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1. An effective field theory of magneto-elasticity

   https://doi.org/10.21468/SciPostPhys.12.5.155  

   Pavaskar, Shashin; Penco, Riccardo; Rothstein, Ira (January 2022, SciPost Physics)

   We utilize the coset construction to derive the effective field theory of magnon-phonon interactions in (anti)-ferromagnetic and ferrimagnetic insulating materials. The action is used to calculate the equations of motion which generalize theLandau-Lifshitz and stress equations to allow for magneto-acoustic couplings to all orders in the fields at lowest order in the derivative expansion. We also include the symmetry breaking effects due to Zeeman, and Dzyaloshinsky-Moriya interactions. This effective theory is a toolbox for the study of magneto-elasticphenomena from first principles. As an example we use this theory to calculate the leading order contribution to the magnon decay width dueto its the decay into phonons. 

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2. Auxiliary field deformations of (semi-)symmetric space sigma models

   https://doi.org/10.1007/JHEP01(2025)096  

   Bielli, Daniele; Ferko, Christian; Smith, Liam; Tartaglino-Mazzucchelli, Gabriele (January 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> We generalize the auxiliary field deformations of the principal chiral model (PCM) introduced in [1] and [2] to sigma models whose target manifolds are symmetric or semi-symmetric spaces, including a Wess-Zumino term in the latter case. This gives rise to a new infinite family of classically integrable ℤ₂and ℤ₄coset models of the form which are of interest in applications of integrability to worldsheet string theory and holography. We demonstrate that every theory in this infinite class admits a zero-curvature representation for its equations of motion by exhibiting a Lax connection. 

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3. Fractionalization of coset non-invertible symmetry and exotic Hall conductance

   https://doi.org/10.21468/SciPostPhys.17.3.095  

   Hsin, Po-Shen; Kobayashi, Ryohei; Zhang, Carolyn (January 2024, SciPost Physics)

   We investigate fractionalization of non-invertible symmetry in (2+1)D topological orders. We focus on coset non-invertible symmetries obtained by gauging non-normal subgroups of invertible0 $0$-form symmetries. These symmetries can arise as global symmetries in quantum spin liquids, given by the quotient of the projective symmetry group by a non-normal subgroup as invariant gauge group. We point out that such coset non-invertible symmetries in topological orders can exhibit symmetry fractionalization: each anyon can carry a “fractional charge” under the coset non-invertible symmetry given by a gauge invariant superposition of fractional quantum numbers. We present various examples using field theories and quantum double lattice models, such as fractional quantum Hall systems with charge conjugation symmetry gauged and finite group gauge theory from gauging a non-normal subgroup. They include symmetry enrichedS_3 $S_3$andO(2) $O\left(2\right)$gauge theories. We show that such systems have a fractionalized continuous non-invertible coset symmetry and a well-defined electric Hall conductance. The coset symmetry enforces a gapless edge state if the boundary preserves the continuous non-invertible symmetry. We propose a general approach for constructing coset symmetry defects using a “sandwich” construction: non-invertible symmetry defects can generally be constructed from an invertible defect sandwiched by condensation defects. The anomaly free condition for finite coset symmetry is also identified. 

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4. Gauge-fixing local H symmetry in supergravities

   https://doi.org/10.1007/JHEP12(2024)027  

   Kallosh, Renata; Samtleben, Henning; Van_Proeyen, Antoine (December 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We discuss known maximalD-dimensional supergravities of two types: type I withG/Hcoset spaces and type II derived by compactification from higher dimensions without dualization, these have less manifest symmetries. In 4Dand 6Din type I models we perform explicit gauge-fixing of localHsymmetries in unitary gauges: symmetric, Iwasawa and partial Iwasawa. In 4Dsupergravity I in symmetric gauge globalH-invariance and nonlinearly realizedG-symmetry are valid on shell, classically. The globalH-symmetry andG-symmetry in Iwasawa-type gauges in type I and in type II supergravities are not manifest, if at all present. This fact raises the issue of the gauge equivalence of the S-matrix of various gauge-fixedD-dimensional supergravities and its relation to the ones computable using superamplitude methods. 

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5. Global B(G) with adelic coefficients and transfer factors at non-regular elements

   https://doi.org/10.1007/s00209-024-03454-3  

   Bertoloni_Meli, Alexander (March 2024, Mathematische Zeitschrift)

   The goal of this paper is extend Kottwitz’s theory of B(G) for global fields. In particular, we show how to extend the definition of “B(G) with adelic coefficients” from tori to all connected reductive groups. As an application, we give an explicit construction of certain transfer factors for non-regular semisimple elements of non-quasisplit groups. This generalizes some results of Kaletha and Taibi. These formulas are used in the stabilization of the cohomology of Shimura and Igusa varieties. 

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