Georgi-Glashow Research Articles

Is doublet-triplet splitting necessary?

We demonstrate that it is not necessary to substantially break the mass degeneracy between the Standard Model Higgs boson doublet and the corresponding scalar leptoquark, where these two fields comprise a single five-dimensional SU(5) representation. More precisely, we show that the experimental data on partial proton decay lifetimes cannot place any meaningful bound on the mass of the scalar leptoquark, also known as the color triplet, if one includes effects of higher-dimensional operators. We use the Georgi-Glashow model for our demonstration and point out that the complete suppression of proton decay via the scalar leptoquark mediation is not in conflict with the partial suppression of the gauge mediated two-body proton decay signatures. Finally, we derive a proper limit on the cutoff scale of the aforementioned higher-dimensional operators and outline how this scenario could be tested. Published by the American Physical Society 2024

A modified dyon solution in a non-Abelian gauge model

A modified SU(2) Georgi-Glashow model is considered here, and it is shown that besides the well-known Julia-Zee dyon solution, the model can also have a modified dyon solution. The properties of the modified dyon solution are studied using analytical and numerical methods. A comparative analysis of the modified dyon and the Julia-Zee dyon shows that their properties are significantly different. In particular, except for the BPS case, the energy and electric charge of the modified dyons exceed considerably those of the Julia-Zee dyons. At the same time, the energy and electric charge of the modified dyon are bounded for all admissible parameter values, whereas those of the Julia-Zee dyon can be arbitrarily large in the BPS case.

Exact oscillations and chaos on a non-Abelian coil

We construct new exact solutions of the Georgi-Glashow model in 3+1 dimensions. These configurations are periodic in time but lead to a stationary energy density and no energy flux. Nevertheless, they possess a characteristic frequency which manifests itself through non-trivial resonances on test fields. This allows us to interpret them as non-Abelian self sustained coils. We show that for larger energies a transition to chaotic behavior takes place, which we characterize by Poincaré sections, Fourier spectra and exponential growth of the geodesic deviation in an effective Jacobi metric, the latter triggered by parametric resonances.

Magnetic monopoles in extensions of Georgi–Glashow model

We discuss a class of effective extensions of the SU(2) Georgi–Glashow model and discuss its Bogomol’nyi–Prasad–Sommerfield (BPS) limit. We identify a specific subclass of these models that admit analytical solutions of the monopole type. We present some concrete examples and find that the resulting monopoles tend to have their energy concentrated not in their center, but rather in a spherical shell around it.

Higher Flavor Symmetries in the Standard Model

AbstractA study of the generalized global flavor symmetries of the Standard Model is initiated. The presence of nonzero triangle diagrams between the U(3)5 flavor currents and the hypercharge current intertwines them in the form of a higher‐group which mixes the zero‐form flavor symmetries with the one‐form magnetic hypercharge symmetry. This higher symmetry structure greatly restricts the possible flavor symmetries that may remain unbroken in any ultraviolet completion that includes magnetic monopoles. In the context of unification, this implies tight constraints on the combinations of fermion species which may be joined into multiplets. Three of four elementary possibilities are reflected in the classic unification models of Georgi–Glashow, , and Pati–Salam. The final pattern is realized non‐trivially in trinification, which exhibits the sense in which Standard Model Yukawa couplings which violate these flavor symmetries may be thought of as spurions of the higher‐group. Such modifications of the ultraviolet flavor symmetries are possible only if new vector‐like matter is introduced with masses suppressed from the unification scale by the Yukawa couplings.

