Gauge Symmetry Group Research Articles

Quantum 2‐body Hamiltonian for topological color codes

AbstractWe introduce a two‐body quantum Hamiltonian model with spins‐${1 \over 2}$ located on the vertices of a 2D spatial lattice. The model exhibits an exact topological degeneracy in all coupling regimes. This is a remarkable non‐perturbative effect. The model has a Z2× Z2 gauge group symmetry and string‐net integrals of motion. There exists a gapped phase in which the low‐energy sector reproduces an effective topological color code model. High energy excitations fall into three families of anyonic fermions that turn out to be strongly interacting. All these, and more, are new features not present in honeycomb lattice models like Kitaev model.

Interacting anyonic fermions in a two-body color code model

We introduce a two-body quantum Hamiltonian model of spin $\frac{1}{2}$ on a two-dimensional spatial lattice with exact topological degeneracy in all coupling regimes. There exists a gapped phase in which the low-energy sector reproduces an effective color code model. High-energy excitations fall into three families of anyonic fermions that turn out to be strongly interacting. The model exhibits a ${\mathbf{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbf{Z}}_{2}$ gauge-group symmetry and string-net integrals of motion, which are related to the existence of topological charges that are invisible to moving high-energy fermions.

Heavy Higgs boson with a light sneutrino next-to-lightest supersymmetric particle in the MSSM with enhancedSU(2)D-terms

The minimal supersymmetric extension of the standard model provides a solution to the hierarchy problem and leads to the presence of a light Higgs. A Higgs boson with mass above the present experimental bound may only be obtained for relatively heavy third generation squarks, requiring a precise, somewhat unnatural balance between different contributions to the effective Higgs mass parameter. It was recently noticed that somewhat heavier Higgs bosons, which are naturally beyond the CERN LEP bound, may be obtained by enhanced weak $SU(2)$ D-terms. Such contributions appear in models with an enhanced electroweak gauge symmetry, provided the supersymmetry breaking masses associated with the scalars responsible for the breakdown of the enhanced gauge symmetry group to the standard model one are larger than the enhanced symmetry breaking scale. In this article we emphasize that the enhanced $SU(2)$ D-terms will not only raise the Higgs boson mass but also affect the spectrum of the nonstandard Higgs bosons, sleptons, and squarks, which therefore provide a natural contribution to the $T$ parameter, compensating for the negative one coming from the heavy Higgs boson. The sleptons and nonstandard Higgs bosons of these models, in particular, may act in a way similar to the so-called inert Higgs doublet. The phenomenological properties of these models are emphasized, and possible cosmological implications as well as collider signatures are described.

On higher spin interactions with matter

Cubic couplings between a complex scalar field and a tower of symmetric tensor gauge fields of all ranks are investigated. A symmetric conserved current, bilinear in the scalar field and containing r derivatives, is provided for any rank r>0 and is related to the corresponding rigid symmetry of Klein-Gordon's Lagrangian. Following Noether's method, the tensor gauge fields interact with the scalar field via minimal coupling to the conserved currents. The corresponding cubic vertex is written in a compact form by making use of Weyl's symbols. This enables the explicit computation of the non-Abelian gauge symmetry group, the current-current interaction between scalar particles mediated by any gauge field and the corresponding four-scalar elastic scattering tree amplitude. The exact summation of these amplitudes for an infinite tower of gauge fields is possible and several examples for a definite choice of the coupling constants are provided where the total amplitude exhibits fast (e.g. exponential) fall-off in the high-energy limit. Nevertheless, the long range interaction potential is dominated by the exchange of low-spin particles in the low-energy limit.

The many vacua of gauged extended supergravities

A novel method is presented which employs advanced numerical techniques used in the engineering sciences to find and study the properties of nontrivial vacua of gauged extended supergravity models. While this method only produces approximate numerical data rather than analytic results, it overcomes the previous limitation of only being able to find vacua with large residual unbroken gauge symmetry groups. The effectiveness of this method is demonstrated by applying it to the technically most challenging D>=3 scalar potential -- that of SO(8) X SO(8) gauged N=16 Chern-Simons Supergravity in D=3. Extensive data on the properties of 99 different vacua (92 of them new) of this model are given. Furthermore, techniques are briefly discussed which should allow using this numerical information as an input to the construction of semi-automatic stringent analytic proofs on the locations and properties of vacua. It hence is argued that these combined techniques presumably are powerful enough to systematically map all the nontrivial vacua of every supergravity model.

