Additional Symmetry Research Articles

Revisiting the minimal Nelson-Barr model

Abstract We revisit the minimal Nelson-Barr model for solving the strong CP problem through the idea of spontaneous CP breaking. The minimal model suffers from the quality problem, which means that the strong CP angle is generated by higher-dimensional operators and one-loop effects. Consequently, it has been considered that there is a cosmological domain wall problem and that leptogenesis does not work. We point out that just imposing an additional approximate global symmetry solves the quality problem. We also propose a simple solution to the domain wall problem and show that the thermal leptogenesis scenario works.

Sensing equivalent kinematics enables robot-assisted mirror rehabilitation training via a broaden learning system

IntroductionRobot-assisted mirror therapy has been widely developed to help remodeling of premotor cortex for patients suffering from motor disability of limbs. Nevertheless, it is difficult to achieve real-time adaptive control in robot-assisted mirror rehabilitation training, particularly for patients with varying levels of limb impairment.MethodsThis paper proposes an equivalent kinematics control framework based on the Broaden Learning System model for active robotic mirror rehabilitation, where people’s bilateral upper limbs actively perform mirror movements to enhance the impaired limb’s participation. The framework accommodates a broaden learning model from sensing multi-kinematic features to adjust the robotic damping coefficient in assisting human participants to complete mirror-symmetry training. Besides, in order to adapt to inter-patients’ variability with different disability levels, a challenge-level modification interface is also fused for safer training. This model is verified by additional symmetry indicator such as position trajectory error and force.ResultsExperimental results show that the weaker subjects can also maintain mirror movement with the stronger subjects under the help of this model and verify the performance of framework in mirror-symmetry effects and movement smoothness. This leads us to believe that the framework can safely and efficiently assist human participants in completing mirror-symmetry movement.DiscussionThe framework has the potential to improve outcomes in smoother and safer mirror-symmetry training by sensing multi-kinematic features. Future studies are necessary to involve clinical trials with actual patients.

Majoron-driven leptogenesis in gauged U(1)Lμ−Lτ model

We propose a novel leptogenesis scenario in the gauged U(1)Lμ−Lτ model. Achieving successful leptogenesis in the U(1)Lμ−Lτ symmetric phase is challenging due to the absence of a CP phase, caused by restriction from the gauge symmetry. To overcome this issue, we introduce an additional global symmetry, U(1)B−L, and a scalar field Φ responsible for breaking this symmetry. Through the kinetic misalignment mechanism, the Majoron field associated with U(1)B−L symmetry breaking has a kinetic motion in the early Universe. Subsequently, time-dependent Majoron field background induces the background CP phase dynamically, leading to successful leptogenesis in the U(1)Lμ−Lτ symmetric phase. Furthermore, Majoron itself serves as a dark matter candidate in this scenario. As one of the phenomenological applications, we consider the model that can also explain the muon g−2 anomaly. Published by the American Physical Society 2024

Can CP be conserved in the two-Higgs-doublet model?

We study the conditions under which the CP violation in the quark mixing matrix can leak into the scalar potential of the real two-Higgs-doublet model (2HDM) via divergent radiative corrections, thereby spoiling the renormalizability of the model. We show that any contributing diagram must involve 12 Yukawa-coupling insertions and a factor of the U(1)PQ-breaking scalar potential parameter λ5, thereby requiring at least six loops; this also implies that the 2HDM with only softly broken U(1)PQ is safe from divergent leaks of CP violation to all orders. We demonstrate that additional symmetries of the six-loop diagrams in the type I and II 2HDMs guarantee that all of the divergent CP-violating contributions cancel at this order. We also show that these symmetries are violated at seven loops and enumerate the classes of diagrams that can contribute to CP-violating divergences, providing evidence that the real 2HDM is theoretically inconsistent starting at the seven-loop level. Published by the American Physical Society 2024

Muon g−2 and lepton flavor violation in supersymmetric GUTs

We present a class of supersymmetric (SUSY) GUT models that can explain the apparent discrepancy between the SM predictions and experimental values of muon g−2 while providing testable signals for lepton flavor violation in charged lepton decays. Moreover, these models predict LSP neutralino abundance that is compatible with the Planck dark matter bounds. We find that scenarios in the framework of SU(4)c×SU(2)L×SU(2)R unification, with additional symmetries to explain fermion masses and neutrino oscillations, provide interesting benchmarks for the search of SUSY by correlating a possible manifestation of it in dark matter, rare lepton decays, and LHC signals. Published by the American Physical Society 2024