Dynamics of strongly-coupled chiral gauge theories

We study the dynamics of SU(N) chiral gauge theories with massless fermions belonging to various combinations of the symmetric, antisymmetric or fundamental representations. We limit ourselves to the gauge-anomaly-free and asymptotically free systems. These theories have a global symmetry group with the associated ’t Hooft anomaly-matching conditions severely limiting the possible RG flows. Recent developments on the applications of the generalized symmetries and the stronger requirement of the matching of the mixed anomalies also give further indications on the possible IR dynamics. In vectorlike theories such as the quantum chromodynamics (QCD), gauge-invariant “quark-antiquark” condensates form and characterize the IR dynamics, and the anomaly matching involves the Nambu-Goldstone (NG) bosons. In some other special cases, such as the Bars-Yankielowicz (BY) or Georgi-Glashow (GG) models, a hypothetical solution was proposed in the literature, with no global symmetry breaking and with some simple set of composite massless fermions saturating all the anomalies. For the BY and GG systems, actually, a more plausible candidate for their IR physics is the dynamical Higgs phase, with a few simple bi-fermion color-flavor locked condensates, breaking the color and flavor symmetries, partially or totally. Remarkably, the ’t Hooft anomaly-matching (and generalized anomaly-matching) conditions are automatically satisfied in this phase. Another interesting possibility, occurring in some chiral gauge theories, is dynamical Abelianization, familiar from N = 2 supersymmetric gauge theories. We explore here even more general types of possible IR phases than the ones mentioned above, for wider classes of models. With the help of large-N arguments we look for IR free theories, whereas the MAC (maximal attractive channel) criterion might suggest some simple bi-fermion condensates characterizing the IR dynamics of the systems. In many cases the low-energy effective theories are found to be described by quiver-like gauge theories, some of the (nonAbelian) gauge groups are infrared-free while some others might be asymptotically free.

Infrared physics of the 3D SU(2) adjoint Higgs model at the crossover transition

We study the crossover phase transition of the SU(2) Georgi-Glashow model in three dimensions. In this model, a confining condensate of topological ’t Hooft-Polyakov monopoles exists in the Higgs regime. We use lattice Monte Carlo simulations to study the monopole gas across a crossover transition, and demonstrate that gradient flow can be used to renormalize the otherwise divergent monopole number density. The condensation of the monopoles means that the theory admits also a massive photon-like excitation. We show that the renormalized monopole number density is approximately proportional to the square of the photon mass, in agreement with semiclassical results. Our results give insight into behaviour of the Higgs regime near crossover, which has boarder implications for beyond the Standard Model theories containing adjoint scalar fields.

Callan-Rubakov effect and higher charge monopoles

In this paper we study the interaction between magnetic monopoles and massless fermions. In the low energy limit, the monopole’s magnetic field polarizes the fermions into purely in-going and out-going modes. Consistency requires that the UV fermion-monopole interaction leads to non-trivial IR boundary conditions that relate the in-going to out-going modes. These non-trivial boundary conditions lead to what is known as the Callan-Rubakov effect. Here we derive the effective boundary condition by explicitly integrating out the UV degrees of freedom for the general class of spherically symmetric SU(N) monopoles coupled to massless fermions of arbitrary representation. We then show that the boundary conditions preserve symmetries without ABJ-type anomalies. As an application we explicitly derive the boundary conditions for the stable, spherically symmetric monopoles associated to the SU(5) Georgi-Glashow model and comment on the relation to baryon number violation.

Anomalies and phases of strongly coupled chiral gauge theories: Recent developments

After many years of investigations, our understanding of the dynamics of strongly coupled chiral gauge theories is still quite unsatisfactory today. Conventional wisdom about strongly coupled gauge theories, successfully applied to QCD, is not always as useful in chiral gauge theories. Recently, some new ideas and techniques have been developed, which involve concepts of generalized symmetries, of gauging a discrete center symmetry, and of generalizing the ’t Hooft anomaly matching constraints to include certain mixed symmetries. This new development has been applied to chiral gauge theories, leading to many interesting, sometimes quite unexpected, results. For instance, in the context of generalized Bars–Yankielowicz and generalized Georgi–Glashow models, these new types of anomalies give a rather clear indication in favor of the dynamical Higgs phase, against confining, flavor symmetric vacua. Another closely related topic is strong anomaly and the effective low-energy action representing it. It turns out that they have significant implications on the phase of chiral gauge theories, giving indications consistent with the findings based on the generalized anomalies. Some striking analogies and contrasts between the massless QCD and chiral gauge theories seem to emerge from these discussions. The aim of this work is to review these developments.

