Symmetry Breaking Pattern Research Articles (Page 1)

Abstract We present and analyze two minimal extensions of the Standard Model featuring a spontaneously broken global, chiral, and anomaly-free U(1) D symmetry. This breaking generates naturally small Dirac neutrino masses via a seesaw mechanism and yields a physical massless Goldstone boson, the Diracon. Although both models share the same particle content and scalar potential, their distinct symmetry breaking pattern leads to remarkably different phenomenological and cosmological signatures. In the first model, the Diracon couples weakly to charged leptons but right-handed neutrinos can be efficiently produced in the early Universe, resulting in stringent constraints from the effective number of relativistic species, ∆N eff. Conversely, in the second one, right-handed neutrino production is suppressed, and flavour-violating processes such as $$ \mu \to e\mathcal{D} $$ μ → e D provide the most promising probes. These simple but elegant models showcase the complementarity between cosmological observations and low-energy flavour experiments in the search for physics beyond the Standard Model.

Abstract We present a new framework of grand unification that is equipped with an axion solution to the strong CP problem without a domain wall problem when the Peccei-Quinn (PQ) symmetry is spontaneously broken after inflation. Our grand unified theory (GUT) is based on a symmetry breaking pattern, SU(10) × SU(5)1 → SU(5) V ⊃ SU(3) C × SU(2) L × U(1) Y , where SU(5)1 and a special embedding of SU(5)2 ⊂ SU(10) are broken to a diagonal subgroup SU(5) V . The model contains a vector-like pair of PQ-charged fermions that transform as (anti-)fundamental representations under SU(10), so that the domain wall number is one. However, after the GUT symmetry breaking, the number of vector-like pairs of PQ-charged colored fermions is larger than one, which seems to encounter the domain wall problem. This apparent inconsistency is resolved by small instanton effects on the axion potential which operate as a PQ-violating bias term and allow the decay of domain walls. We propose a domain-wall-free UV completion for an IR model where the domain wall number appears larger than one. The model gives a prediction for a dark matter axion window, which is different from that of the ordinary post-inflationary QCD axion with domain wall number one.

Symmetry breaking plays a central role in classifying the phases of quantum many-body systems. Recent developments have highlighted a novel symmetry-breaking pattern, in which the strong symmetry of a density matrix spontaneously breaks to the weak symmetry. This strong-to-weak symmetry breaking is typically detected using multireplica correlation functions, such as the Rényi-2 correlator. In this Letter, we propose a practical protocol for detecting strong-to-weak symmetry breaking in experiments using the randomized measurement toolbox. Our scheme involves collecting the results of random Pauli measurements for (i)the original quantum state and (ii)the quantum state after evolution with the charged operators. Based on the measurement results, with a large number of samples, we can obtain an unbiased estimate of the Rényi-2 correlator. With a small sample size, we can still provide an alternative approach to estimate the phase boundary to a decent accuracy. We perform numerical simulations of Ising chains with all-to-all decoherence as an exemplary demonstration. Our result opens the opportunity for the experimental studies of the novel quantum phases in mixed quantum states.

Abstract This paper studies generic surface defects for multiscalar critical models using a perturbative ε expansion in 4 − ϵ dimensions. The beta functions of the defect couplings for a generic multiscalar bulk with quartic interactions are computed at first non-trivial order in ε. Specific bulks of interest are then considered: O(N), hypercubic, hypertetrahdral, and biconical O ( m ) × O ( n ) . In each case, we compute fixed points for the defect couplings and determine the remaining bulk symmetry. Expanding beyond the O(N) model, we find a greater variety of patterns of symmetry breaking.

The Nambu-Goldstone modes on the exotic chiral condensed phase with chiral and tensor-type quark-antiquark condensates are investigated by using the two-point vertex functions. It is shown that one of the Nambu-Goldstone modes appears as a result of meson mixing. As is well known, another method to find the Nambu-Goldstone modes is given by the use of the algebraic commutation relations between broken generators and massless modes obtained through the spontaneous symmetry breaking. This method is adopted to the cases of the chiral symmetry breakings due to the tensor-type condensate and the inhomogeneous chiral condensate. The result obtained by the use of the meson two-point vertex functions is obviously reproduced in the case of the tensor-type condensate. Furthermore, we investigate the general rules for determining the broken symmetries and the Nambu-Goldstone modes algebraically. As examples, the symmetry breaking pattern and the Nambu-Goldstone modes due to the tensor-type condensate or the inhomogeneous chiral condensate are shown by adopting the general rules developed in this paper in the algebraic method. Published by the American Physical Society 2025

Symmetry plays a fundamental role in quantum many-body physics, and a central concept is spontaneous symmetry breaking. Recent developments highlight new symmetry-breaking patterns known as strong-to-weak spontaneous symmetry breaking, characterized by two different order parameters: the fidelity correlator and the Rényi-2 correlator which are inequivalent. In this work, we propose the Wightman correlator as an alternative diagnostic tool. This construction relies on the introduction of the thermofield double state for a generic density matrix, which maps the strong symmetry of the density matrix to the doubled symmetry of the pure state, allowing the Wightman correlator to emerge naturally as a standard probe of symmetry breaking. We prove the equivalence between the Wightman correlator and the fidelity correlator, and examine explicit examples. Additionally, we discuss a susceptibility interpretation of the Wightman correlator. The validity of Wightman correlator has wide applications for understanding strong-to-weak spontaneous symmetry breaking.

