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1. Foliated fracton order from gauging subsystem symmetries

   https://doi.org/10.21468/SciPostPhys.6.4.041  

   Shirley, Wilbur; Slagle, Kevin; Chen, Xie (January 2019, SciPost Physics)

   Based on several previous examples, we summarize explicitly thegeneral procedure to gauge models with subsystem symmetries, which aresymmetries with generators that have support within a sub-manifold ofthe system. The gauging process can be applied to any local quantummodel on a lattice that is invariant under the subsystem symmetry. Wefocus primarily on simple 3D paramagnetic states with planar symmetries.For these systems, the gauged theory may exhibit foliated fracton orderand we find that the species of symmetry charges in the paramagnetdirectly determine the resulting foliated fracton order. Moreover, wefind that gauging linear subsystem symmetries in 2D or 3D models resultsin a self-duality similar to gauging global symmetries in 1D. 

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2. Generalized symmetries in 2D from string theory: SymTFTs, intrinsic relativeness, and anomalies of non-invertible symmetries

   https://doi.org/10.1007/JHEP11(2024)004  

   Franco, Sebastián; Yu, Xingyang (November 2024, Journal of High Energy Physics)

   Generalized global symmetries, in particular non-invertible and categorical symmetries, have become a focal point in the recent study of quantum field theory (QFT). In this paper, we investigate aspects of symmetry topological field theories (SymTFTs) and anomalies of non-invertible symmetries for 2D QFTs from a string theory perspective. Our primary focus is on an infinite class of 2D QFTs engineered on D1-branes probing toric Calabi-Yau 4-fold singularities. We derive 3D SymTFTs from the topological sector of IIB supergravity and discuss the resulting 2D QFTs, which can be intrinsically relative or absolute. For intrinsically relative QFTs, we propose a sufficient condition for them to exist. For absolute QFTs, we show that they exhibit non-invertible symmetries with an elegant brane origin. Furthermore, we find that these non-invertible symmetries can suffer from anomalies, which we discuss from a top-down perspective. Explicit examples are provided, including theories for including theories for Y(p,k)(ℙ2), Y(2,0)(ℙ1×ℙ1), and ℂ4/ℤ4 geometries. 

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3. Quantum symmetries in orbifolds and decomposition

   https://doi.org/10.1007/JHEP02(2022)108  

   Robbins, Daniel G.; Sharpe, Eric; Vandermeulen, Thomas (February 2022, Journal of High Energy Physics)

   A bstract In this paper, we introduce a new set of modular-invariant phase factors for orbifolds with trivially-acting subgroups, analogous to discrete torsion and generalizing quantum symmetries. After describing their basic properties, we generalize decomposition to include orbifolds with these new phase factors, making a precise proposal for how such orbifolds are equivalent to disjoint unions of other orbifolds without trivially-acting subgroups or one-form symmetries, which we check in numerous examples. 

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4. Symmetries as Ground States of Local Superoperators: Hydrodynamic Implications

   https://doi.org/10.1103/PRXQuantum.5.040330  

   Moudgalya, Sanjay; Motrunich, Olexei I (November 2024, PRX Quantum)

   Symmetry algebras of quantum many-body systems with locality can be understood using commutant algebras, which are defined as algebras of operators that commute with a given set of local operators. In this work, we show that these symmetry algebras can be expressed as frustration-free ground states of a local superoperator, which we refer to as a “super-Hamiltonian.” We demonstrate this for conventional symmetries such as ${\mathbb{Z}}_2$, $U\left(1\right)$, and $SU\left(2\right)$, where the symmetry algebras map to various kinds of ferromagnetic ground states, as well as for unconventional ones that lead to weak ergodicity-breaking phenomena of Hilbert-space fragmentation (HSF) and quantum many-body scars. In addition, we show that the low-energy excitations of this super-Hamiltonian can be understood as approximate symmetries, which in turn are related to slowly relaxing hydrodynamic modes in symmetric systems. This connection is made precise by relating the super-Hamiltonian to the superoperator that governs the operator relaxation in noisy symmetric Brownian circuits and this physical interpretation also provides a novel interpretation for Mazur bounds for autocorrelation functions. We find examples of gapped (gapless) super-Hamiltonians indicating the absence (presence) of slow modes, which happens in the presence of discrete (continuous) symmetries. In the gapless cases, we recover hydrodynamic modes such as diffusion, tracer diffusion, and asymptotic scars in the presence of $U\left(1\right)$symmetry, HSF, and a tower of quantum scars, respectively. In all, this demonstrates the power of the commutant-algebra framework in obtaining a comprehensive understanding of exact symmetries and associated approximate symmetries and hydrodynamic modes, and their dynamical consequences in systems with locality. Published by the American Physical Society2024 

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5. Reduction of symmetries of simple hybrid mechanical systems,

   Irazu, M; Colombo, L; Bloch, A (December 2021, IFACPapersOnLine)

   Abstract: This paper investigates reduction by symmetries in simple hybrid mechanical systems, in particular, symplectic and Poisson reduction for simple hybrid Hamiltonian and Lagrangian systems. We give general conditions for whether it is possible to perform a symplectic reduction for simple hybrid Lagrangian system under a Lie group of symmetries and we also provide sufficient conditions for perform 

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