Octions: An E8 description of the Standard Model

We interpret the elements of the exceptional Lie algebra e8(−24) as objects in the Standard Model, including lepton and quark spinors with the usual properties, the Standard Model Lie algebra su(3)⊕su(2)⊕u(1), and the Lorentz Lie algebra so(3,1). Our construction relies on identifying a complex structure on spinors and then working in the enveloping algebra. The resulting model naturally contains Grand Unified Theories based on SO(10) (Georgi), SU(5) (Georgi–Glashow), and SU(4) ×SU(2) ×SU(2) (Pati–Salam). We then briefly speculate on the role of the remaining elements of e8 and propose a mechanism leading to exactly three generations of particles.

Gauge enhanced quantum criticality beyond the standard model

Standard lore ritualizes our quantum vacuum in the four-dimensional spacetime (4D) governed by one of the candidate Standard Models (SMs), while lifting towards some grand unification-like structure (GUT) at higher energy scales. In contrast, in our work, we introduce an alternative view that the SM is a low energy quantum vacuum arising from various neighbor vacua competition in an immense quantum phase diagram. In general, we can regard the SM arising near the gapless quantum criticality (either critical points or critical regions) between the competing neighbor vacua. In particular detail, we demonstrate how the $su(3)\ifmmode\times\else\texttimes\fi{}su(2)\ifmmode\times\else\texttimes\fi{}u(1)$ SM with 16n Weyl fermions arises near the quantum criticality between the GUT competition of Georgi-Glashow $su(5)$ and Pati-Salam $su(4)\ifmmode\times\else\texttimes\fi{}su(2)\ifmmode\times\else\texttimes\fi{}su(2)$. We propose two enveloping toy models. Model I is the conventional $so(10)$ GUT with a Spin(10) gauge group plus GUT-Higgs potential inducing various Higgs transitions. Model II modifies model I by adding a new 4D discrete torsion class of Wess-Zumino-Witten-like term built from GUT-Higgs field [which matches a nonperturbative global mixed gauge-gravity anomaly captured by a 5D invertible topological field theory ${w}_{2}{w}_{3}(TM)={w}_{2}{w}_{3}({V}_{\mathrm{SO}(10)})$], which manifests a beyond-Landau-Ginzburg quantum criticality between Georgi-Glashow and Pati-Salam models, with extra beyond the Standard Model excitations emerging near a hypothetical quantum critical region. If the internal symmetries were treated as global symmetries (or weakly coupled to probe background fields), we suggest a particular low-energy realization of model II as an analogous gapless 4D deconfined quantum criticality with new beyond the SM fractionalized fragmentary excitations of color-flavor separation, and gauge enhancement including a dark gauge force sector, altogether requiring a double fermionic Spin structure named DSpin. If the internal symmetries are dynamically gauged (as they are in our quantum vacuum), we suggest the model II's 4D criticality as a boundary criticality such that only appropriately gauge enhanced dynamical GUT gauge fields can propagate into an extradimensional 5D bulk. The phenomena may be regarded as SM deformation or ``morphogenesis.'' Although our derivation is based on kinematics and global anomaly matching constraints between UV parent and various candidate IR field theories, the constraints are still highly subtle and suggestive. Future verifications on the IR dynamics will be desirable.

Analytic nonhomogeneous condensates in the (2+1)-dimensional Yang-Mills-Higgs-Chern-Simons theory at finite density

We construct the first analytic examples of non-homogeneous condensates in the Georgi-Glashow model at finite density in $(2+1)$ dimensions. The non-homogeneous condensates, which live within a cylinder of finite spatial volume, possess a novel topological charge that prevents them from decaying in the trivial vacuum. Also the non-Abelian magnetic flux can be computed explicitly. These solutions exist for constant and non-constant Higgs profile and, depending on the length of the cylinder, finite density transitions occur. In the case in which the Higgs profile is not constant, the full system of coupled field equations reduce to the Lam\'e equation for the gauge field (the Higgs field being an elliptic function). For large values of this length, the energetically favored configuration is the one with a constant Higgs profile, while, for small values, it is the one with non-constant Higgs profile. The non-Abelian Chern-Simons term can also be included without spoiling the integrability properties of these configurations. Finally, we study the stability of the solutions under a particular type of perturbations.