Linear Programming with Unitary-Equivariant Constraints

Unitary equivariance is a natural symmetry that occurs in many contexts in physics and mathematics. Optimization problems with such symmetry can often be formulated as semidefinite programs for a dp+q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d^{p+q}$$\\end{document}-dimensional matrix variable that commutes with U⊗p⊗U¯⊗q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$U^{\\otimes p} \\otimes {\\bar{U}}^{\\otimes q}$$\\end{document}, for all U∈U(d)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$U \\in \ extrm{U}(d)$$\\end{document}. Solving such problems naively can be prohibitively expensive even if p+q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p+q$$\\end{document} is small but the local dimension d is large. We show that, under additional symmetry assumptions, this problem reduces to a linear program that can be solved in time that does not scale in d, and we provide a general framework to execute this reduction under different types of symmetries. The key ingredient of our method is a compact parametrization of the solution space by linear combinations of walled Brauer algebra diagrams. This parametrization requires the idempotents of a Gelfand–Tsetlin basis, which we obtain by adapting a general method inspired by the Okounkov–Vershik approach. To illustrate potential applications of our framework, we use several examples from quantum information: deciding the principal eigenvalue of a quantum state, quantum majority vote, asymmetric cloning and transformation of a black-box unitary. We also outline a possible route for extending our method to general unitary-equivariant semidefinite programs.

Quantized Integrated Shift Effect in Multigap Topological Phases.

We show that certain three-dimensional multigap topological insulators can host quantized integrated shift photoconductivities due to bulk invariants that are defined under reality conditions imposed by additional symmetries. We recast the quantization in terms of the integrated torsion tensor and the non-Abelian Berry connection constituting Chern-Simons forms. Physically, we recognize that the topological quantization emerges purely from virtual transitions contributing to the optical response. Our findings provide another quantized electromagnetic dc response due to the nontrivial band topology, beyond the quantum anomalous Hall effect of Chern insulators and quantized circular photogalvanic effect found in Weyl semimetals.

Surprises in the theory of elasticity: pairwise atomic interactions, central forces, and Cauchy relations

Although the theory of elasticity has been well known for many years there are still some commonly accepted misconceptions that continue to be taught in solid-state physics courses. In this paper we review some of these misconceptions through a detailed study of the relationship between macroscopic and microscopic theories of elasticity in a simple-cubic crystal with one atom per primitive cell. The analysis is performed at different stages of complexity. In the first-neighbor approximation we find that the crystal is simply unstable. If pairwise interaction up to second neighbors is considered the crystal is stable but the elastic constants present additional symmetries known as Cauchy relations which are not observed experimentally. The reasons for this behavior are analyzed, pointing out that the invariance of the potential energy with respect to rotations implies necessarily that pairwise interactions must be central. Only if the atomic interactions involve the participation of 3-bodies or more, the forces are non-central and the resulting elastic tensor may be acceptable.

Self-dualities and Galois symmetries in Feynman integrals

It is well-known that all Feynman integrals within a given family can be expressed as a finite linear combination of master integrals. The master integrals naturally group into sectors. Starting from two loops, there can exist sectors made up of more than one master integral. In this paper we show that such sectors may have additional symmetries. First of all, self-duality, which was first observed in Feynman integrals related to Calabi-Yau geometries, often carries over to non-Calabi-Yau Feynman integrals. Secondly, we show that in addition there can exist Galois symmetries relating integrals. In the simplest case of two master integrals within a sector, whose definition involves a square root r, we may choose a basis (I1, I2) such that I2 is obtained from I1 by the substitution r → −r. This pattern also persists in sectors, which a priori are not related to any square root with dependence on the kinematic variables. We show in several examples that in such cases a suitable redefinition of the integrals introduces constant square roots like 3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{3} $$\\end{document}. The new master integrals are then again related by a Galois symmetry, for example the substitution 3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{3} $$\\end{document} → −3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ -\\sqrt{3} $$\\end{document}. To handle the case where the argument of a square root would be a perfect square we introduce a limit Galois symmetry. Both self-duality and Galois symmetries constrain the differential equation.

One dimensional staggered bosons, clock models, and their noninvertible symmetries

We study systems of staggered boson Hamiltonians in a one dimensional lattice and in particular how the translation symmetry by one unit in these systems is in reality a noninvertible symmetry closely related to T-duality. We also study the simplest systems of clock models derived from these staggered boson Hamiltonians. We show that the noninvertible symmetries of these lattice models together with the discrete ZN symmetry predict that these are critical points with a U(1) current algebra at c=1 and radius 2N whenever N>4. We also present an independent computation of this value that arises directly from the staggered boson variables and does not use these additional symmetries. We also present a theoretical estimate of the values of critical coupling constants away from the self-dual symmetry point in these clock models. Published by the American Physical Society 2024

Resonant multiscalar production in the generic complex singlet model in the multi-TeV region

