Gauge Group SU Research Articles

Models of accidental dark matter with a fundamental scalar

We consider models of accidental dark matter, namely models in which the dark matter is a composite state that is stable thanks to an accidental symmetry of the theory. The fundamental constituents are vectorlike fermions, taken to be fragments of representations of the grand unifying gauge group SU(5), as well as a scalar singlet. All the new fields are charged under a new confining gauge group, which we take to be SU(N), leading to models with complex dark matter. We analyse the models in the context of SU(5) grand unification with a non-standard approach recently proposed in the literature. The advantage of including the scalar mainly resides in the fact that it allows several undesired accidental symmetries to be broken, leading to a larger set of viable models with respect to previous literature, in which only fermions (or only scalars) were considered. Moreover these models present distinct novelties, namely dark states with non-zero baryon and lepton number and the existence of composite hybrid states of fermions and scalars. We identify phenomena that are specific to the inclusion of the scalar and discuss possibilities to test this setup.

An effective gauge field theory of the nucleon interactions

We discuss the possibility of constructing an effective gauge field theory of the nucleon interactions based on the ideas of isotopic invariance as well as hypercharge invariance as a local gauge symmetry and spontaneous breaking of this symmetry. The constructed effective field theory predicts the structure of interactions of protons and neutrons with ρ- and σ-mesons, and with pi-mesons and photons, as well as interactions of these particles with each other. The Lagrangian of the theory consists of several parts involving dimension 4 and 5 gauge invariant operators. Feynman rules for physical degrees of freedom that follow on from the Lagrangian define the structure of diagrams for one-boson exchanges between nucleons, predicting the internucleon one-boson-exchange potential as well as nucleon scattering amplitudes. The range of applicability of the effective theory is discussed and estimates are made of the resulting coupling constants. The theory predicts the mass of the neutral ρ 0-meson to be about 1 MeV larger than the mass of the charged mesons ρ ±. The vector ω-meson, which is a sterile particle with respect to the considered gauge group SU I (2) × U Y (1), can be added to the scheme via a gauge-invariant operator of dimension 5, as shown in the appendix.

Large-N integrated correlators in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 SYM: when resurgence meets modularity

Exact expressions for certain integrated correlators of four half-BPS operators in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 supersymmetric Yang-Mills theory with gauge group SU(N) have been recently obtained thanks to a beautiful interplay between supersymmetric localisation and modular invariance. The large-N expansion at fixed Yang-Mills coupling of such integrated correlators produces an asymptotic series of perturbative terms, holographically related to higher derivative interactions in the low energy expansion of the type IIB effective action, as well as exponentially suppressed corrections at large N, interpreted as contributions from coincident (p, q)-string world-sheet instantons. In this work we define a manifestly modular invariant Borel resummation of the perturbative large-N expansion of these integrated correlators, from which we extract the exact non-perturbative large-N sectors via resurgence analysis. Furthermore, we show that in the ’t Hooft limit such modular invariant non-perturbative completions reduce to known resurgent genus expansions. Finally, we clarify how the same non-perturbative data is encoded in the decomposition of the integrated correlators based on SL(2, ℤ) spectral theory.

Candidate phases for SU(2) adjoint QCD$_4$ with two flavors from $\mathcal{N}=2$ supersymmetric Yang-Mills theory