We present exact results in softly broken supersymmetric SU(NC) chiral gauge theories with charged fermions in one antisymmetric, NF fundamental, and NC+NF−4 antifundamental representations. We achieve this by considering the supersymmetric version of these theories and utilizing anomaly mediated supersymmetry breaking at a scale m≪Λ to generate a vacuum. The connection to nonsupersymmetric theories is then conjectured in the limit m→∞. For odd NC, we determine the massless fermions and unbroken global symmetries in the infrared. For even NC, we find global symmetries are nonanomalous and no massless fermions. In all cases, the symmetry breaking patterns differ from what the tumbling hypothesis would suggest.

An SU(8) theory was previously found to be the minimal simple gauge group where all three-generational Standard Model (SM) fermions can be nontrivially embedded. It is maximally broken into a subgroup of SU(8)→G441≡SU(4)s⊗SU(4)W⊗U(1)X0 at the grand unified theory scale by the SU(8) adjoint Higgs field of 63H. Gauge symmetries in the strong and the weak sectors are extended by one and two ranks, respectively. The sequential strong-weak-weak (SWW) symmetry breaking stages were found to generate the observed hierarchical SM quark/lepton masses as well as the Cabibbo-Kobayashi-Maskawa mixing pattern with the precise flavor identifications [The global B− L symmetry in the flavor-unified SU(N) theories, . and The standard model quark/lepton masses and the Cabibbo-Kobayashi-Maskawa mixing in an SU(8) theory, .]. We further study the possible weak-strong-weak and weak-weak-strong symmetry breaking patterns and compare with the results that we have obtained by following the SWW sequence. The two-loop renormalization group equations following both patterns are analyzed, where we cannot achieve the gauge coupling unification in the field theory framework. Through these analyses, we suggest the gauge coupling unification to be interpreted in the context of the affine Lie algebra.

The spectrum and dynamics of near-extremal black holes is strongly modified by quantum effects at low temperatures. When the extremal limit does not preserve any supersymmetry, the density of states goes to zero at extremality and no extremal black holes remain. However, when the extremal limit is supersymmetric, a large microscopic degeneracy survives and there is a gap to the first excited black hole visible from gravity. In this article we study large N quantum mechanical models where supersymmetry is explicitly broken, allowing us to interpolate between these two qualitatively different pictures. We propose and analyze deformations of N = 2 SYK models with such a pattern of (super) symmetry breaking which violate the U(1) R-symmetry. These models feature a lifting of the BPS degeneracy and a closing of the spectral gap, and we further show that the large N soft effective action is given by a modification of the N = 2 Schwarzian theory in which the U(1)R mode becomes massive.

Spontaneous symmetry breaking and self-organized pattern formation in nonlinear systems are fundamental phenomena with broad implications. Studying these effects in cold atomic gases, particularly through the optical control of laser-dressed Rydberg atoms, bridges atomic physics and modern optics. Here, we investigate the ground-state matter-wave pattern formation in cold Rydberg-dressed Bose-Einstein condensates (BECs) with considerations of the Lee-Huang-Yang (LHY) correction and Raman-induced spin-orbit coupling (SOC). A surprising discovery is that the combination of these effects can induce spontaneous symmetry breaking in a plane-wave state of matter waves, giving rise to a variety of exotic self-organized structures, including stripes, positive and negative hexagons, squares, black-eye patterns, and quasi-lattices, among others. Furthermore, we uncover intriguing structural behaviors by considering inter- and intra-specific nonlocal interactions and the hard-core (contact, short-range) and soft-core (long-range) interactions. Our findings advance optical control of quantum matter, with potential applications in atomic-based information processing.

