Fundamental Representation Of SU Research Articles

Gravitating anisotropic merons and squashed spheres in the three-dimensional Einstein-Yang-Mills-Chern-Simons theory

We construct the first analytic examples of self-gravitating anisotropic merons in the Einstein-Yang-Mills-Chern-Simons theory in three dimensions. The gauge field configurations have different meronic parameters along the three Maurer-Cartan 1-forms and they are topologically nontrivial as the Chern-Simons invariant is nonzero. The corresponding backreacted metric is conformally a squashed three-sphere. The amount of squashing is related to the degree of anisotropy of the gauge field configurations that we compute explicitly in different limits of the squashing parameter. Moreover, the spectrum of the Dirac operator on this background is obtained explicitly for spin-1/2 spinors in the fundamental representation of SU(2), and the genuine non-Abelian contributions to the spectrum are identified. The physical consequences of these results are discussed.

Standard model gauge fields localized on non-Abelian vortices in six dimensions

Abstract A brane-world SU(5) grand unified theory model with global non-Abelian vortices is constructed in six-dimensional spacetime. We find a solution with a vortex associated to SU(3) separated from another vortex associated to SU(2). This 3–2 split configuration achieves a geometric Higgs mechanism for SU(5) → SU(3) × SU(2) × U(1) symmetry breaking. A simple deformation potential induces a domain wall between non-Abelian vortices, leading to a linear confining potential. The confinement stabilizes the vortex separation moduli, and ensures the vorticities of the SU(3) and SU(2) groups are identical. This dictates the equality of the numbers of fermion zero modes in the fundamental representation of SU(3) (quarks) and SU(2) (leptons), leading to quark/lepton generations. The standard model massless gauge fields are localized on the non-Abelian vortices thanks to a field-dependent gauge kinetic function. We perform fluctuation analysis with an appropriate gauge fixing and obtain a four-dimensional effective Lagrangian of unbroken and broken gauge fields at quadratic order. We find that SU(3) × SU(2) × U(1) gauge fields are localized on the vortices and exactly massless. Complications in analyzing the spectra of gauge fields with the nontrivial gauge kinetic function are neatly worked out by a vector-analysis-like method.

Flavor, temperature and magnetic field dependence of the QCD phase diagram: magnetic catalysis and its inverse

We study dynamical chiral symmetry breaking for quarks in the fundamental representation of SU(N c) for the N f number of light quark flavors. We also investigate the phase diagram of quantum chromodynamics at finite temperature T and/or in the presence of a constant external magnetic field eB. The unified formalism for this analysis is provided by a symmetry-preserving Schwinger–Dyson equation treatment of a vector × vector contact interaction model which encodes several well-established features of quantum chromodynamics to mimic the latter as closely as possible. Deconfinement and chiral symmetry restoration are triggered above a critical value of N f at T = 0 = eB. On the other hand, increasing temperature itself screens strong interactions, thus ensuring that a smaller value of N f is sufficient to restore chiral symmetry at higher temperatures. We also observe the well-known phenomenon of magnetic catalysis for a strong enough magnetic field. However, we note that if the effective coupling strength of the model decreases as a function of magnetic field, it can trigger inverse magnetic catalysis in a certain window of this functional dependence. Our model allows for the simultaneous onset of dynamical chiral symmetry breaking and confinement for each case. Qualitative as well as quantitative predictions of our simple but effective model are in reasonably satisfactory agreement with lattice results and other reliable and refined predictions based upon intricate continuum studies of quantum chromodynamics.

Scattering amplitudes in mathcal{N} = 3 supersymmetric SU(N) Chern-Simons-matter theory at large N

We study mathcal{N} = 3 supersymmetric Chern-Simons-matter theory coupled to matter in the fundamental representation of SU(N). In the ’t Hooft large N limit, we compute the exact 2 → 2 scattering amplitudes of the fundamental scalar superfields to all orders in the ’t Hooft coupling λ. Our computations are presented in mathcal{N} = 1 superspace and make significant use of the residual SO(2)R symmetry in order to solve for the exact four-point correlator of the scalar superfields. By taking the on-shell limit, we are able to extract the exact 2 → 2 scattering amplitudes of bosons/fermions in the symmetric, anti-symmetric and adjoint channels of scattering. We find that the scattering amplitude of the mathcal{N} = 3 theory in the planar limit is tree-level exact to all orders in the ’t Hooft coupling λ. The result is consistent with the conjectured bosonization duality and is expected to have enhanced symmetry structures such as dual superconformal symmetry and Yangian symmetry.

