Discrete Symmetry Research Articles

Topological Strings on Non-commutative Resolutions

In this paper we propose a definition of torsion refined Gopakumar–Vafa (GV) invariants for Calabi–Yau threefolds with terminal nodal singularities that do not admit Kähler crepant resolutions. Physically, the refinement takes into account the charge of five-dimensional BPS states under a discrete gauge symmetry in M-theory. We propose a mathematical definition of the invariants in terms of the geometry of all non-Kähler crepant resolutions taken together. The invariants are encoded in the A-model topological string partition functions associated to non-commutative (nc) resolutions of the Calabi–Yau. Our main example will be a singular degeneration of the generic Calabi–Yau double cover of P3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {P}}^3$$\\end{document} and leads to an enumerative interpretation of the topological string partition function of a hybrid Landau–Ginzburg model. Our results generalize a recent physical proposal made in the context of torus fibered Calabi–Yau manifolds by one of the authors and clarify the associated enumerative geometry.

Imperfect Axion Precludes the Domain Wall Problem.

The QCD axion needs not be an exact pseudoscalar for solving the strong CP problem. Its imperfectness can play a profound role cosmologically. We propose effective operators, where the Peccei-Quinn field linearly couples to standard model particles, provide a dynamical solution to the domain wall problem that prevails in postinflationary axion models with discrete symmetry. Such interactions generate a thermal potential that drives the axion field to a universal value throughout the Universe at high temperatures thus preventing the birth of domain walls when the QCD potential switches on. We discuss generic conditions for this mechanism to work and several concrete examples. Combining with existing electric dipole moment and fifth force constraints, a lower bound on the axion mass is obtained around 10^{-5} eV. Our findings make a strong case for complementary axion searches with both quality preserving and violating interactions.

Emergent strong zero mode through local Floquet engineering

Periodically driven quantum systems host exotic phenomena that often do not have any analog in undriven systems. Floquet prethermalization and dynamical freezing of certain observables, via the emergence of conservation laws, are realized by controlling the drive frequency. Recent experimental developments in synthetic quantum matter, such as superconducting qubits and cold atoms, have opened avenues for implementing local Floquet engineering which can achieve spatially modulated quantum control of states. Here, we uncover the novel memory effects of local periodic driving in a nonintegrable spin-half staggered Heisenberg chain. For a boundary-driven protocol at the dynamical freezing frequency, we show the formation of an approximate strong zero mode, a prethermal quasilocal operator, due to the emergence of a discrete global Z2 symmetry. This is captured by constructing an accurate effective Floquet Hamiltonian using a higher-order partially resummed Floquet-Magnus expansion. The lifetime of the boundary spin can be exponentially enhanced by enlarging the set of suitably chosen driven sites. We demonstrate that in the asymptotic limit, achieved by increasing the number of driven sites, a strong zero mode emerges, where the lifetime of the boundary spin grows exponentially with system size. The nonlocal processes in the Floquet Hamiltonian play a pivotal role in the total freezing of the boundary spin in the thermodynamic limit. The novel dynamics of the boundary spin is accompanied by a rich structure of entanglement in the Floquet eigenstates where specific bipartitions yield an area-law scaling while the entanglement for random bipartitions scales as a volume-law. Our work addresses the long-standing question of the existence of a strong zero mode in a nonintegrable model and elucidates the complex nature of thermalization in locally driven systems. Published by the American Physical Society 2024

Fluxbranes, generalized symmetries, and Verlinde’s metastable monopole

The stringy realization of generalized symmetry operators involves wrapping “branes at infinity”. We argue that in the case of continuous (as opposed to discrete) symmetries, the appropriate objects are fluxbranes. We use this perspective to revisit the phase structure of Verlinde’s monopole, a proposed particle satisfies the Bogomol’nyi-Prasad-Sommerfield (BPS) condition when gravity is decoupled, but is non-BPS and metastable when gravity is switched on. Geometrically, this monopole is obtained from branes wrapped on locally stable but globally trivial cycles of a compactification geometry. The fluxbrane picture allows us to characterize electric (respectively magnetic) confinement (respectively screening) in the 4D theory as a result of monopole decay. In the presence of the fluxbrane, this decay also creates lower-dimensional fluxbranes, which in the field theory is interpreted as the creation of an additional topological field theory sector. Published by the American Physical Society 2024