Probing the dynamics of chiral SU(N) gauge theories via generalized anomalies

We study symmetries and dynamics of chiral $SU(N)$ gauge theories with matter Weyl fermions in a two-index symmetric ($\ensuremath{\psi}$) or antisymmetric tensor ($\ensuremath{\chi}$) representation, together with $N\ifmmode\pm\else\textpm\fi{}4+p$ fermions in the antifundamental ($\ensuremath{\eta}$) and $p$ fermions in the fundamental ($\ensuremath{\xi}$) representations. They are known as the Bars-Yankielowicz (the former) and the generalized Georgi-Glashow models (the latter). The conventional 't Hooft anomaly matching algorithm is known to allow a confining, chirally symmetric vacuum in all these models, with a simple set of massless baryonlike composite fermions describing the infrared physics. We analyzed recently one of these models ($\ensuremath{\psi}\ensuremath{\eta}$ model), by applying the ideas of generalized symmetries and the consequent, stronger constraints involving certain mixed anomalies, finding that the confining, chirally symmetric, vacuum is actually inconsistent. In the present paper, this result is extended to a wider class of the Bars-Yankielowicz and the generalized Georgi-Glashow models. It is shown that for all these models with $N$ and $p$ both even, at least, the generalized anomaly matching requirement forbids the persistence of the full chiral symmetries in the infrared if the system confines. The most natural and consistent possibility is that some bifermion condensates form, breaking the color gauge symmetry dynamically, together with part of the global symmetry.

Classical production of ’t Hooft–Polyakov monopoles from magnetic fields

We show that in the SU(2) Georgi-Glashow model, 't Hooft-Polyakov monopoles are produced by a classical instability in magnetic fields above the Ambjorn-Olesen critical field, which coincides approximately with the field at which Schwinger pair production becomes unsuppressed. Below it, monopoles can be produced thermally, and we show that the rate is higher than for pointlike monopoles by calculating the sphaleron energy as a function of the magnetic field. The results can be applied to production of monopoles in heavy-ion collisions or in the early Universe.

Magnetic monopoles in pure $SU (2)$ Yang–Mills theory with a gauge-invariant mass

In this paper, we show the existence of magnetic monopoles in the pure $SU(2)$ Yang--Mills theory even in absence of scalar fields when the gauge-invariant mass term is introduced. This result follows from the recent proposal for obtaining the gauge field configurations in the Yang-Mills theory from the solutions of the field equations in the "complementary" gauge-scalar model with the radial length of the scalar field being fixed. The gauge-invariant mass term is obtained through a change of variables and a gauge-independent description of the Brout-Englert-Higgs mechanism which neither relies on the spontaneous breaking of gauge symmetry nor on the assumptions of the nonvanishing vacuum expectation value of the scalar field. According to these procedures, we solve under the static and spherically symmetric ansatz the field equations of the $SU(2)$ Yang-Mills theory coupled with an adjoint scalar field whose radial degree of freedom is fixed, and obtain a gauge field configuration of magnetic monopole with a minimum magnetic charge in the massive $SU(2)$ Yang-Mills theory. We compare the magnetic monopole obtained in this way in the massive Yang--Mills theory with the Wu-Yang magnetic monopole in the pure Yang-Mills theory and the 't Hooft-Polyakov magnetic monopole in the Georgi-Glashow model.