Resolution of Hagedorn singularity in superstrings with gravito-magnetic fluxes

We consider closed type II and orientifold backgrounds where supersymmetry is spontaneously broken by asymmetric geometrical fluxes. We show that these can be used to describe thermal ensembles with chemical potentials associated to “gravito-magnetic” fluxes. The thermal free energy is computed at the one-loop string level, and it is shown to be free of the usual Hagedorn-like instabilities for a certain choice of the chemical potentials. In the closed string gravitational sector, as well as in the open string matter sector of the proposed orientifold construction, the free energy turns out to have “Temperature duality” symmetry, F(T/TH)=F(TH/T), which requires interchanging the space–time spinor representations S↔C. For small temperatures, T→0, the anti-spinor C decouples from the spectrum while for large temperatures, T→∞, the spinor S decouples. In both limits the free energy vanishes, as we recover a conventional type II superstring theory. At the self dual point T=TH, the thermal spectra of S and C are identical. At this point there are extra massless scalars in the adjoint representation of an SO(4) non-Abelian gauge symmetry group arising from the closed-string sector.

Extra gauge invariance from an extra dimension

We describe higher-dimensional theories whose low-energy 4D descriptions contain larger gauge or global symmetry groups. As an example, we construct a Higgsless $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1{)}_{B\ensuremath{-}L}$ model of electroweak symmetry breaking. The 5D SU(2) gauge invariance contains both the weak SU(2) gauge group and a custodial symmetry that protects the rho parameter. Fermions obtain isospin-violating masses while maintaining universal gauge couplings among all three generations. As a further example, we construct a model of chiral color based on a single SU(3).

Geometric Algebra and Particle Dynamics

In a recent publication [1] it was shown how the geometric algebra G4,1, the algebra of 5-dimensional space-time, can generate relativistic dynamics from the simple principle that only null geodesics should be allowed. The same paper showed also that Dirac equation could be derived from the condition that a function should be monogenic in that algebra; this construction of the Dirac equation allows a choice for the imaginary unit and it was suggested that different imaginary units could be assigned to the various elementary particles. An earlier paper [2] had already shown the presence of standard model gauge group symmetry in complexified G1,3, an algebra isomorphic to G4,1.

Preon Model and Family Replicated E6 Unification

Previously we suggested a new preon model of composite quark-leptons and bosons with the 'flipped' E6 ◊ f E6 gauge symmetry group. We assumed that preons are dyons having both hyper-electric g and hyper-magnetic ˜ g charges, and these preons-dyons are confined by hyper-magnetic strings which are an N = 1 supersymmetric non-Abelian flux tubes created by the condensation of spreons near the Planck scale. In the present paper we show that the existence of the three types of strings with tensions Tk = kT0 (k = 1,2,3) producing three (and only three) generations of composite quark-leptons, also provides three generations of composite gauge bosons ('hyper-gluons') and, as a consequence, predicts the family replicated (E6) 3 unification at the scale 10 17 GeV. This group of unification has the possibility of breaking to the group of symmetry: (SU(3)C) 3 ◊ (SU(2)L) 3 ◊ (U(1)Y ) 3 ◊ (U(1)(B L)) 3 which undergoes the breakdown to the Standard Model at lower energies. Some predictive advantages of the family replicated gauge groups of symmetry are briefly discussed.

Coupling Nonlinear Sigma-Matter to Yang-Mills Fields: Symmetry Breaking Patterns

We extend the traditional formulation of Gauge Field Theory by incorporating the (non-Abelian) gauge group parameters (traditionally simple spectators) as new dynamical (nonlinear-sigma-model-type) fields. These new fields interact with the usual Yang-Mills fields through a generalized minimal coupling prescription, which resembles the so-called Stueckelberg transformation [1], but for the non-Abelian case. Here we study the case of internal gauge symmetry groups, in particular, unitary groups U(N). We show how to couple standard Yang-Mills Theory to Nonlinear-Sigma Models on cosets of U(N): complex projective, Grassman and flag manifolds. These different couplings lead to distinct (chiral) symmetry breaking patterns and Higgs-less mass-generating mechanisms for Yang-Mills fields.

Prospects to search for E6 isosinglet quarks in ATLAS

We consider pair production of new down-type isosinglet quarks originating from E6, which is the favorite gauge symmetry group in superstring inspired GUT models. The study concentrates on the possibility of observing the pair production of the lightest of the new quarks, D, in the ATLAS detector at the forthcoming LHC accelerator, in the channel DD̄→ZjZj . Both signal and background events are studied using tree level event generators based on Monte Carlo techniques. The detector effects are taken into account using the ATLAS fast simulation tool. It is shown that ATLAS can observe the D quark within the first year of low luminosity LHC operation if its mass is less than 650 GeV. For the case of two years of full luminosity running, 1 TeV can be reached with about three sigma significance.

