Adjoint Representation Of SU Research Articles

Dark Majorana particles from the minimal walking technicolor theory

We investigate the possibility of a dark matter candidate emerging from a minimal walking technicolor theory. In this case, techniquarks as well as technigluons transform under the adjoint representation of SU(2) of technicolor. It is therefore possible to have technicolor neutral bound states between a techniquark and a technigluon. We investigate this scenario by assuming that such a particle can have a Majorana mass and we calculate the relic density. We identify the parameter space where such an object can account for the full dark matter density avoiding constraints imposed by the CDMS and the LEP experiments.

LIGHT PSEUDO-GOLDSTONE BOSONS WITHOUT EXPLICIT SYMMETRY BREAKING

A mechanism is discussed to obtain light scalar fields from a spontaneously broken continuous symmetry without explicitly breaking it. If there is a continuous manifold of classical vacua in orbit space, its tangent directions describe classically massless fields that may acquire mass from perturbations of the potential that do not break the symmetry. We consider the simplest possible example, involving a scalar field in the adjoint representation of SU (N). We study the scalar mass spectrum and its renormalization group running at one-loop level including scalar and pseudoscalar Yukawa couplings to a massive Dirac fermion.

B–τ Yukawa non-unification in supersymmetric SU(5) with an Abelian flavor symmetry

We present a supersymmetric SU(5)×U(1)H model, free from gauge anomalies, where the Abelian factor U(1)H, introduced to account for the hierarchy of fermion masses and mixings, is broken by the same adjoint representations of SU(5) that also break the GUT symmetry. The model predicts approximate, but never exact, b–τ Yukawa unification. The deviations are related to group theoretical coefficients and can naturally be at the level of 10–20%.

Confining QCD strings, Casimir scaling, and a Euclidean approach to high-energy scattering

We compute the chromo-field distributions of static color-dipoles in the fundamental and adjoint representation of SU(Nc) in the loop-loop correlation model and find Casimir scaling in agreement with recent lattice results. Our model combines perturbative gluon exchange with the non-perturbative stochastic vacuum model which leads to confinement of the color-charges in the dipole via a string of color-fields. We compute the energy stored in the confining string and use low-energy theorems to show consistency with the static quark-antiquark potential. We generalize Meggiolaro's analytic continuation from parton-parton to gauge-invariant dipole-dipole scattering and obtain a Euclidean approach to high-energy scattering that allows us in principle to calculate S-matrix elements directly in lattice simulations of QCD. We apply this approach and compute the S-matrix element for high-energy dipole-dipole scattering with the presented Euclidean loop-loop correlation model. The result confirms the analytic continuation of the gluon field strength correlator used in all earlier applications of the stochastic vacuum model to high-energy scattering.

The holomorphic effective action inN=2D=4 supergauge theories with various gauge groups

We consider the theory of hypermultiplets in arbitrary representations of arbitrary semisimple gauge groups coupled to gauge superfields. Using the N=2 harmonic superspace formulation of these models, we find the general structure of the holomorphic effective action depending on the gauge superfield with values in the Cartan subalgebra of the gauge algebra. We find explicit expressions for the effective actions in the cases where the hypermultiplets are in the fundamental and adjoint representations of SU(n), SO(n), and Sp(2n).

Mixing Angle and Glashow Algebra

Considering transformations in the basis of fundamental fields on a principalfiber bundle, without modification in the space-time sector, we construct analgebra GA, which we call Glashow algebra. The structure constants of thisalgebra depend on a mixing angle. The Lagrangian of the gauge theory ofelectroweak interactions without masses is obtained using a representation of GAwhich is the transformed of the adjoint representation of SU(2)⊗ U(1), anddoes not coincide with the adjoint representation of GA. The mixing angle isautomatically present in the theory if GA is used.

Adjoint QCD2 and the non-abelian Schwinger mechanism

Massless Majorana fermions in the adjoint representation of SU(N_c) are expected to screen gauge interactions in 1+1 dimensions, analogous to a similar Higgs phenomena known for 1+1-dimensional U(1) gauge theory with massless fundamental fermions (Schwinger model). Using the light-cone formalism and large-N_c limit, a non-abelian analogue of the Schwinger boson is shown to be responsible for the screening between heavy test charges. This adjoint boson does not exist simply as a physical state, but boundstates are built entirely from this particle.