Large N renormalization group flows in 3d mathcal{N} = 1 Chern-Simons-Matter theories

We discuss 3d mathcal{N} = 1 supersymmetric SU(N) and U(N) Chern-Simons-matter theories, with Nf matter superfields in the fundamental representation of SU(N) or U(N). In the large N ’t Hooft limit with fixed ’t Hooft coupling λ these theories have one (for Nf = 1) or two (for Nf> 1) exactly marginal deformations in the superpotential. At finite N these couplings acquire a beta function. We compute the beta function exactly for λ = 0, at leading order in 1/N. For Nf = 1 we find four fixed points, one of which is triply-degenerate. We show that at large N there are at most six fixed points for any λ, and conjecture that there are exactly six, with three of them stable (including a point with enhanced mathcal{N} = 2 supersymmetry). The strong-weak coupling dualities of mathcal{N} = 1 Chern-Simons-matter theories map each of these fixed points to a dual one. We show that at large N the phase structure near each of the three stable fixed points is different. For Nf> 1 we analyze the fixed points at weak coupling, and we work out the action of the strong-weak coupling duality on the marginal and relevant superpotential couplings at large N (which was previously known only for Nf = 1). In addition, we compute in these theories the 2-point and 3-point functions of the lowest gauge-invariant singlet superfield at large N, for all values of λ and of the superpotential couplings, and use them to test the large N dualities. This computation is one of the ingredients needed for a computation of the beta function at order 1/N for all λ, which we leave for future work. We also discuss Chern-Simons-matter theories with extra Hubbard-Stratonovich type singlet fields, and suggest dualities between them.

New vortex-string worldsheet theories from supersymmetric localization

We use supersymmetric localization techniques to study the low-energy dynamics of BPS vortex-strings in four-dimensional mathcal{N}=2 theories. We focus on theories with SU(Nc) × U(1) gauge group and Nf hypermultiplets, all in the fundamental representation of SU(Nc) but with general U(1) charges. Recently, we proposed a condition that determines whether the low-energy string dynamics is captured by a two-dimensional worldsheet theory that decouples from the bulk [1]. For strings for which this decoupling applies, we propose a prescription for extracting the two-sphere partition function of the string worldsheet theory from the four-ellipsoid partition function of the parent theory. We obtain a general formula for the worldsheet two-sphere partition function in terms of the parameters of the four-dimensional theory and identify mathcal{N}=left(2,2right) GLSMs that possess these partition functions in a large class of examples. In these examples, the weak coupling regime of the four-dimensional theory is mapped to the weak coupling regime of the worldsheet theory. In addition, we study the classical string zero-modes in flat space and obtain predictions for the worldsheet spectra, which agree with the low-energy spectra of the GLSMs obtained in the localization analysis. For Nf = 2Nc = 4, we discuss the map between string worldsheet theories under four-dimensional S-duality and use our prescription to study examples in which the weak coupling regime of the four-dimensional theory is mapped to the strong coupling regime of the worldsheet theory.

Spinorial flux tubes in SO(N) gauge theories in 2+1 dimensions

We investigate whether one can observe in SO(3) and SO(4) (lattice) gauge theories the presence of spinorial flux tubes, i.e. ones that correspond to the fundamental representation of SU(2); and similarly for SO(6) and SU(4). We do so by calculating the finite volume dependence of the Jp = 2+ glueball in 2 + 1 dimensions, using lattice simulations. We show how this provides strong evidence that these SO(N) gauge theories contain states that are composed of (conjugate) pairs of winding spinorial flux tubes, i.e. ones that are in the (anti)fundamental of the corresponding SU(N′) gauge theories. Moreover, these two flux tubes can be arbitrarily far apart. This is so despite the fact that the fields that are available in the SO(N) lattice field theories do not appear to allow us to construct operators that project onto single spinorial flux tubes.

Vortex-strings in mathcal{N}=2 SQCD and bulk-string decoupling

We study vortex-strings in four-dimensional mathcal{N}=2 supersymmetric SU(Nc) × U(1) gauge theories with Nf hypermultiplets in the fundamental representation of SU(Nc) and general U(1) charges. If Nf> Nc, the vacuum is not gapped and the low-energy theory contains both the vacuum massless excitations and the string zero-modes. The question we address in this work is whether the vacuum and the string moduli decouple at low energies, allowing a description of the low-energy dynamics in terms of a two-dimensional theory on the string worldsheet. We find a simple condition controlling the bulk-string coupling: if there exist two flavors such that the product of their U(1) charge difference with the magnetic flux carried by the string configuration is not an integer multiple of 2π, the string has zero-modes that decay slower than 1/r, where r is the radial distance from the string core. These modes are coupled to the vacuum massless excitations even at low energies. If, however, all such products are integer multiples of 2π, long-range modes of this type do not exist and the string moduli decouple from the bulk at low energies. This condition turns out to coincide with the condition of trivial Aharonov-Bohm phases for the particles in the spectrum. In addition to a derivation of the bulk-string decoupling criterion using classical analysis of the string zero-modes, we provide a non-perturbative derivation of the criterion, which uses supersymmetric localization techniques.