This study introduces a novel contrastive learning-based X-ray diffraction (XRD) analysis framework, an SE(3)-equivariant graph neural network (E3NN) based Atomic Cluster Expansion Neural Network (EACNN), which reduces the strong dependency on databases and initial models in traditional methods. By integrating E3NN with atomic cluster expansion (ACE) techniques, a dual-tower contrastive learning model has been developed, mapping crystal structures and XRD patterns to a continuous embedding space. The EACNN model retains hierarchical features of crystal systems through symmetry-sensitive encoding mechanisms and utilizes relationship mining via contrastive learning to replace rigid classification boundaries. This approach reveals gradual symmetry-breaking patterns between monoclinic and orthorhombic crystal systems in the latent space, effectively addressing the recognition challenges associated with low-symmetry systems and small sample space groups. Our investigation further explores the potential for model transfer to experimental data and multimodal extensions, laying the theoretical foundation for establishing a universal structure–property mapping relationship.

We examine the vacuum stability of gauge symmetry breaking in five dimensions, compactified on the S1/(Z2×Z2′) orbifold. We consider SU(N), Sp(N), SO(2N), and SO(2N+1) theories in the bulk, and provide an exhaustive classification of possible parity assignments that lead to stable orbifolds and of the corresponding symmetry breaking patterns. We use these results in the search for viable asymptotic grand unification theories (aGUT), testing the stability criteria on models based on SU(6) and SU(8). As a result, we identify two viable aGUTs: a unique SU(6) pathway down to the Standard Model, and one SU(8) model leading to an intermediate Pati-Salam partial unification. Published by the American Physical Society 2025

Strong-to-weak spontaneous symmetry breaking (SWSSB) has recently emerged as a universal feature of quantum mixed-state phases of matter. While various information-theoretic diagnostics have been proposed to define and characterize SWSSB phases, relating these diagnostics to observables which can be efficiently and scalably probed on modern quantum devices remains challenging. Here we propose a new observable for SWSSB in mixed states, called the Rényi-1 correlator, which naturally suggests a route toward scalably detecting certain SWSSB phases in experiment. Specifically, if the canonical purification (CP) of a given mixed state can be reliably prepared, then SWSSB in the mixed state can be detected via ordinary two-point correlation functions in the CP state. We discuss several simple examples of CP states which can be efficiently prepared on quantum devices, and whose reduced density matrices exhibit SWSSB. The Rényi-1 correlator also satisfies several useful theoretical properties: it naturally inherits a stability theorem recently proven for the closely related fidelity correlator, and it directly defines SWSSB as a particular pattern of ordinary spontaneous symmetry breaking in the CP state.

We report the results of an extensive numerical study of the Sp(4) lattice gauge theory coupled to fermion matter content consisting of three (Dirac) flavors, transforming in the two-index antisymmetric representation of the gauge group. In the presence of (degenerate) fermion masses, the theory has an enhanced global SU(6) symmetry, broken explicitly and spontaneously to its SO(6) subgroup. This symmetry breaking pattern makes the theory interesting for applications in the context of composite Higgs models, as well as for the implementation of top partial compositeness. Alternatively, it can also provide a dynamical realization of the strongly interacting massive particle paradigm for the origin of dark matter. We adopt the standard plaquette gauge action, along with the Wilson-Dirac formulation for the fermions, and apply the (rational) hybrid Monte Carlo algorithm in our ensemble generation process. We monitor the autocorrelation and topology of the ensembles. We explore the bare parameter space, and identify the weak and strong coupling regimes, which are separated by a line of first-order bulk phase transitions. We measure two-point correlation functions between meson operators that transform as nontrivial representations of SO(6), and extract the ground-state masses, in all accessible spin and parity channels. We assess the size of finite volume effects, and restrict attention to measurements in which these systematic effects are negligibly small compared to the statistical uncertainties. The accuracy of our data enables us to extract the decay constants of the composite particles in the pseudoscalar, vector and axial-vector channels. In addition, we measure the mass of the first excited state for one of the channels, the vector meson, by performing a generalized eigenvalue problem analysis involving two different meson operators. Spectral quantities show a mass dependence that is compatible with the expectation that, at long distances, the theory undergoes confinement, accompanied by the spontaneous breaking of the approximate global symmetries acting on the matter fields. Finally, we discuss the continuum and massless extrapolations within the framework of Wilson chiral perturbation theory, after setting the physical scale using the gradient flow method, and compare the results to those of existing studies in the quenched approximation, as well as to the literature on closely related theories.Published by the American Physical Society2025

We study the homogeneous breaking of spatial translation symmetry concomitantly with the spontaneous breaking of other internal and spacetime symmetries, including dilations. We use the symmetry-breaking pattern as the only input to derive, via the coset construction, general effective field theories for the symmetry-originated modes associated with Goldstone’s theorem, namely the Nambu-Goldstone candidates. Through explicit computations, we show that integrating out the explicit massive Nambu-Goldstone candidates or imposing symmetric constraints, namely the inverse Higgs constraints, to express massive modes in terms of the massless ones leads to physically distinct effective field theories. This sensitivity to the chosen method can be traced back to the homogeneous breaking of translations, the homogeneous aspect of the breaking induces a mixing between internal and spacetime symmetries at the level of the Lie algebra. This, in turn, leads to subtle discussions about the inverse Higgs constraints, in particular that they lead to a loss of generality in our specific examples. The derived general effective field theories also give rise to a broad class of theories exhibiting emergent enhanced shift symmetries, which constrain the mobility of the modes. The latter are referred to as fractonic modes.

