Adjoint Scalar Research Articles

Shapes of magnetic monopoles in effective SU(2) models

We present a systematic exploration of a general family of effective $SU(2)$ models with an adjoint scalar. First, we discuss a redundancy in this class of models and use it to identify seemingly different, yet physically equivalent models. Next, we construct the Bogomol'nyi-Prasad-Sommerfield (BPS) limit and derive analytic monopole solutions. In contrast to the 't Hooft-Polyakov monopole, included here as a special case, these solutions tend to exhibit more complex energy density profiles. Typically, we obtain monopoles with a hollow cavity at their core where virtually no energy is concentrated; accordingly, most of the monopole's energy is stored in a spherical shell around its core. Moreover, the shell itself can be structured, with several "sub-shells". A recipe for the construction of these analytic solutions is presented.

Early evolution of optimal perturbations in a viscosity-stratified channel

Abstract

’t Hooft–Polyakov Monopole and Instanton-like Topological Solution in Gauge-Higgs Unification

We consider 't Hooft-Polyakov monopole (TPM) as a topological soliton in the 5-dimensional (5D) theory of gauge-Higgs unification. This scenario provides a very natural framework to incorporate the TPM, since the adjoint scalar is builtin as the extra-space component of higher dimensional gauge field. In the process of the analysis, we realize that the condition to be satisfied by the Bogomolny-Prasad-Sommerfield (BPS) state of TPM, the BPS monopole, is equivalent to an (anti-)self-dual condition for the higher dimensional gauge field. This observation, in turn, suggests the presence of instanton-like topological soliton living in the 4D space (including the extra dimension), instead of the 4D space-time in the case of ordinary instanton, say "space-like instanton" with finite energy, instead of finite action. We construct the field configuration for the space-like instanton and calculate its mass, handled by the compactification scale. Next we discuss the BPS monopole, as an anti-self-dual gauge field. We start by constructing a hedgehog-type solution as what is obtained by a local gauge transformation from a trivial vacuum. We also argue in some detail that the relation between these two types of topological solitons becomes manifest through the unified description by use of the ansatz adopted by 't Hooft.

Holographic Wilson lines as screened impurities

In Landau Fermi liquids, screened impurities support quasi-bound states, representing electrons bound to the impurity but making virtual excursions away. Signals of these quasi-bound states are electron-impurity scattering phase shifts and the corresponding resonances in cross sections. We consider large-N , strongly-coupled (3 + 1)-dimensional mathcal{N} = 4 supersymmetric SU(N ) Yang-Mills theory on the Coulomb branch, where an adjoint scalar has a non-zero expectation value that breaks SU(N ) → SU(N − 1) × U(1). In the holographic dual we re-visit well-known solutions for a probe D3-brane that describe this theory with a symmetric-representation Wilson line “impurity”. We present evidence that the adjoint scalar screens the Wilson line, by showing that quasi-bound states form at the impurity, producing U(1)-impurity scattering phase shifts and corresponding resonances in cross sections. The quasi-bound states appear holographically as quasi-normal modes of probe D3-brane fields, even in the absence of a black hole horizon, via a mechanism that we argue is generic to screened defects in holography. We also argue that well-known generalisations of these probe D3-brane solutions can describe lattices of screened Wilson/’t Hooft line impurities.

Skyrme–Faddeev model from 5d super-Yang–Mills

We consider 5d Yang–Mills–Higgs theory with a compact ADE-type gauge group G and one adjoint scalar field on R3,1×R+, where R+=[0,∞) is the half-line. The maximally supersymmetric extension of this model, with five adjoint scalars, appears after a reduction of 6d N=(2,0) superconformal field theory on R3,1×R+×S1 along the circle S1. We show that in the low-energy limit, when momenta along R3,1 are much smaller than along R+, the 5d Yang–Mills–Higgs theory reduces to a nonlinear sigma model on R3,1 with a coset G/H as its target space. Here H is a closed subgroup of G determined by the Higgs-field asymptotics at infinity. The 4d sigma model describes an infinite tower of interacting fields, and in the infrared it is dominated by the standard two-derivative kinetic term and the four-derivative Skyrme–Faddeev term.