We study four-dimensional adjoint QCD with gauge group SU(2)SU(2) and two Weyl fermion flavors, which has an SU(2)_RSU(2)R chiral symmetry. The infrared behavior of this theory is not firmly established. We explore candidate infrared phases by embedding adjoint QCD into {\mathcal N}=2𝒩=2 supersymmetric Yang-Mills theory deformed by a supersymmetry-breaking scalar mass MM that preserves all global symmetries and ’t Hooft anomalies. This includes ’t Hooft anomalies that are only visible when the theory is placed on manifolds that do not admit a spin structure. The consistency of this procedure is guaranteed by a nonabelian spin-charge relation involving the SU(2)_RSU(2)R symmetry that is familiar from topologically twisted {\mathcal N}=2𝒩=2 theories. Since every vacuum on the Coulomb branch of the {\mathcal N}=2𝒩=2 theory necessarily matches all ’t Hooft anomalies, we can generate candidate phases for adjoint QCD by deforming the theories in these vacua while preserving all symmetries and ’t Hooft anomalies. One such deformation is the supersymmetry-breaking scalar mass MM itself, which can be reliably analyzed when MM is small. In this regime it gives rise to an exotic Coulomb phase without chiral symmetry breaking. By contrast, the theory near the monopole and dyon points can be deformed to realize a candidate phase with monopole-induced confinement and chiral symmetry breaking. The low-energy theory consists of two copies of a \mathbb{CP}^1ℂℙ1 sigma model, which we analyze in detail. Certain topological couplings that are likely to be present in this \mathbb{CP}^1ℂℙ1 model turn the confining solitonic string of the model into a topological insulator. We also examine the behavior of various candidate phases under fermion mass deformations. We speculate on the possible large-MM behavior of the deformed {\mathcal N}=2𝒩=2 theory and conjecture that the \mathbb{CP}^1ℂℙ1 phase eventually becomes dominant.

Discrete global symmetries: gauging and twisted compactification

Discrete global symmetries of 4d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 SCFTs are studied via two operations: gauging and twisted compactification. We consider gauging of discrete symmetries in several well-known 4d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 SCFTs, including SU(n) SQCD with 2n flavors, theories of class S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{S} $$\\end{document} of type A2n−1, and Argyres-Douglas theories of type (AN, AN), as well as propose new 4d SCFTs as a result. The wreathing technique, which involves gauging a subgroup of the automorphism group of the quiver diagram of the corresponding 3d mirror theory, is exploited. This allows us to understand several properties of discretely gauged theories, including moduli spaces and how discrete gauging affects the mixed ’t Hooft anomaly between the 1-form symmetry and the 0-form flavor symmetry. Many examples are viewed through the lens of the Argyres-Seiberg duality and its generalization. We also examine discrete gauging of SU(2) SQCD with 4 flavors by various ℤ2 and ℤ2 × ℤ2 subgroups of the permutation group S4 using the superconformal index. Regarding compactification, we propose a magnetic quiver for 4d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 SU(n) SQCD with 2n flavors compactified on a circle with a ℤ2 twist. The twisted compactification by non-invertible symmetries of the 4d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 SYM theory with gauge group SU(N) is revisited. The non-invertible symmetry naturally gives rise to a ℤk action on the scalar fields parametrizing the moduli space. Upon examining the ℤk invariant chiral ring of the Higgs branch, we find that, in addition to the largest branch of the moduli space that is expected to be captured by the ABJ(M) theory, there exist in general nilpotent operators that lead to a branch of the moduli space which is a radical ideal.

Ghost-gluon vertex in the presence of the Gribov horizon: General kinematics

Correlation functions are important probes for the behavior of quantum field theories. Already at tree-level, the refined Gribov-Zwanziger (RGZ) effective action for Yang-Mills theories provides a good approximation for the gluon propagator, as compared to that calculated by nonperturbative methods such as lattice field theory and Dyson-Schwinger equations. However, the study of higher correlation functions of the RGZ theory is still at its beginning. In this work we evaluate the ghost-gluon vertex function in Landau gauge at one-loop level, in d=4 space-time dimensions for the gauge groups SU(2) and SU(3). More precisely, we extend the analysis conducted in [1] for the soft-gluon limit to an arbitrary kinematic configuration. We introduce renormalization group effects by means of a toy model for the running coupling and investigate the impact of such a model in the ultraviolet tails of our results. We find that RGZ results match fairly closely those from lattice simulations, Schwinger-Dyson equations and the Curci-Ferrari model for three different kinematic configurations. This is compatible with RGZ being a feasible theory for the strong interaction in the infrared regime. Published by the American Physical Society 2024

Towards a Standard Model with six fermion generations and a new breaking scale?