A flavor-unified theory based on the simple Lie algebra of su(8) was previously proposed to generate the observed three-generational Standard Model quark/lepton mass hierarchies and the Cabibbo-Kobayashi-Maskawa mixing pattern due to their non-universal symmetry properties. A level-1 affine Lie algebra of sû8kU=1 with the N = 1 supersymmetric extension is found to unify three gauge couplings through the maximally symmetry breaking pattern.

The interplay of symmetry and topology in quantum many-body mixed states has recently garnered significant interest. In a phenomenon not seen in pure states, mixed states can exhibit average symmetries—symmetries that act on component states while leaving the ensemble invariant. In this work, we systematically characterize symmetry-protected topological (SPT) phases of short-range entangled (SRE) mixed states of spin systems—protected by both average and exact symmetries—by studying their pure Choi states in a doubled Hilbert space, where the familiar notions and tools for SRE and SPT pure states apply. This advantage of the doubled space comes with a price: extra symmetries as well as subtleties around how hermiticity and positivity of the original density matrix constrain the possible SPT invariants. Nevertheless, the doubled-space perspective allows us to obtain a systematic classification of mixed-state SPT (MSPT) phases. We also investigate the robustness of MSPT invariants under symmetric finite-depth quantum channels, the bulk-boundary correspondence for MSPT phases, and the consequences of the MSPT invariants for the separability of mixed states and the symmetry-protected sign problem. In addition to MSPT phases, we study the patterns of spontaneous symmetry breaking (SSB) of mixed states, including the phenomenon of exact-to-average SSB, and the order parameters that detect them. Mixed-state SSB is related to an ingappability constraint on symmetric Lindbladian dynamics.

With the in-depth subjects chiasma among different research areas, many people are applying concepts and methods in theoretical high-energy physics to condensed matter systems. One of the most intensely studied tools is the Anti-de Sitter space/Conformal Field Theory (AdS/CFT) correspondence. It effectively permits a perturbative treatment of strongly coupled systems. Thus, it has been a focused topic in theoretical physics and high-energy physics. It represents a significant breakthrough in understanding quantum gravity. This paper focuses on the realisation of the duality in Jackiw-Teitelboim (JT) gravity and Sachdev-Ye-Kitaev (SYK) Model. To this end, the author derived the action, free energy, thermal entropy, and low-energy dynamics. The symmetry breaking pattern of the SYK model following previous works are also considered. These results were compared with the counterparts in Euclidean JT theory as a cut-out of the complete nearly AdS space in two dimensions. Based on the similarity in the mathematical form of these quantity and symmetry breaking process, the author concludes that the SYK model, as many believed, is a promising candidate for the holographic dual of the JT theory.

Abstract The future space-borne gravitational wave (GW) detectors would provide a promising probe for the new physics beyond the standard model that admits the first-order phase transitions. The predictions for the GW background vary sensitively among different concrete particle physics models but also share a large degeneracy in the model buildings, which motivates an effective model description on the phase transition based on different patterns of the electroweak symmetry breaking (EWSB). In this paper, using the scalar N-plet model as a demonstration, we propose an effective classification for three different patterns of EWSB: (1) radiative symmetry breaking with classical scale invariance, (2) the Higgs mechanism in a generic scalar extension, and (3) higher-dimensional operators. We conclude that a strong first-order phase transition could be realized for (1) and (2) with a small quartic coupling and a small isospin of an additional N-plet field for the light scalar field model with and without the classical scale invariance, and (3) with a large mixing coupling between scalar fields and a large isospin of the N-plet field for the heavy scalar field model.

The phase diagram and symmetry breaking patterns of a holographic CFT with U(1) × SU(2) symmetry are analyzed using the simplest holographic action, namely Einstein-Yang-Mills (YM) theory with a negative cosmological constant. This is relevant for both condensed matter and QCD applications. With a U(1) and an “isospin” chemical potential turned on, we determine all possible symmetry breaking patterns, which are associated to the condensation of spin-one order parameters. The possible IR asymptotics of the Einstein-YM solutions are derived analytically, both for 2+1 and 3+1 boundary dimensions. The competing solutions are then computed numerically, both at zero and non-zero temperature, from which the full three-dimensional phase diagram is determined. We find a surface of second order phase transitions that separate uncondensed and condensed phases. In some regions with a large fraction of charged to neutral degrees of freedom, the phase transition becomes first order.