One-loop pseudo-Goldstone masses in the minimal SO(10) Higgs model

We calculate the prominent perturbative contributions shaping the one-loop scalar spectrum of the minimal non-supersymmetric renormalizable $SO(10)$ Higgs model whose unified gauge symmetry is spontaneously broken by an adjoint scalar. Focusing on its potentially realistic $45\oplus 126$ variant in which the rank is reduced by a VEV of the 5-index self-dual antisymmetric tensor, we provide a thorough analysis of the corresponding one-loop Coleman-Weinberg potential, paying particular attention to the masses of the potentially tachyonic pseudo-Goldstone bosons (PGBs) transforming as $(8,1,0)$ and $(1,3,0)$ under the Standard Model gauge group. The results confirm the assumed existence of extended regions in the parameter space supporting a locally stable SM-like quantum vacuum inaccessible at the tree-level. The effective potential (EP) tedium is compared to that encountered in the previously studied $45\oplus 16$ $SO(10)$ Higgs model where the polynomial corrections to the relevant pseudo-Goldstone masses turn out to be easily calculable within a very simplified purely diagrammatic approach.

Emergent Inert Adjoint Scalar Field in SU(2) Yang-Mills Thermodynamics due to Coarse-Grained Topological Fluctuations

We compute the phase and the modulus of an energy- and pressure-free, composite, adjoint, and inert field in an SU(2) Yang-Mills theory at large temperatures. This field is physically relevant in describing part of the ground-state structure and the quasiparticle masses of excitations. The field possesses nontrivial -winding on the group manifold . Even at asymptotically high temperatures, where the theory reaches its Stefan-Boltzmann limit, the field , though strongly power suppressed, is conceptually relevant: its presence resolves the infrared problem of thermal perturbation theory.

Phases of one dimensional large N gauge theory in a 1/D expansion

We consider large N Yang Mills theory with D adjoint scalar fields in d dimensions for d=0 or 1. We show the existence of a non-trivial saddle point of the functional integral at large D which is characterized by a mass gap for the adjoint scalars. We integrate out the adjoint scalars in a 1/D expansion around the saddle point. In case of one dimension which is regarded as a circle, this procedure leads to an effective action for the Wilson line. We find an analogue of the confinement/deconfinement transition which consists of a second order phase transition from a uniform to a non-uniform eigenvalue distribution of the Wilson line, closely followed by a Gross-Witten-Wadia transition where a gap develops in the eigenvalue distribution. The phase transition can be regarded as a continuation of a Gregory-Laflamme transition. Our methods involve large values of the dimensionless 'tHooft coupling. The analysis in this paper is quantitatively supported by earlier numerical work for D=9.

Classical spin chains and exact three-dimensional superpotentials

We study exact effective superpotentials of four-dimensional N = 2 supersymmetric gauge theories with gauge group U ( N ) and various amounts of fundamental matter on R 3 × S 1 , broken to N = 1 by turning on a classical superpotential for the adjoint scalar. On general grounds these superpotentials can easily be constructed once we identify a suitable set of coordinates on the moduli space of the gauge theory. These coordinates have been conjectured to be the phase space variables of the classical integrable system which underlies the N = 2 gauge theory. The sought low energy effective superpotential can then be constructed from the conserved quantities in the integrable system. For the gauge theory under study these integrable systems are degenerations of the classical, inhomogeneous, periodic SL ( 2 , C ) spin chain. Ambiguities in the degeneration provide multiple coordinate patches on the gauge theory moduli space. By studying the vacua of these superpotentials in several examples we find that the spin chain provides coordinate patches that parametrize holomorphically the part of the gauge theory moduli space which is connected to the electric (as opposed to magnetic or baryonic) Higgs and Coulomb branch vacua. The baryonic branch root is on the edge of some coordinate patches. As a product of our analysis all maximally confining (non-baryonic) Seiberg–Witten curve factorizations for N f ⩽ N c are obtained, explicit up to one constraint for equal mass flavors and up to two constraints for unequal mass flavors. Gauge theory addition and multiplication maps are shown to have a natural counterpart in this construction. Furthermore it is shown how to integrate in the meson fields in this formulation in order to obtain three- and four-dimensional Affleck–Dine–Seiberg-like superpotentials.