SU(2) with fundamental fermions and scalars

We present preliminary results on the lattice simulation of an SU(2) gauge theory with two fermion flavors and one strongly interacting scalar field, all in the fundamental representation of SU(2). The motivation for this study comes from the recent proposal of “fundamental” partial compositeness models featuring strongly interacting scalar fields in addition to fermions. Here we describe the lattice setup for our study of this class of models and a first exploration of the lattice phase diagram. In particular we then investigate how the presence of a strongly coupled scalar field affects the properties of light meson resonances previously obtained for the SU(2) model. Preprint: CP3-Origins-2017-047 DNRF90

Residual non-Abelian dark matter and dark radiation

We propose a novel particle physics model in which vector dark matter (VDM) and dark radiation (DR) originate from the same non-Abelian dark sector. We show an illustrating example where dark SU(3) is spontaneously broken into SU(2) subgroup by the nonzero vacuum expectation value (VEV) of a complex scalar in fundamental representation of SU(3). The massless gauge bosons associated with the residual unbroken SU(2) constitute DR and help to relieve the tension in Hubble constant measurements between Planck and Hubble Space Telescope. In the meantime, massive dark gauge bosons associated with the broken generators are VDM candidates. Intrinsically, this non-Abelian VDM can interact with non-Abelian DR in the cosmic background, which results in a suppressed matter power spectrum and leads to a smaller σ8 for structure formation.

One-loop renormalization of the chiral Lagrangian for spinless matter fields in the SU(N) fundamental representation

We perform the leading one-loop renormalization of the chiral Lagrangian for spinless matter fields living in the fundamental representation of SU(N). The Lagrangian can also be applied to any theory with a spontaneous symmetry breaking of SU(N)L × SU(N)R to SU and spinless matter fields in the fundamental representation. For QCD, the matter fields can be kaons or pseudoscalar heavy mesons. Using the background field method and heat kernel expansion techniques, the divergences of the one-loop effective generating functional for correlation functions of single matter fields are calculated up to , where p denotes a small momentum or Goldstone boson mass. The divergences are absorbed by counterterms not only from the third order but also from the second order chiral Lagrangian.

Non-Abelian vortices with a twist

Non-Abelian flux-tube (string) solutions carrying global currents are found in the bosonic sector of four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories. The specific model considered here possesses ${U(2)}_{\text{local}}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(2)}_{\text{global}}$ symmetry, with two scalar doublets in the fundamental representation of SU(2). We construct string solutions that are stationary and translationally symmetric along the ${x}^{3}$ direction, and they are characterized by a matrix phase between the two doublets, referred to as ``twist.'' Consequently, twisted strings have nonzero (global) charge, momentum, and in some cases even angular momentum per unit length. The planar cross section of a twisted string corresponds to a rotationally symmetric, charged non-Abelian vortex, satisfying first-order Bogomolny-type equations and second-order Gauss constraints. Interestingly, depending on the nature of the matrix phase, some of these solutions even break cylindrical symmetry in ${\mathbb{R}}^{3}$. Although twisted vortices have higher energy than the untwisted ones, they are expected to be linearly stable since one can keep their charge (or twist) fixed with respect to small perturbations.

Heavy squarks and light sleptons in gauge mediation. From the viewpoint of 125 GeV Higgs boson and muon g − 2

In the framework of gauge mediation models, we investigate scenarios with heavy squarks and light sleptons, motivated by the recent discovery of the Higgs boson and the deviation of the muon anomalous magnetic moment (g − 2) from the SM prediction. We show that only models with a messenger multiplet in the adjoint representation of SU(5) GUT gauge group are the unique possibility that sleptons are light enough to explain the muon g − 2 in the minimal setup. We also show that, if there is an additional source of the Higgs soft masses, the muon g − 2 can be explained with messenger multiples in the fundamental representation of SU(5) with the help of the light higgsino. Some phenomenological aspects of these models are also discussed.

Extended Semiotic Squares of Three Attributes, the Fundamental Representation of SU(3) and Linguistic Flexibility

Extended Semiotic Squares of Three Attributes, the Fundamental Representation of SU(3) and Linguistic Flexibility