RG flows and fixed points of O(N)r models

By means of ϵ and large N expansions, we study generalizations of the O(N) model where the fundamental fields are tensors of rank r rather than vectors, and where the global symmetry (up to additional discrete symmetries and quotients) is O(N)r, focusing on the cases r ≤ 5. Owing to the distinct ways of performing index contractions, these theories contain multiple quartic operators, which mix under the RG flow. At all large N fixed points, melonic operators are absent and the leading Feynman diagrams are bubble diagrams, so that all perturbative fixed points can be readily matched to full large N solutions obtained from Hubbard-Stratonovich transformations. The family of fixed points we uncover extend to arbitrary higher values of r, and as their number grows superexponentially with r, these theories offer a vast generalization of the critical O(N) model.We also study sextic O(N)r theories, whose large N limits are obscured by the fact that the dominant Feynman diagrams are not restricted to melonic or bubble diagrams. For these theories the large N dynamics differ qualitatively across different values of r, and we demonstrate that the RG flows possess a numerous and diverse set of perturbative fixed points beginning at rank four.

Direct bounds on Left-Right gauge boson masses at LHC Run 2

While the third run of the Large Hadron Collider (LHC) is ongoing, the underlying theory that extends the Standard Model remains so far unknown. Left-Right Models (LRMs) introduce a new gauge sector, and can restore parity symmetry at high enough energies. If LRMs are indeed realized in nature, the mediators of the new weak force can be searched for in colliders via their direct production. We recast existing experimental limits from the LHC Run 2 and derive generic bounds on the masses of the heavy LRM gauge bosons. As a novelty, we discuss the dependence of the WR and ZR total width on the LRM scalar content, obtaining model-independent bounds within the specific realizations of the LRM scalar sectors analysed here. These bounds avoid the need to detail the spectrum of the scalar sector, and apply in the general case where no discrete symmetry is enforced. Moreover, we emphasize the impact on the WR production at LHC of general textures of the right-handed quark mixing matrix without manifest left-right symmetry. We find that the WR and ZR masses are constrained to lie above 2 TeV and 4 TeV, respectively.

Quantum gravity effects on dark matter and gravitational waves

We explore how quantum gravity effects, manifested through the breaking of discrete symmetry responsible for both dark matter and domain walls, can have observational effects through cosmic microwave background observations and gravitational waves. To illustrate the idea we consider a simple model with two scalar fields and two Z2 symmetries, one being responsible for dark matter stability, and the other spontaneously broken and responsible for domain walls, where both symmetries are assumed to be explicitly broken by quantum gravity effects. We show the recent gravitational wave spectrum observed by several pulsar timing array projects can help constrain such effects. Published by the American Physical Society 2024

Capturing the edge of chaos as a spectral submanifold in pipe flows

An extended turbulent state can coexist with the stable laminar state in pipe flows. We focus here on short pipes with additional discrete symmetries imposed. In this case, the boundary between the coexisting basins of attraction, often called the edge of chaos, is the stable manifold of an edge state, which is a lower-branch travelling wave solution. We show that a low-dimensional submanifold of the edge of chaos can be constructed from velocity data using the recently developed theory of spectral submanifolds (SSMs). These manifolds are the unique smoothest nonlinear continuations of non-resonant spectral subspaces of the linearized system at stationary states. Using very low-dimensional SSM-based reduced-order models, we predict transitions to turbulence or laminarization for velocity fields near the edge of chaos.

Modular flavor models with positive modular weights: a new lepton model building

We propose an interesting assignment of positive modular weights for fields in a modular non-Abelian discrete flavor symmetry. By this assignment, we can construct inverse seesaw and linear seesaw models without any additional symmetries which possess good testability in current experiments. At first, we discuss possibilities for positive modular weights from a theoretical point of view. Then we show concrete examples of inverse seesaw and linear seesaw scenarios applying modular A4 symmetry as examples and demonstrate some predictions as well as consistency with experimental results such as neutrino masses and mixings.

Vortex solitons in topological disclination lattices.

The existence of thresholdless vortex solitons trapped at the core of disclination lattices that realize higher-order topological insulators is reported. The study demonstrates the interplay between nonlinearity and higher-order topology in these systems, as the vortex state in the disclination lattice bifurcates from its linear topological counterpart, while the position of its propagation constant within the bandgap and localization can be controlled by its power. It is shown that vortex solitons are characterized by strong field confinement at the disclination core due to their topological nature, leading to enhanced stability. Simultaneously, the global discrete rotational symmetry of the disclination lattice imposes restrictions on the maximal possible topological charge of such vortex solitons. The results illustrate the strong stabilizing action that topologically nontrivial structures may exert on excited soliton states, opening new prospects for soliton-related applications.