We propose here an enhanced version of the Standard Model based on the same local gauge group SU(3) c ⨂ SU(2) L ⨂ U(1) Y that undergoes a spontaneous symmetry breaking up to SU(3) c ⨂ U(1) em . We prove that it can naturally predict: (i) the electric and weak charges’ quantization, (ii) the muon anomalous magnetic moment discrepancy Δa μ , along with (iii) a realistic Higgs spectrum, (iv) a viable neutrino phenomenology, and (v) FCNCs suppression. This promising outcome—without spoiling any of the experimentally validated predictions of the Standard Model—occurs by simply assuming there are six non-universal fermion generations and two distinct scalar doublets. The latter ones develop different breaking scales, the old Standard Model scale v ≃ 246 GeV and a higher scale V —most likely in 1–100 TeV region, to be tested at LHC.

New symmetries of the two-Higgs-doublet model

The Two Higgs Doublet Model invariant under the gauge group SU(2)×U(1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$SU(2)\ imes U(1)$$\\end{document} is known to have six additional global discrete or continuous symmetries of its scalar sector. We have discovered regions of parameter space of the model which are basis and renormalization group invariant to all orders of perturbation theory in the scalar and gauge sectors, but correspond to none of the hitherto considered symmetries. We therefore identify seven new symmetries of the model and discuss their phenomenology. Soft symmetry breaking is required for some of these models so that electroweak symmetry breaking can occur. We show that, at least at the two-loop level, it is possible to extend some of these symmetries to include fermions.

A New Look at b → s Observables in 331 Models

Flavour changing neutral current (FCNC) processes are described by loop diagrams in the Standard Model (SM), while in 331 models, based on the gauge group SU(3)C×SU(3)L×U(1)X, they are dominated by tree-level exchanges of a new heavy neutral gauge boson Z′. By exploiting this feature, observables related to FCNC decays of K, Bd and Bs mesons can be considered in several variants of 331 models. The variants are distinguished by the value of a parameter β that plays a key role in this framework. Imposing constraints on the ΔF=2 observables, we select possible ranges for the mass of the Z′ boson in correspondence to the values β=±k/3, with k=1,2. The results are used to determine the impact of 331 models on b→s processes and on the correlations among them, in the light of new experimental data recently released.

The [formula omitted] vertex in a left–right model

We consider the one-loop corrections to the Zbb¯ vertex in a CP-conserving left–right model (LRM), viz. a model with gauge group SU(2)L×SU(2)R×U(1). We allow the gauge coupling constants of SU(2)L and SU(2)R to be different. The spontaneous symmetry breaking is accomplished only by doublets and/or singlets of SU(2)L and SU(2)R. The lightest massive neutral gauge boson of our LRM is assumed to have the same Yukawa couplings to bottom-quark pairs as the Z of the Standard Model (SM); this assumption has the advantage that, then, the infrared divergences automatically cancel down in the subtraction of the Zbb¯ vertex in the SM from the same vertex in the LRM. We effect a proper renormalization of the Zbb¯ vertex and check explicitly both its gauge invariance and the cancellation of all the ultraviolet divergences. We find out that a LRM with the above assumptions cannot achieve a better fit to the Zbb¯ vertex than a multi-Higgs extension of the SM, viz. both models can only achieve a decent fit when one admits scalar particles with very low masses ≲50 GeV. This is true even when we allow for markedly different gauge coupling constants of SU(2)L and SU(2)R.

Oblique corrections from leptoquarks

We present general formulas for the oblique-correction parameters S, T, U, V, W, and X in a model of New Physics having arbitrary numbers of scalar leptoquarks of the five permissible types. We allow for a general mixing among the scalars of the various electric charges, viz. −4/3, −1/3, 2/3, and 5/3. We then extend the formulas to the case of a New Physics model with additional scalars in any representations of the gauge group SU(2) × U(1), mixing arbitrarily among themselves.

