marginally running doubletrace coupling. We explore its hydrodynamic behavior at finite temperature and make contact with recent symmetrybased formulations of magnetohydrodynamics. We also argue that discrete global symmetries on the boundary are dual to discrete gauge theories in the bulk. Such gauge theories have a bulk ChernSimons description: we clarify the conventional 0form case and work out the 1form case. Depending on boundary conditions, such discrete symmetries may be embedded in continuous higherform symmetries that are spontaneously broken. We study the resulting boundary Goldstone mode, which in the 1form case may be thought of as a boundary photon. Our results clarify how the global form of the field theory gauge group is encoded in holography. Finally, we study the interplay of Maxwell and ChernSimons terms put together. We work out the operator content and demonstrate the existence of new backreacted anisotropic scaling solutions that carry higherform charge.