One-dimensional classical adjoint SU(2) Coulomb gas

The equation of state of a one-dimensional classical nonrelativistic Coulomb gas of particles in the adjoint representation of SU(2) is given. The problem is solved both with and without sources in the fundamental representation at either end of the system. The gas exhibits confining properties at low densities and temperatures and deconfinement in the limit of high densities and temperatures. However, there is no phase transition to a regime where the string tension vanishes identically; true deconfinement only happens for infinite densities and temperatures. In the low density, low temperature limit, a new type of collective behavior is observed.

“Gluelump” spectrum and adjoint source potential in lattice QCD 3

We calculate the potential between “quarks” which are in the adjoint representation of SU(2) color in the three-dimensional lattice theory. We work in the scaling region of the theory and at large quark separations R. We also calculate the masses M Qg of color-singlet bound states formed by coupling an adjoint quark to adjoint glue (“gluelumps”). Good scaling behavior is found for the masses of both magnetic (angular momentum J = 0) and electric ( J = 1) gluelumps, and the magnetic gluelump is found to be the lowest-lying state. It is naively expected that the potential for adjoint quarks should saturate above a separation R scr where it becomes energetically favorable to produce a pair of gluelumps. We obtain a good estimate of the naive screening distance R scr. However we find little evidence of saturation in the potential out to separations R of about 1.5 R scr.

Matrix generalizations of some dynamic field theories

We introduce matrix generalizations of the Navier-Stokes (NS) equation for fluid flow, and the Kardar-Parisi-Zhang (KPZ) equation for interface growth. The underlying field, velocity for the NS equation, or the height in the case of KPZ, is promoted to a matrix that transforms as the adjoint representation of SU ( N). Perturbative expansions simplify in the N → ∞ limit, dominated by planar graphs. We provide the results of a one-loop analysis, but have not succeeded in finding the full solution of the theory in this limit.

Adjoint “quarks” and the physics of confinement

The quark-antiquark potential and the chromoelectric fields generated by ``quarks'' in the adjoint representation of SU(2) color are analyzed in the scaling region of the theory. New results with interesting implications for our understanding of the confinement mechanism are presented. In particular, the formation of color-electric flux-tubes between adjoint quarks is demonstrated in four-dimensional SU(2) color. The flux-tubes for fundamental and adjoint representation quarks are shown to have very similar cross-sections. This result could imply that the QCD vacuum is dual to a type I superconductor.

Adjoint “quark” color fields in four-dimensional lattice gauge theory: Vacuum screening and penetration

The fields generated by “quarks” in the adjoint representation of SU(2) color are analyzed in the scaling region of the four-dimensional lattice theory. Evidence of vacuum screening of adjoint quarks is obtained from a comparison of quark-antiquark ( Q Q ) flux-tubes for quarks in the adjoint (“isospin” j = 1) and fundamental ( j = 1 2 ) representations. The component ε j of the color-electric field strength in the direction parallel to the Q Q axis is calculated. Near the quarks the ratio of fields ε j=1 ε j= 1 2 approaches the value 8 3 , which is equal to the ratio of SU(2) Casimirs. In between the quarks, the ratio falls well below 8 3 at large R. ε j also falls off rapidly as a function of distance x ⊥ perpendicular to the Q Q axis. However, the ratio ε j=1 ε j= 1 2 depends very weakly on x ⊥. The flux-tubes in the two representations thus appear to have very similar cross-sections. This result could imply that the QCD vacuum is dual to a type I superconductor.

Folds in 2D string theories

We study maps from a 2D world sheet to a 2D target space which include folds. The geometry of folds is discussed and a metric on the space of folded maps is written down. We show that the latter is not invariant under area-preserving diffeomorphisms of the target space. The contribution to the partition function of maps associated with a given fold configuration is computed. We derive a description of folds in terms of Feynman diagrams. A scheme to sum up the contributions of folds to the partition function in a special case is suggested and is shown to be related to the Baxter-Wu lattice model. An interpretation of folds as trajectories of particles in the adjoint representation of SU(N) gauge group in the large-N limit which in eract in an unusual way with the gauge fields is discussed.

String spectrum of (1+1)-dimensional large-N QCD with adjoint matter.