Moduli spaces of cold holographic matter

We use holography to study (3+1)-dimensional N=4 supersymmetric Yang-Mills theory with gauge group SU(Nc), in the large-Nc and large-coupling limits, coupled to a single massless (n+1)-dimensional hypermultiplet in the fundamental representation of SU(Nc), with n=3,2,1. In particular, we study zero-temperature states with a nonzero baryon number charge density, which we call holographic matter. We demonstrate that a moduli space of such states exists in these theories, specifically a Higgs branch parameterized by the expectation values of scalar operators bilinear in the hypermultiplet scalars. At a generic point on the Higgs branch, the R-symmetry and gauge group are spontaneously broken to subgroups. Our holographic calculation consists of introducing a single probe Dp-brane into AdS5 times S^5, with p=2n+1=7,5,3, introducing an electric flux of the Dp-brane worldvolume U(1) gauge field, and then obtaining explicit solutions for the worldvolume fields dual to the scalar operators that parameterize the Higgs branch. In all three cases, we can express these solutions as non-singular self-dual U(1) instantons in a four-dimensional space with a metric determined by the electric flux. We speculate on the possibility that the existence of Higgs branches may point the way to a counting of the microstates producing a nonzero entropy in holographic matter. Additionally, we speculate on the possible classification of zero-temperature, nonzero-density states described holographically by probe D-branes with worldvolume electric flux.

Supersymmetric grand unification with light color-triplet

We construct a natural model of the supersymmetric SU(6) unification, in which the symmetry breaking, down to the standard model gauge group, results in the number of pseudo-Nambu–Goldstone superfields with interesting properties. Namely, besides the Higgs doublet–antidoublet pair which is responsible for the electroweak phase transition, the Nambu–Goldstone sector consists of multiplets in the anti- and fundamental representations of SU(5). While being strictly massless in the supersymmetric limit, they acquire the weak scale masses as a result of its breaking. The color-triplet components of this light sector could, in principle, mediate an unacceptably fast proton decay; however, because of the natural TeV/MGUT suppression of the Yukawa couplings to the light quarks and leptons, their existence is compatible with the experimental bound on proton lifetime. This suppression is made further interesting, since it results in the lifetime, of the lightest of the above-mentioned colored particles from 1 s to 1 day, long enough for it to appear stable in the detector. Furthermore, we argue that the accommodation of the color-triplet pseudo-Nambu–Goldstones, without fine-tuning or contradicting observations, implies SU(6) unification.

Chiral helix in AdS/CFT correspondence with flavor

The D3/D7 holographic model aims at a better approximation to QCD by adding to N=4 SYM theory N_f of N=2 supersymmetric hypermultiplets in the fundamental representation of SU(N_c) -- the "flavor fields" representing the quarks. Motivated by a recent observation of the importance of the Wess-Zumino-like (WZ) term for realizing the chiral magnetic effect within this model, we revisit the phase diagram of the finite temperature, massless D3/D7 model in the presence of external electric/magnetic fields and at finite chemical potential. We point out that the A-V-V triangle anomaly represented by the WZ term in the D7 brane probe action implies the existence of new phases that have been overlooked in the previous studies. In the case of an external magnetic field and at finite chemical potential, we find a "chiral helix" phase in which the U(1)_A angle of D7 brane embedding increases monotonically along the direction of the magnetic field -- this is a geometric realization of the chiral spiral phase in QCD. We also show that in the case of parallel electric and magnetic fields (E,B) there exists a phase in which the D7 brane spontaneously begins to rotate, so that the U(1)_A angle changes as a function of time -- this may be called the "spontaneous rotation" phase; it is a geometrical realization of a phase with non-zero chiral chemical potential. Our results call for a more thorough study of the (T,B,E,\mu) phase diagram of the massless D3/D7 model taking a complete account of the WZ term. We also speculate about the possible phase diagram in the massive case.

Two dimensional fermions in three dimensional YM

Dirac fermions in the fundamental representation of SU(N) live on the surface of a cylinder embedded in $R^3$ and interact with a three dimensional SU(N) Yang Mills vector potential preserving a global chiral symmetry at finite $N$. As the circumference of the cylinder is varied from small to large, the chiral symmetry gets spontaneously broken in the infinite $N$ limit at a typical bulk scale. Replacing three dimensional YM by four dimensional YM introduces non-trivial renormalization effects.

Two dimensional fermions in four dimensional YM

Dirac fermions in the fundamental representation of SU(N) live on a two dimensional torus flatly embedded in $R^4$. They interact with a four dimensional SU(N) Yang Mills vector potential preserving a global chiral symmetry at finite $N$. As the size of the torus in units of $\frac{1}{\Lambda_{SU(N)}}$ is varied from small to large, the chiral symmetry gets spontaneously broken in the infinite $N$ limit.

Study of Relativistic Corrections due to Spin–Orbit Interaction of Fermion–Dyon System Under SU(2) Gauge Potential in Moduli Space

Investigating energy eigen values of fermion–dyon system under the fundamental representation of SU(2) isospin group, it is shown that the equation contains an extra term, which depicts interaction of spin moment with a vector field. The study of fermion–dyon interaction in non-abelian gauge theory has also been undertaken and the splitting of energy level of the system has been carried out.