Gauge unification in extra dimensions: power corrections vs. higher dimension operators

Power-like loop corrections to gauge couplings are a generic feature of higher-dimensional field theories. In supersymmetric grand unified theories in d = 5 dimensions, such corrections arise only in the presence of a vacuum expectation value of the adjoint scalar of the gauge multiplet. We show that, using the analysis of the exact quantum effective action by Intriligator, Morrison and Seiberg, these power corrections can be understood as the effect of higher dimension operators. Such operators, both classical and quantum, are highly constrained by gauge symmetry and supersymmetry. As a result, even non-perturbatively large contributions to gauge coupling unification can be unambiguously determined within 5d low-energy effective field theory. Since no massive hypermultiplet matter exists in 6 dimensions, the predictivity is further enhanced by embedding the 5d model in a 6d gauge theory relevant at smaller distances. Thus, large and quantitatively controlled power-law contributions to gauge couplings arise naturally and can, in the most extreme case, lead to calculable TeV-scale power law unification. We identify a simple 5d SU(5) model with one massless 10 in the bulk where the power-law effect is exactly MSSM-like.

Holographic RG flows and universal structures on the Coulomb branch of supersymmetric large- gauge theory

We report on our results of D3-brane probing a large class of generalised type IIB supergravity solutions presented very recently in the literature. The structure of the solutions is controlled by a single non-linear differential equation. These solutions correspond to renormalisation group flows from pure N=4 supersymmetric gauge theory to an N=2 gauge theory with a massive adjoint scalar. The gauge group is SU(n) with n large. After presenting the general result, we focus on one of the new solutions, solving for the specific coordinates needed to display the explicit metric on the moduli space. We obtain an appropriately holomorphic result for the coupling. We look for the singular locus, and interestingly, the final result again manifests itself in terms of a square root branch cut on the complex plane, as previously found for a set of solutions for which the details are very different. This, together with the existence of the single simple non-linear differential equation, is further evidence in support of an earlier suggestion that there is a very simple model --perhaps a matrix model with relation to the Calogero-Moser integrable system-- underlying this gauge theory physics.

Metastable strings in Abelian Higgs models embedded in non-Abelian theories: Calculating the decay rate

We study the fate of U(1) strings embedded in a non-Abelian gauge theory with a hierarchical pattern of the symmetry breaking: G->U(1) at V->nothing at v, V>>v. While in the low-energy limit the Abrikosov-Nielsen-Olesen string (flux tube) is perfectly stable, being considered in the full theory it is metastable. We consider the simplest example: the magnetic flux tubes in the SU(2) gauge theory with adjoint and fundamental scalars. First, the adjoint scalar develops a vacuum expectation value V breaking SU(2) down to U(1). Then, at a much lower scale, the fundamental scalar (quark) develops a vacuum expectation value v creating the Abrikosov-Nielsen-Olesen string. (We also consider an alternative scenario in which the second breaking, U(1)->nothing, is due to an adjoint field.) We suggest an illustrative ansatz describing an "unwinding" in SU(2) of the winding inherent to the Abrikosov-Nielsen-Olesen strings in U(1). This ansatz determines an effective 2D theory for the unstable mode on the string world-sheet. We calculate the decay rate (per unit length of the string) in this ansatz and then derive a general formula. The decay rate is exponentially suppressed. The suppressing exponent is proportional to the ratio of the monopole mass squared to the string tension, which is quite natural in view of the string breaking through the monopole-antimonopole pair production. We compare our result with the one given by Schwinger's formula dualized for describing the monopole-antimonopole pair production in the magnetic field.