We propose gauging matrix models of string theory to eliminate unwanted non-singlet states. To this end we perform a discretised light-cone quantisation of large N gauge theory in 1+1 dimensions, with scalar or fermionic matter fields transforming in the adjoint representation of SU(N). The entire spectrum consists of bosonic and fermionic closed-string excitations, which are free as N tends to infinity. We analyze the general features of such bound states as a function of the cut-off and the gauge coupling, obtaining good convergence for the case of adjoint fermions. We discuss possible extensions of the model and the search for new non-critical string theories.

On the zero mode of the Poisson gauge theory

The fundamentals of the Diff(S 2) and the SDiff(S 2) gauge theories are developed. It is shown that the adjoint representation of SU (∞) is described by a divergentless two-dimensional vector field defined on the sphere. The SU (∞) Yang-Mills gauge action obtained earlier by Floratos et al. is reviewed. The problem of the zero modes is solved without need of any constraint. The fundamental representations of SU (∞) and the gauge-matter couplings are discussed.

SU(2) adjoint thermal structure

We investigate the Wilson line and the susceptibility in the adjoint representation of SU(2) lattice gauge theory at finite temperature near to and above the deconfinement transition. Our simulations were performed on the lattices of sizes 6 × 8 3, 6 × 12 3, 6 × 18 3 and 6 × 24 3. In the region close to the deconfinement temperature we find that the critical properties of the adjoint Wilson line is consistent with the critical behavior of the (ø 4) 3 scalar field theory. However, we further note that well above this temperature region the adjoint Wilson line continues to rise. The adjoint susceptibility is shown to be smoothly increasing at and above the deconfinement temperature. Thus we may conclude that the adjoint susceptibility does not show the same type of critical fluctuations as is seen in the fundamental representation.

Generalized skein relations from Chern-Simons field theory

Using a variational approach based only on three-dimensional properties of Chern-Simons theory, a skein relation for the expectation value of Wilson line operators in the adjoint representation of SU(2) is derived in the large k limit. The result agrees with that obtained from rational conformal field theory. The generalization to arbitrary representations is then straightforward, once an important phase factor present is understood.

Comparison of two gauge-nonequivalent IAnsäItzeB for charged vortices in SU(2) gauge theory with Chern-Simons term.

We discuss in detail the possible connection between the two topologically equivalent but gauge-nonequivalent Ansa$uml---tze for charged (neutral) vortices in an SU(2) non-Abelian Higgs model with (without) a Chern-Simons term. In particular, we show that when the magnitude of the two Higgs fields are proportional to each other in the Ansatz where the global gauge group is SU(2) then the field equations and the energy functional in the two Ansa$uml---tze have identical form in terms of the corresponding dimensionless Ginzburg-Landau-type parameters \ensuremath{\eta} and \ensuremath{\lambda}. In this case we show that for a wide range of parameters the charged (as well as neutral) one-vortex energy in the Ansatz, in which the fields are in the adjoint representation of SU(2) so that the global gauge group is SU(2)/${Z}_{2}$, is less than the corresponding energy in the Ansatz where the global gauge group is SU(2). For the neutral case we also obtain an exact and approximate analytic one-vortex solution in case \ensuremath{\lambda}=1 and 2, respectively (and \ensuremath{\eta}=1). Finally we show that charged (as well as neutral) ${Z}_{3}$ vortices of the SU(3) gauge theory repel each other in the dominant part of the type-II region of superconductivity (i.e., \ensuremath{\lambda}>\ensuremath{\eta}).

Clebsch–Gordan coefficients for SU(5) unification models

The Clebsch–Gordan coefficients for the product (1001)⊗(1001), where (1001) is the adjoint representation of SU(5), with respect to the group basis and the subgroup basis in the reduction SU(5)⊇SU(3)×SU(2)×U(1) are computed. One of the basic tools in this computation is the exhaustive use of the Verma algorithm to find bases for the weight subspaces of dimension higher than 1. It allows for the construction of bases in a systematic way by using the so-called Verma inequalities. Only the coefficients for the dominant weights are calculated. The other ones can be obtained by using the elements of finite order (charge conjugation operators) of SU(5).

The beta-function for a two-parameter SU(3) Wilson action

The beta-function for a Wilson action consisting of terms in both the fundamental and adjoint representations of SU(3) is studied quantitatively using a Monte Carlo renormalization group technique known as the improved radio method.