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1. Massless fermions in uniform flux background on $T^2\times R$ : Vacuum quantum numbers from single-particle filled modes using lattice regulator

   https://doi.org/10.1103/PhysRevD.111.014502  

   Karthik, Nikhil; Narayanan, Rajamani; Romero, Ray (January 2025, Physical Review D)

   The quantum numbers of monopoles in $R^3$in the presence of massless fermions have been analyzed using a uniform flux background in $S^2\times R$coupled to fermions. An analogous study in $T^2\times R$is performed by studying the discrete symmetries of the Dirac Hamiltonian in the presence of a static uniform field on $T^2$with a total flux of $Q$in the continuum. The degenerate ground states are classified based on their transformation properties under $\frac{\pi }{2}$rotations of $T^2$that leave the background field invariant. We find that the lattice analysis with overlap fermions exactly reproduces the transformation properties of the single-particle zero modes in the continuum. Whereas the transformation properties of the single-particle negative energy states can be studied in the continuum and the lattice, we are also able to study the transformation properties and the particle number (charge) of the many-body ground state on a finite lattice, and we show that the contributions from the fully filled single-particle states cannot be ignored. Published by the American Physical Society2025 

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2. Gluon moment and parton distribution function of the pion from $N_f=2+1+1$ lattice QCD

   https://doi.org/10.1103/PhysRevD.109.114509  

   Good, William; Hasan, Kinza; Chevis, Allison; Lin, Huey-Wen (June 2024, Physical Review D)

   We present the first calculation of the pion gluon moment from lattice QCD in the continuum-physical limit. The calculation is done using clover fermions for the valence action with three pion masses, 220, 310 and 690 MeV, and three lattice spacings, 0.09, 0.12, and 0.15 fm, using ensembles generated by MILC Collaboration with $2+1+1$flavors of highly improved staggered quarks (HISQ). On the lattice, we nonperturbatively renormalize the gluon operator in RI/MOM scheme using the cluster-decomposition error reduction (CDER) technique to enhance the signal-to-noise ratio of the renormalization constant. We extrapolate the pion gluon moment to the continuum-physical limit and obtain $⟨x{⟩}_g=0.394\left(58{)}_{\mathrm{stat}+\mathrm{NPR}}\right(39{)}_{\text{mixing}}$in the $\overline{\mathrm{MS}}$scheme at 2 GeV, with first error being the statistical error and uncertainties in nonperturbative renormalization, and the second being a systematic uncertainty estimating the effect of ignoring quark mixing. Our pion gluon momentum fraction has a central value lower than two recent single-ensemble lattice-QCD results near physical pion mass but is consistent with the recent global fits by JAM and xFitter and with most QCD-model estimates. Published by the American Physical Society2024 

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3. Treelike structure of symmetry topological field theories and multisector QFTs

   https://doi.org/10.1103/PhysRevD.109.106013  

   Baume, Florent; Heckman, Jonathan J; Hübner, Max; Torres, Ethan; Turner, Andrew P; Yu, Xingyang (May 2024, Physical Review D)

   The global symmetries of a $D$-dimensional quantum field theory (QFT) can, in many cases, be captured in terms of a ( $D+1$)-dimensional symmetry topological field theory (SymTFT). In this work we construct a ( $D+1$)-dimensional theory which governs the symmetries of QFTs with multiple sectors which have connected correlators that admit a decoupling limit. The associated symmetry field theory decomposes into a SymTree, namely a treelike structure of SymTFTs fused along possibly nontopological junctions. In string-realized multisector QFTs, these junctions are smoothed out in the extradimensional geometry, as we demonstrate in examples. We further use this perspective to study the fate of higher-form symmetries in the context of holographic large $M$averaging where the topological sectors of different large $M$replicas become dressed by additional extended operators associated with the SymTree. Published by the American Physical Society2024 

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4. Scale separation on ${\mathrm{AdS}}_3\times S^3$ with and without supersymmetry

   https://doi.org/10.1103/mp1n-9vgy  

   Proust, Aymeric; Samtleben, Henning; Sezgin, Ergin (June 2025, Physical Review D)

   Six-dimensional chiral gauged Einstein-Maxwell supergravity admits a two-parameter rotating dyonic string solution whose near horizon limit is the direct product of three-dimensional Anti-De Sitter space and a squashed three-sphere $S^3$. For a particular relation between the two parameters, the solution preserves $1/2$supersymmetry. We determine the complete Kaluza-Klein spectrum of the theory around these ${\mathrm{AdS}}_3$backgrounds. For the supersymmetric backgrounds, the states organize into infinite towers of long and short multiplets of $\mathrm{OSp}\left(2\right|2)$. In a certain limit of parameters, both the supersymmetric and the nonsupersymmetric spectra exhibit scale separation. In the latter case there are five topologically massive vectors and five scalars retaining finite masses with integer conformal dimensions, and in the supersymmetric case there are supersymmetric partners with half integer conformal dimensions, while all other masses diverge. Published by the American Physical Society2025 

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5. 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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