Charge instability of JMaRT geometries

We perform a detailed study of linear perturbations of the JMaRT family of non-BPS smooth horizonless solutions of type IIB supergravity beyond the near-decoupling limit. In addition to the unstable quasi normal modes (QNMs) responsible for the ergo-region instability, already studied in the literature, we find a new class of ‘charged’ unstable modes with positive imaginary part, that can be interpreted in terms of the emission of charged (scalar) quanta with non zero KK momentum. We use both matched asymptotic expansions and numerical integration methods. Moreover, we exploit the recently discovered correspondence between JMaRT perturbation theory, governed by a Reduced Confluent Heun Equation, and the quantum Seiberg-Witten (SW) curve of N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 SYM theory with gauge group SU(2) and Nf = (0, 2) flavours.

Conformally invariant nonlinear electrodynamic actions and its non-abelian extensions

In this work, formal theoretical aspects concerning conformally invariant functional actions of electrodynamics are presented and discussed. In particular, the origin of the conformal and duality invariant Lagrangians of [I. Bandos et al., J. High Energy Phys. 10 (2021) 031; I. Bandos, K. Lechner, D. Sorokin and P. Townsend, Phys. Rev. D 102 (2020) 121703] (e.g. ModMax) and also Born–Infeld types are analyzed being its non-abelian counterpart presented and discussed explicitly for the gauge group SU(2). Implications on the properties of the gravitational field are briefly discussed by means of new symmetries of the field equations.

Exact large charge in mathcal{N} = 4 SYM and semiclassical string theory

In four-dimensional mathcal{N} = 4 super Yang-Mills theory with gauge group SU(N), we present a closed-form solution for a family of integrated four-point functions involving stress tensor multiplet composites of arbitrary R-charge. These integrated correlators are shown to be equivalent to a one-dimensional semi-infinite lattice of harmonic oscillators with nearest-neighbor interactions, evolving over the fundamental domain of SL(2, ℤ). The solution, exceptionally simple in an SL(2, ℤ)-invariant eigenbasis, is exact in the R-charge p, rank N, and complexified gauge coupling τ. This permits a systematic and non-perturbative large charge expansion for any N and τ. Especially novel is a double-scaled “gravity regime” in which p ~ N2 ≫ 1, holographically dual to a large charge regime of semiclassical type IIB string theory in AdS5 × S5. Our results in this limit provide a holographic computation of integrated semiclassical string amplitudes at arbitrary string coupling, including an emergent string scale with a large charge dressing factor. We compare to extremal correlators in superconformal QCD, for which we predict new genus expansions at large charge scaling with N.

Defect correlators in a mathcal{N} = 2 SCFT at strong coupling

We study the correlation function between one single-trace scalar operator and a circular Wilson loop in the 4d mathcal{N} = 2 superconformal field theory with gauge group SU(N) and matter transforming in the symmetric and anti-symmetric representations. By exploiting supersymmetric localization, we resum the perturbative expansion of this correlator in the large-N ’t Hooft limit. Furthermore, using both analytical and numerical techniques, we provide a prediction for the leading term of its strong coupling expansion and we compare this prediction to numerical Padé resummations of the perturbative series.

Emergent N=4 Supersymmetry from N=1.

We discover a four-dimensional N=1 supersymmetric field theory that is dual to the N=4 super Yang-Mills theory with gauge group SU(2n+1) for each n. The dual theory is constructed through the diagonal gauging of the SU(2n+1) flavor symmetry of three copies of a strongly coupled superconformal field theory (SCFT) of Argyres-Douglas type. We find that this theory flows in the infrared to a strongly coupled N=1 SCFT that lies on the same conformal manifold as N=4 super Yang-Mills with gauge group SU(2n+1). Our construction provides a hint on why certain N=1, 2 SCFTs have identical central charges (a=c).