Skyrme-Faddeev Lagrangian from reformulated Georgi-Glashow model

Recently we proposed a decomposition for fields of the Georgi-Glashow model and interpreted Cho's decomposition as a result of some constraints on Georgi-Glashow's fields. Now, using the decomposition form that Faddeev and Niemi proposed, we introduce a simple and novel method to derive the Skyrme-Faddeev Lagrangian from the reformulation of the Georgi-Glashow model with an extra constraint. As we showed before, this extra constraint leads to the appearance of both vortices and monopoles.

Are there monopoles in the quark-gluon plasma?

Monopole-like objects have been identified in multiple lattice studies, and there is now a significant amount of literature on their importance in phenomenology. Some analytic indications of their role, however, are still missing. The 't Hooft-Polyakov monopoles, originally derived in the Georgi-Glashow model, are an important dynamical ingredient in theories with extended supersymmetry ${\cal N} = 2,\,4$, and help explain the issues related with electric-magnetic duality. There is no such solution in QCD-like theories without scalar fields. However, all of these theories have instantons and their finite-$T$ constituents known as instanton-dyons (or instanton-monopoles). The latter leads to semiclassical partition functions, which for ${\cal N} = 2,\,4$ theories were shown to be identical ("Poisson dual") to the partition function for monopoles. We show how, in a pure gauge theory, the semiclassical instanton-based partition function can also be Poisson-transformed into a partition function, interpreted as the one of moving and rotating monopoles.

Monopole-Based Scenarios of Confinement and Deconfinement in 3D and 4D

This review discusses confinement, as well as the topological and critical phenomena, in the gauge theories which provide the condensation of magnetic monopoles. These theories include the 3D SU(N) Georgi-Glashow model, the 4D [U(1)] N - 1 -invariant compact QED , and the [U(1)] N - 1 -invariant dual Abelian Higgs model. After a general introduction to the string models of confinement, an analytic description of this penomenon is provided at the example of the 3D SU(N) Georgi-Glashow model, with a special emphasis placed on the so-called Casimir scaling of k-string tensions in that model. We further discuss the string representation of the 3D [U(1)] N - 1 -invariant compact QED, as well as of its 4D generalization with the inclusion of the Θ -term. We compare topological effects, which appear in the latter case, with those that take place in the 3D QED extended by the Chern-Simons term. We further discuss the string representation of the ’t Hooft-loop average in the [U(1)] N - 1 -invariant dual Abelian Higgs model extended by the Θ -term, along with the topological effects caused by this term. These topological effects are compared with those occurring in the 3D dual Abelian Higgs model (i.e., the dual Landau-Ginzburg theory) extended by the Chern-Simons term. In the second part of the review, we discuss critical properties of the weakly-coupled 3D confining theories. These theories include the 3D compact QED, along with its fermionic extension, and the 3D Georgi-Glashow model.

(2+1)−d Georgi-Glashow model near critical temperature

We study correlations functions of magnetic vortices $V$ and Polyakov loop $P$ operators in the 2+1 dimensional Georgi-Glashow model in the vicinity of the deconfining phase transition. In this regime the (dimensionally reduced) model is mapped onto a free theory of two massive Majorana fermions. We utilize this fermionic representation to explicitly calculate the expectation values of $V$ and $P$ as well as their correlators. In particular we show that the $VV$ correlator is large, and thus the anomalous breaking of the magnetic $U(1)$ symmetry is order one effect in the near critical region. We also calculate the contribution of magnetic vortices to the entropy and the free energy of the system.

Non-Abelian monopoles as the origin of dark matter

We suggest that dark matter may be partially constituted by a dilute ’t Hooft–Polyakov monopoles gas. We reach this conclusion by using the Georgi–Glashow model coupled to a dual kinetic mixing term [Formula: see text] where [Formula: see text] is the electromagnetic field and [Formula: see text] the ’t Hooft tensor. We show that these monopoles carry both (Maxwell) electric and (Georgi–Glashow) magnetic charges and the electric charge quantization condition is modified in terms of a dimensionless real parameter. This parameter could be determined from milli-charged particle experiments.