We develop benchmarks for resonant discalar production in the generic complex singlet scalar extension of the Standard Model (SM) with no additional symmetries, which contains two new scalars. These benchmarks maximize discalar resonant production modes at future pp colliders: pp→h2→h1h1, pp→h2→h1h3, and pp→h2→h3h3, where h1 is the observed SM-like Higgs boson and h2,3 are new scalars. The decays h2→h1h3 and h2→h3h3 may be the only way to discover h3, leading to a discovery of two new scalars at once. Current LHC and projected future collider (HL-LHC, FCC-ee+HL-LHC, ILC500+HL-LHC) constraints on this model are used to produce benchmarks at the HL-LHC for h2 masses between 250 GeV and 1 TeV and a future pp collider (FCC-hh) for h2 masses between 250 GeV and 12 TeV. We update the current LHC bounds on the singlet-Higgs boson mixing angle for these benchmarks. As the mass of h2 approaches the multi-TeV region, certain limiting behaviors of the maximum rates are uncovered due to theoretical constraints on the parameters. These limits, which can be derived analytically, are BR(h2→h1h1)→0.25, BR(h2→h3h3)→0.5, and BR(h2→h1h3)→0. It can also be shown that the maximum rates of pp→h2→h1h1 and pp→h2→h3h3 approach the same value. Hence, all three h2→hihj decays are promising discovery modes for h2 masses at and below O(1 TeV), while above O(1 TeV) the decays h2→h1h1 and h2→h3h3 are more encouraging. We choose benchmark masses for h3 to produce a large range of decay signatures including multi-b, multivector boson, and multi-SM-like Higgs production. As we will show, the behavior of the maximum rates leads to the surprising conclusion that in the multi-TeV region this model may be discovered in the Higgs quartet production mode via h2→h3h3→4h1 decays before Higgs triple production is observed. The maximum di- and four Higgs production rates are similar in the multi-TeV range. Published by the American Physical Society 2024

Solving the area-length systems in discrete gravity using homotopy continuation

Abstract Area variables are intrinsic to connection formulations of general relativity, in contrast to the fundamental length variables prevalent in metric formulations. Within 4D discrete gravity, particularly based on triangulations, the area-length system establishes a relationship between area variables associated with triangles and the edge length variables. This system is comprised of polynomial equations derived from Heron’s formula, which relates the area of a triangle to its edge lengths. Using tools from numerical algebraic geometry, we study the area-length systems. In particular, we show that given the ten triangular areas of a single 4-simplex, there could be up to 64 compatible sets of edge lengths. Moreover, we show that these 64 solutions do not, in general, admit formulae in terms of the areas by analyzing the Galois group, or monodromy group, of the problem. We show that by introducing additional symmetry constraints, it is possible to obtain such formulae for the edge lengths. We take the first steps toward applying our results within discrete quantum gravity, specifically for effective spin foam models.

Neutrino Masses from Generalized Symmetry Breaking

We explore generalized global symmetries in theories of physics beyond the standard model. Theories of Z′ bosons generically contain “noninvertible” chiral symmetries, whose presence indicates a natural paradigm to break this symmetry by an exponentially small amount in an ultraviolet completion. For example, in models of gauged lepton family difference such as the phenomenologically well motivated U(1)Lμ−Lτ, there is a noninvertible lepton number symmetry which protects neutrino masses. We embed these theories in gauged non-Abelian horizontal lepton symmetries, e.g., U(1)Lμ−Lτ⊂SU(3)H, where the generalized symmetries are broken nonperturbatively by the existence of lepton family magnetic monopoles. In such theories, either Majorana or Dirac neutrino masses may be generated through quantum gauge theory effects from the charged lepton Yukawas, e.g., yν∼yτexp(−Sinst). These theories require no bevy of new fields nor additional global symmetries but are instead simple, natural, and predictive: The discovery of a lepton family Z′ at low energies will reveal the scale at which Lμ−Lτ emerges from a larger gauge symmetry. Published by the American Physical Society 2024

Symmetries and Invariant Solutions of Higher-Order Evolution Systems

In this paper, we investigate evolution systems in two components, characterized by higher-order spatial derivatives and the presence of two arbitrary functions. Our study begins with an analysis of a fourth-order system. We perform a detailed group classification and identify specific forms of the constitutive functions that allow the system to exhibit additional symmetries in addition to spatial and temporal translations. We extend these results to nth-order systems. Moreover, we derive invariant solutions for these systems. Finally, for each order n, we are able to find non-negative solutions.

Matrix stretching

Abstract We consider the tensor products of square matrices of different sizes and introduce the stretching maps, which can be viewed as a generalized matricization. Stretching maps conserve algebraic properties of the tensor product, but are not necessarily injective. Dropping the injectivity condition allows us to construct examples of stretching maps with additional symmetry properties. Furthermore, this leads to the averaging of the tensor product and possibly could be used to compress the data.