Free energy on the sphere for non-abelian gauge theories

We compute the Sd partition function of the fixed point of non-abelian gauge theories in continuous d, using the ϵ-expansion around d = 4. We illustrate in detail the technical aspects of the calculation, including all the factors arising from the gauge-fixing procedure, and the method to deal with the zero-modes of the ghosts. We obtain the result up to NLO, i.e. including two-loop vacuum diagrams. Depending on the sign of the one-loop beta function, there is a fixed point with real gauge coupling in d > 4 or d < 4. In the first case we extrapolate to d = 5 to test a recently proposed construction of the UV fixed point of 5d SU(2) Yang-Mills via a susy-breaking deformation of the E1 SCFT. We find that the F theorem allows the proposed RG flow. In the second case we extrapolate to d = 3 to test whether QCD3 with gauge group SU(nc) and nf fundamental matter fields flows to a CFT or to a symmetry-breaking case. We find that within the regime with a real gauge coupling near d = 4 the CFT phase is always favored. For lower values of nf we compare the average of F between the two complex fixed points with its value at the symmetry-breaking phase to give an upper bound of the critical value {n}_f^{ast } below which the symmetry-breaking phase takes over.

331 model predictions for rare B and K decays, and ∆F = 2 processes: an update

Motivated by the improved results from the HPQCD lattice collaboration on the hadronic matrix elements entering ∆Ms,d in {B}_{s,d}^0-{overline{B}}_{s,d}^0 mixings and the increase of the experimental branching ratio for Bs→ μ+μ−, we update our 2016 analysis of various flavour observables in four 331 models, M1, M3, M13 and M16 based on the gauge group SU(3)C× SU(3)L× U(1)X. These four models, which are distinguished by the quantum numbers, are selected among 24 331 models through their consistency with the electroweak precision tests and simultaneously by the relation {C}_9^{textrm{NP}}=-{bC}_{10}^{textrm{NP}} with 2 ≤ b ≤ 5, which after new result on Bs→ μ+μ− from CMS is favoured over the popular relation {C}_9^{textrm{NP}}=-{C}_{10}^{textrm{NP}} predicted by several leptoquark models. In this context we investigate in particular the dependence of various observables on |Vcb|, varying it in the broad range [0.0386, 0.043], that encompasses both its inclusive and exclusive determinations. Imposing the experimental constraints from εK, ∆Ms, ∆Md and the mixing induced CP asymmetries {S}_{psi {K}_S} and {S}_{psi {K}_S} , we investigate for which values of |Vcb| the four models can be made compatible with these data and what is the impact on B and K branching ratios. In particular we analyse NP contributions to the Wilson coefficients C9 and C10 and the decays Bs,d→ μ+μ−, {K}^{+}to {pi}^{+}nu overline{nu} and {K}_Lto {pi}^0nu overline{nu} . This allows us to illustrate how the value of |Vcb| determined together with other parameters of these models is infected by NP contributions and compare it with the one obtained recently under the assumption of the absence of NP in εK, ∆Ms, ∆Md and {S}_{psi {K}_S} .

Words to describe a black hole

We revamp the constructive enumeration of 1/16-BPS states in the maximally supersymmetric Yang-Mills in four dimensions, and search for ones that are not of multi-graviton form. A handful of such states are found for gauge group SU(2) at relatively high energies, resolving a decade-old enigma. Along the way, we clarify various subtleties in the literature, and prove a non-renormalization theorem about the exactness of the cohomological enumeration in perturbation theory. We point out a giant-graviton-like feature in our results, and envision that a deep analysis of our data will elucidate the fundamental properties of black hole microstates.

A survey of family unification models with bifundamental matter

Extensions of the Standard Model have been attempted from the bottom up and from the top down, yet there remains a largely unexplored middle ground. In this paper, using the Mathematica package LieART, we exhaustively enumerate embeddings of the Standard Model within the class of theories with bifundamental fermions in product gauge group SU(a)×SU(b)×SU(c) with no more generators than E6, while achieving SM family unification rather than replication. We incorporate simple phenomenological constraints and find 151 unique models, including 9 that have only vector-like particle content beyond-the-Standard Model (BSM) particles, which we conjecture belong to 5 infinite families of such models. We describe the potentially most viable models: namely, the 9 with strictly vector-like BSM content along with the 29 models we found with no more than 30 additional BSM chiral particles. These include models with fractional electric charge color singlets, and hence magnetic monopoles with multiple Dirac charge. This latter collection of models predicts chiral particles with masses near the electroweak scale accessible to current and future collider experiments.