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1. Gravity as a gapless phase and biform symmetries

   https://doi.org/10.1007/JHEP02(2023)151  

   Hinterbichler, Kurt; Hofman, Diego M.; Joyce, Austin; Mathys, Grégoire (February 2023, Journal of High Energy Physics)

   A bstract We study effective field theories (EFTs) enjoying (maximal) biform symmetries. These are defined by the presence of a conserved (electric) current that has the symmetries of a Young tableau with two columns of equal length. When these theories also have a topological (magnetic) biform current, its conservation law is anomalous. We go on to show that this mixed anomaly uniquely fixes the two-point function between the electric and magnetic currents. We then perform a Källén-Lehmann spectral decomposition of the current-current correlator, proving that there is a massless mode in the spectrum, whose masslessness is protected by the anomaly. Furthermore, the anomaly gives rise to a universal form of the EFT whose most relevant term — which resembles the linear Einstein action — dominates the infrared physics. As applications of this general formalism, we study the theories of a Galileon superfluid and linearized gravity. Thus, one can view the masslessness of the graviton as being protected by the anomalous biform symmetries. The associated EFT provides an organizing principle for gravity at low energies in terms of physical symmetries, and allows interactions consistent with linearized diffeomorphism invariance. These theories are not ultraviolet-complete — the relevant symmetries can be viewed as emergent — nor do they include the nonlinearities necessary to make them fully diffeomorphism invariant, so there is no contradiction with the expectation that quantum gravity cannot have any global symmetries. 

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2. Framed 𝔼n-algebras from quantum field theory

   https://doi.org/10.1142/S0129055X23500113  

   Elliott, Chris; Gwilliam, Owen (August 2023, Reviews in Mathematical Physics)

   This paper addresses the following question: given a topological quantum field theory on [Formula: see text] built from an action functional, when is it possible to globalize the theory so that it makes sense on an arbitrary smooth oriented n-manifold? We study a broad class of topological field theories — those of AKSZ type — and obtain an explicit condition for the vanishing of the framing anomaly, i.e. the obstruction to performing this globalization procedure. We also interpret our results in terms of identifying the observables as an algebra over the framed little n-disks operad. Our analysis uses the BV formalism for perturbative field theory and the notion of factorization homology. 

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3. Entanglement entropy of a color flux tube in (2+1)D Yang-Mills theory

   https://doi.org/10.1007/JHEP12(2024)177  

   Amorosso, Rocco; Syritsyn, Sergey; Venugopalan, Raju (December 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We construct a novel flux tube entanglement entropy (FTE²), defined as the excess entanglement entropy relative to the vacuum of a region of color flux stretching between a heavy quark-anti-quark pair in pure gauge Yang-Mills theory. We show that FTE²can be expressed in terms of correlators of Polyakov loops, is manifestly gauge-invariant, and therefore free of the ambiguities in computations of the entanglement entropy in gauge theories related to the choice of the center algebra. Employing the replica trick, we compute FTE²for SU(2) Yang-Mills theory in (2+1)D and demonstrate that it is finite in the continuum limit. We explore the properties of FTE²for a half-slab geometry, which allows us to vary the width and location of the slab, and the extent to which the slab cross-cuts the color flux tube. Following the intuition provided by computations of FTE²in (1+1)D, and in a thin string model, we examine the extent to which our FTE²results can be interpreted as the sum of an internal color entropy and a vibrational entropy corresponding to the transverse excitations of the string. 

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4. 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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5. Three-loop effective potential for softly broken supersymmetry

   https://doi.org/10.1103/PhysRevD.109.015019  

   Martin, Stephen P (January 2024, Physical Review D)

   The effective potential has been previously calculated through three-loop order, in Landau gauge, for a general renormalizable theory using dimensional regularization. However, dimensional regularization is not appropriate for softly broken supersymmetric gauge theories, because it explicitly violates supersymmetry. In this paper, I obtain the three-loop effective potential using a supersymmetric regulator based on dimensional reduction. Checks follow from the vanishing of the effective potential in examples with supersymmetric vacua, and from renormalization scale invariance in examples for which supersymmetry is broken, either spontaneously or explicitly by soft terms. As byproducts, I obtain the three-loop Landau gauge anomalous dimension for the scalar component of a chiral supermultiplet, and the beta function for the field-independent vacuum energy. 

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