Chirp asymmetry as an analogue of leptogenesis

The effective conjugation symmetry that arises in the rotating wave frame is the analogue of the charge conjugation symmetry in field theory. Breaking this effective conjugation symmetry leads to asymmetries between up-chirped and down-chirped excitation in quantum optical systems. We use semiclassical quantum optics theory to describe these processes and experimentally characterize the asymmetry in the optical response in chirped, two-color saturated absorption spectroscopy (SAS) in an atomic vapor cell. Doing so demonstrates a theoretical and phenomenological correspondence to the simplest model of leptogenesis, the process by which our universe purportedly went from equal amounts of matter and antimatter to its present matter excess. The understanding of the asymmetry as due to a broken discrete symmetry under chirp illuminates the underlying processes responsible for other chirp asymmetries previously noted in the literature.

Topological interfaces crossed by defects and textures of continuous and discrete point group symmetries in spin-2 Bose-Einstein condensates

We systematically and analytically construct a set of spinor wave functions representing defects and textures that continuously penetrate interfaces between coexisting, topologically distinct magnetic phases in a spin-2 Bose-Einstein condensate. These include singular and nonsingular vortices carrying mass or spin circulation that connect across interfaces between biaxial- and uniaxial nematic, cyclic and ferromagnetic phases, as well as vortices terminating as monopoles on the interface (“boojums”). The biaxial-nematic and cyclic phases exhibit discrete polytope symmetries featuring non-Abelian vortices and we investigate a pair of noncommuting line defects within the context of a topological interface. By numerical simulations, we characterize the emergence of nontrivial defect core structures, including the formation of composite defects. Our results demonstrate the potential of spin-2 Bose-Einstein condensates as experimentally accessible platforms for exploring interface physics, offering a wealth of combinations of continuous and discrete symmetries. Published by the American Physical Society 2024

Heavy axions from twin dark sectors with [formula omitted]-characterized mirror symmetry

The QCD Lagrangian contains a CP violating gluon density term with a physical coefficient θ¯. The upper bound on the electric dipole moment of neutron requires the value of θ¯ to be extremely small. The tiny θ¯ is commonly known as the strong CP problem. In order to solve this puzzle, we construct a θ¯-characterized mirror symmetry between a pair of twin dark sectors with respective discrete symmetries. By taking a proper phase rotation of dark fields, we can perfectly remove the parameter θ¯ from the full Lagrangian. In our scenario, the discrete symmetry breaking, which are responsible for the mass generation of dark colored fermions and dark matter fermions, can be allowed near the TeV scale. This means different phenomena from the popular axion models with high scale Peccei-Quinn global symmetry breaking.

Anomaly-free dark matter models with one-loop neutrino masses and a gauged U(1) symmetry

We systematically study and classify scotogenic models with a local U(1) gauge symmetry. These models give rise to radiative neutrino masses and a stable dark matter candidate, but avoid the theoretical problems of global and discrete symmetries. We restrict the dark sector particle content to up to four scalar or fermionic SU(2) singlets, doublets or triplets and use theoretical arguments based on anomaly freedom, Lorentz and gauge symmetry to find all possible charge assignments of these particles. The U(1) symmetry can be broken by a new Higgs boson to a residual discrete symmetry, that still stabilizes the dark matter candidate. We list the particle content and charge assignments of all non-equivalent models. Specific examples in our class of models that have been studied previously in the literature are the U(1)D scotogenic and singlet-triplet scalar models breaking to Z2. We also briefly discuss the new phenomenological aspects of our model arising from the presence of a new massless dark photon or massive Z′ boson as well as the additional Higgs boson.

Effective brane field theory with higher-form symmetry

We propose an effective field theory for branes with higher-form symmetry as a generalization of ordinary Landau theory, which is an extension of the previous work by Iqbal and McGreevy for one-dimensional objects to an effective theory for p-dimensional objects. In the case of a p-form symmetry, the fundamental field ψ[Cp] is a functional of p-dimensional closed brane Cp embedded in a spacetime. As a natural generalization of ordinary field theory, we call this theory the brane field theory. In order to construct an action that is invariant under higher-form transformation, we generalize the idea of area derivative for one-dimensional objects to higher-dimensional ones. Following this, we discuss various fundamental properties of the brane field based on the higher-form invariant action. It is shown that the classical solution exhibits the area law in the unbroken phase of U(1) p-form symmetry, while it indicates a constant behavior in the broken phase for the large volume limit of Cp. In the latter case, the low-energy effective theory is described by the p-form Maxwell theory. We also discuss brane-field theories with a discrete higher-form symmetry and show that the low-energy effective theory becomes a BF-type topological field theory, resulting in topological order. Finally, we present a concrete brane-field model that describes a superconductor from the point of view of higher-form symmetry.