Topological charge carried by nexuses and center vortices

In this paper we further explore some questions of topological charge arising from transverse intersections of center vortices and nexuses. Topological charge can also be carried by twist or writhe; we introduce a new nexus carrying twist (or equivalently writhe) which carries Chern-Simons number and in some cases topological charge without reference to an intersection with a separate center vortex. This new nexus can also carry topological charge by linking to vortices. In general, no topological charge in $d=4$ arises from static new nexuses, since the charge is the difference of two (equal) Chern-Simons numbers, but it can arise through dynamic reconnection processes, as the author had suggested earlier. Generally, charge carried by transverse intersections is locally fractionalized in units of $1/N$ for gauge group $\mathrm{SU}(N),$ but globally quantized in integral units. We show explicitly that in $d=4$ such global topological charge is a linkage number of the closed two-surface of a center vortex with a nexus world line, and relate this linkage to the Hopf fibration, with homotopy ${\ensuremath{\Pi}}_{3}{(S}^{2})\ensuremath{\simeq}Z;$ this homotopy ensures integrality of the global topological charge. We show that a standard nexus form used earlier, when linked to a center vortex, gives rise naturally to a homotopy ${\ensuremath{\Pi}}_{2}{(S}^{2})\ensuremath{\simeq}Z,$ a homotopy usually associated with 't Hooft--Polyakov monopoles and similar objects which exist by virtue of the presence of an adjoint scalar field which gives rise to spontaneous symmetry breaking. We show that certain integrals related to monopole or topological charge in gauge theories with adjoint scalars also appear in the center vortex-nexus picture, but with a different physical interpretation. We complete earlier work on vortex-nexus intersections to show explicitly how to express globally integral topological charge as composed of essentially independent units of charge $1/N.$

Realistic supersymmetric SU(6)

We present an example of SUSY SU(6) GUT, which predicts an excellent value for $\al_s(M_Z)(\simeq 0.119)$, in comparison with the value $\al_s^0(M_Z)\simeq 0.126$ of minimal SUSY SU(5). A crucial role is played by the vectorlike multiplets from the matter sector, whose masses lie below the GUT scale. For a realistic pattern of fermion masses, the adjoint scalar of SU(6) has VEV along the $SU(4)\times SU(2)\times U(1)$ direction. This also offers a natural resolution of the doublet-triplet (DT) splitting through the pseudo Goldstone Boson mechanism.

QCD with adjoint scalars in 2D: properties in the colourless scalar sector

We present a numerical study of an SU(3) gauged 2D model for adjoint scalar fields, defined by dimensional reduction of pure gauge QCD in (2+1)D at high temperature. In the symmetric phase of its global Z_2 symmetry, two colourless boundstates, even and odd under Z_2, are identified. Their respective contributions (poles) in correlation functions of local composite operators A_n of degree n=2p and 2p+1 in the scalar fields (p=1,2) fulfill factorization. The contributions of two particle states (cuts) are detected. Their size agrees with estimates based on a meanfield-like decomposition of the p=2 operators into polynomials in p=1 operators. No sizable signal in any A_n correlation can be attributed to 1/n times a Debye screening length associated with n elementary fields. These results are quantitatively consistent with the picture of scalar ``matter'' fields confined within colourless boundstates whose residual ``strong'' interactions are very weak.

Mesonic spectrum of two-dimensional supersymmetric theories

We consider a bound state problem for a family of supersymmetric gauge theories with fundamental matter. These theories can be obtained by a dimensional reduction of supersymmetric QCD from three dimensions to 1+1 and subsequent truncation of some of the fields. We find that the models without adjoint scalar converge to well-defined continuum limits and calculate the resulting spectra of these theories. We also find the critical value of coupling at which an additional massless state is observed. By contrast, the models containing adjoint scalars, seem to have a continuous mass spectrum in the limit of infinite volume.

Fundamental matter and SDLCQ

We consider a bound state problem for a family of supersymmetric gauge theories with fundamental matter. These theories can be obtained by a dimensional reduction from three dimension to 1 + 1 of supersymmetric QCD and subsequent truncation of some of the fields. We find that the models without adjoint scalar converge to well-defined continuum limits. We also find the critical value of coupling at which an additional massless state is observed. By contrast, the models containing adjoint scalars, seem to have a continuous mass spectrum in the limit of infinite volume.

Real time correlators in hot(2+1)-dimensional QCD

We use dimensional reduction techniques to relate real time finite T correlation functions in (2+1) dimensional QCD to bound state parameters in a generalized 't Hooft model with an infinite number of heavy quark and adjoint scalar fields. While static susceptibilities and correlation functions of the DeTar type can be calculated using only the light (static) gluonic modes, the dynamical correlators require the inclusion of the heavy modes. In particular we demonstrate that the leading T perturbative result can be understood in terms of the bound states of the 2d model and that consistency requires bound state trajectories composed of both quarks and adjoint scalars. We also propose a non-perturbative expression for the dynamical DeTar correlators at small spatial momenta.