Anomalous U(1) extension of the Standard Model

We present a set of example models in which the Standard Model (SM) symmetry group is extended by a new abelian symmetry. This additional symmetry appears anomalous in the effective low-energy theory; however, the anomalies cancel out when massive chiral fermions not present in the effective low-energy theory are taken into account. These chiral fermions under the new abelian gauge group, are chosen to be vector-like under the SM symmetries, and reside in the same representations as quarks and leptons. This allows us to quantitatively determine the magnitude of tree-level interactions between three vector bosons induced in low-energy effective field theory by the integration of chiral heavy fermions. We also examine the perturbativity constraints of the theory and the ultraviolet cut-off. We conclude by highlighting possible extensions of our work.

Black hole zeroth law of the Einstein-complex scalar-Gauss-Bonnet gravity

The zeroth law of black hole mechanics asserts that the stationary black hole has a constant surface gravity on the event horizon. This study investigates the zeroth law within the Einstein-Scalar-Gauss-Bonnet gravity, particularly involving a complex scalar field (ECSGB). Assuming that the Lie derivative of the complex scalar field is proportional to itself other than stationary, and that ECSGB gravity converges to the Einstein's gravity analyticaly as the coupling constant approaches zero, as well as the minimally coupled matter fields satisfy the dominant energy condition, we demonstrate that the surface gravity remains constant over the entire event horizon without reliance on additional symmetries.

A New Fuzzy Bayesian Inference Approach for Risk Assessments

Bayesian network (BN) inference is an important statistical tool with additive symmetry. However, BN inference cannot deal with the uncertain, fuzzy, random, and conflicting information from experts’ knowledge in the process of conducting a risk assessment. To tackle this issue, a new fuzzy BN inference approach for risk assessments was proposed based on cloud model (CM), interval type-2 fuzzy set (IT2 FS), interval type-2 fuzzy logic system (IT2 FLS), modified Dempster–Shafer (D-S) evidence theory (ET), and Latin hypercube sampling (LHS) methods along the following lines. Firstly, CM was integrated into IT2 FS, and CM-based IT2 FS (CM-IT2 FS) was defined in the IT2 FLS. Secondly, modified D-S ET was utilized to determine the CM-IT2 FS-based a priori probabilities, and the CM-IT2 FS-based BN model was established. Thirdly, the CM-IT2 FS-based a priori probabilities were reduced to the CM-IT1 FS-based ones using a type reducer in the IT2 FLS, LHS was applied to propose a new fuzzy BN inference algorithm, and then, the new algorithm was used in a typical case to perform the fuzzy BN positive inference for risk prediction and the fuzzy BN reverse inference for risk sensitivity analysis. Finally, the BN inference results were analyzed using the proposed algorithm and the two common BN inference algorithms, and the effectiveness of the proposed approach was validated. It can be concluded that the proposed approach was both accurate and promising.

Holographic entanglement renormalisation for fermionic quantum matter

We demonstrate the emergence of a holographic dimension in a system of 2D non-interacting Dirac fermions placed on a torus, by studying the scaling of multipartite entanglement measures under a sequence of renormalisation group (RG) transformations applied in momentum space. Geometric measures defined in this emergent space can be related to the RG beta function of the spectral gap, hence establishing a holographic connection between the spatial geometry of the emergent spatial dimension and the entanglement properties of the boundary quantum theory. We prove, analytically, that changing the boundedness of the holographic space involves a topological transition accompanied by a critical Fermi surface in the boundary theory. We go on to show that this results in the formation of a quantum wormhole geometry that connects the UV and the IR of the emergent dimension. The additional conformal symmetry at the transition also supports a relation between the emergent metric and the stress-energy tensor. In the presence of an Aharonov–Bohm flux, the entanglement gains a geometry-independent piece which is shown to be topological, sensitive to changes in boundary conditions, and related to the Luttinger volume of the system. Upon the insertion of a strong transverse magnetic field, we show that the Luttinger volume is linked to the Chern number of the occupied single-particle Landau levels.

Multi-Unitary Complex Hadamard Matrices

We analyze the set of real and complex Hadamard matrices with additional symmetry constrains. In particular, we link the problem of existence of maximally entangled multipartite states of [Formula: see text] subsystems with [Formula: see text] levels each to the set of complex Hadamard matrices of order [Formula: see text]. To this end, we investigate possible subsets of such matrices which are, dual, strongly dual ([Formula: see text] or [Formula: see text]), two-unitary ([Formula: see text] and [Formula: see text] are unitary), or [Formula: see text]-unitary. Here [Formula: see text] denotes reshuffling of a matrix [Formula: see text] describing a bipartite system, and [Formula: see text] its partial transpose. Such matrices find several applications in quantum many-body theory, tensor networks and classification of multipartite quantum entanglement and imply a broad class of analytically solvable quantum models in [Formula: see text] dimensions.