Topological atom optics and beyond with knotted quantum wavefunctions

Atom optics demonstrates optical phenomena with coherent matter waves, providing a foundational connection between light and matter. Significant advances in optics have followed the realization of structured light fields hosting complex singularities and topologically non-trivial characteristics. However, analogous studies are still in their infancy in the field of atom optics. Here, we investigate and experimentally create knotted quantum wavefunctions in spinor Bose–Einstein condensates which display non-trivial topologies. In our work we construct coordinated orbital and spin rotations of the atomic wavefunction, engineering a variety of discrete symmetries in the combined spin and orbital degrees of freedom. The structured wavefunctions that we create map to the surface of a torus to form torus knots, Möbius strips, and a twice-linked Solomon’s knot. In this paper we demonstrate close connections between the symmetries and underlying topologies of multicomponent atomic systems and of vector optical fields—a realization of topological atom-optics.

Gravitational wave signature of generic disappearance of Z2-symmetry breaking domain walls

Breaking of discrete parity at high scale gives rise to Z2-domain walls (DW). The metastability of such walls can make them relatively long lived and contradict standard cosmology. We consider two classes of theories with similar underlying feature, the left right symmetric theories and two Higgs doublet models. Both of them possess some breaking of Z2 discrete symmetries. As a first step, domains form at a high energy scale during parity breaking. In the second step, these domains further decompose into subdomains due to Z2 symmetry breaking in two Higgs doublet models closer to the electroweak scale. We show that after this two step formation of domains and subdomains, a QCD instanton induced energy difference can remove the domain walls as well as the subdomain walls at around the same time successfully. The removal occurs purely as the result of a chance event taking place with probability very close to 0.25, and does not require one to introduce any non-renormalisable Z2-symmetry breaking term to the Lagrangian. We then investigate the gravitational waves arising from the collapse of such domain walls and show that the peak frequency of these waves lies in the 10−7–10−6 Hz band, corresponding to annihilation temperatures of 1–10 GeV. This frequency band is sensitive to pulsar timing array based experiments such as SKA and NANOGrav. The recent NANOGrav results rule out our DW collapse model for higher values of parity breaking scale above 107 GeV. Our DW collapse model with parity breaking scales below 107 GeV remains consistent with the current NANOGrav results and has a good chance of being seriously tested in future pulsar timing based experiments.

Discrete symmetries tested at 10−4 precision using linear polarization of photons from positronium annihilations

Discrete symmetries play an important role in particle physics with violation of CP connected to the matter-antimatter imbalance in the Universe. We report the most precise test of P, T and CP invariance in decays of ortho-positronium, performed with methodology involving polarization of photons from these decays. Positronium, the simplest bound state of an electron and positron, is of recent interest with discrepancies reported between measured hyperfine energy structure and theory at the level of 10−4 signaling a need for better understanding of the positronium system at this level. We test discrete symmetries using photon polarizations determined via Compton scattering in the dedicated J-PET tomograph on an event-by-event basis and without the need to control the spin of the positronium with an external magnetic field, in contrast to previous experiments. Our result is consistent with QED expectations at the level of 0.0007 and one standard deviation.

Exploring type-I seesaw under S 3 modular symmetry

This work’s novelty lies in using the simplest group i.e. Γ(2) ≃ S 3 modular symmetry implemented on the canonical seesaw to explain neutrino phenomenology. Here, we construct and classify models based on the doublet and singlet representations of supermultiplets under S 3 discrete symmetry along with their respective modular weights, allowing a mass matrix for the neutrino sector with minimal use of free parameters, namely models A, B, C, D. These modular symmetries become advantageous in avoiding the requirements of multiple flavon fields and the intricacies of vacuum alignments. In this way, we endeavor to clarify the effect and significance of modular S 3 symmetry, which is considered in explaining the neutrino phenomenology viable with the current observations. Additionally, we also shed some light on the neutrinoless double beta decay.

Ground state of Rydberg-dressed Bose gas confined in a toroidal trap

The experimental realization of Rydberg dressing technology in ultracold atomic systems provides another superior platform for studying novel states of matter and macroscopic quantum phenomena. In this work, based on the mean-field theory, we have investigated the ground-state phases of a two-component Bose–Einstein condensate with Rydberg interaction and confined in a toroidal trap. The effects of the Rydberg interaction and external potential, especially the Rydberg blockade radius, on the ground-state structure of such a system have been investigated in full parameter space. Our results show that the Rydberg blockade radius, which can be regarded as another controllable parameter, can be used to obtain a variety of ground-state phases. More interestingly, it is found that for weak Rydberg interactions, the Rydberg blockade radius breaks the spontaneous rotational symmetry of the system, leading to the formation of a discrete unit cell structure. For strongly interacting cases, it can be used to realize different orders of discrete rotational symmetry breaking.