Are preons dyons? Naturalness of three generations

In the present paper a model of preons and their composites is constructed in the framework of the superstring-inspired `flipped' E_6\times \widetilde{E_6} gauge symmetry group which reveals a generalized dual symmetry. Here E_6 and \widetilde{E_6} are non-dual and dual sectors of the theory with hyper-electric g and hyper-magnetic \tilde g charges, respectively. We follow the old idea by J. Pati presuming that preons are dyons, which in our model are confined by hyper-magnetic strings -- composite {\bf N}=1 supersymmetric non-Abelian flux tubes created by the condensation of spreons near the Planck scale. Considering preons belonging to the 27-plet of E_6, we have investigated the breakdown of E_6 (and \widetilde{E_6}) near the Planck scale into the SU(6)\times U(1) (and \widetilde{SU(6)}\times \widetilde{U(1)}) gauge group and shown that the six types of strings having fluxes \Phi_n=n\Phi_0 (n=\pm 1,\pm 2,\pm 3) produce three (and only three) generations of composite quark-leptons and bosons. The model predicts the existence of the Family replicated gauge group [E_6]^3 near the Planck scale. The runnings of the corresponding fine structure constants are investigated, and the critical coupling constants at the two phase transition points near the Planck scale are calculated. The model explains the hierarchies of masses in the Standard Model naturally. The compactification in a space-time with five dimensions and its influence on form-factors of composite objects are also briefly discussed.

FLIPPED SU(5), SEESAW SCALE PHYSICS AND DEGENERATE VACUA

We investigate the requirement of the existence of two degenerate vacua of the effective potential as a function of the Weinberg–Salam Higgs scalar field norm, as suggested by the multiple point principle, in an extension of the Standard Model including seesaw scale physics. Results are presented from an investigation of an extension of the Standard Model to the gauge symmetry group SU (3)C× SU (2)L× U (1)′×Ũ(1), where U (1)′ and Ũ(1) originate at the seesaw scale M SS , when heavy (right-handed) neutrinos appear. The consequent unification of the group SU (3)C× SU (2)L× U (1)′ into the flipped SU (5) at the GUT scale leads to the group SU (5)×Ũ(1). We assume the position of the second minimum of the effective potential coincides with the fundamental scale, here taken to be the GUT scale. We solve the renormalization group equations in the one-loop approximation and obtain a top-quark mass of 171±3 GeV and a Higgs mass of 129±4 GeV , in the case when the Yukawa couplings of the neutrinos are less than half that of the top quark at the GUT scale.

Confinement and the center of the gauge group

The question of the role of the center of the gauge group in the phenomenon of confinement in Yang-Mills theory is addressed. The investigation is performed from the most general perspective of considering all possible choices for the gauge symmetry group. In this context, an interesting role is played by G(2) Yang-Mills theory: the simplest pure gauge theory with a trivial center and without 't Hooft flux vortices. Numerical simulations show the presence of a first order finite temperature deconfinement phase transition in G(2) Yang-Mills theory in (3+1) dimensions. Interestingly, the G(2) gauge symmetry can be broken to an SU(3) subgroup by the Higgs mechanism. We investigate the relation between the deconfinement phase transition in G(2) and SU(3) Yang-Mills theories by numerical simulations in the G(2) gauge-Higgs system.

Couplings of vector-spinor representation for SO(10) model building

Higgs multiplet in the vector-spinor representations of SO(10), i.e., the $144+\bar{144}$ multiplet can break the SO(10) gauge symmetry spontaneously in one step down to the Standard Model gauge group symmetry $SU(3)_C\times SU(2)_L\times U(1)_Y$ and a recent analysis has used such vector-spinors for building a new class of SO(10) grand unification models (hep-ph/0506312) . Here we discuss the techniques for the computation of several classes of vector-spinor couplings using the Basic Theorem on the SO(2N) vertex expansion developed by the authors. The computations include the cubic couplings of the vector-spinors with SO(10) tensors, quartic self-couplings of the vector-spinors, and couplings of the vector-spinors with spinor representations of SO(10). The last set include couplings of vector-spinors with the 16-plets of quarks and lepton and with the 16 and $\bar{16}$ of Higgs. These couplings provide a crucial tool for further development of the SO(10) grand unification using vector-spinor representations. These include study of quark-lepton masses, analysis of dimension five operators including baryon and lepton number violating operators, and study of neutrino masses and mixings. Illustrative examples are given for their computation using a sample of vector-spinor couplings.

Conformal higher spin theory

We construct gauge theory of interacting symmetric traceless tensors of all ranks s=0,1,2,3,… which generalizes Weyl-invariant dilaton gravity to the higher spin case, in any dimension d>2. The action is given by the trace of the projector to the subspace with positive eigenvalues of an arbitrary Hermitian differential operator H , and the symmetric tensors emerge after expansion of the latter in power series in derivatives. After decomposition in perturbative series around conformally flat point H=□ with Euclidean metric, the action functional describes conformal higher spin theory. Namely, the linear in fluctuation term cancels, while the one quadratic in fluctuation breaks up as a sum of conformal higher spin theories, the latter being free gauge theories of symmetric traceless tensors of rank s with actions of d−4+2 s order in derivatives (in odd dimensions they are boundary terms), for all integer s, introduced in 4d case by Fradkin and Tseytlin and studied at the cubic order level by Fradkin and Linetsky. Higher orders in interaction are well-defined. The action appears to be the unique functional invariant w.r.t. general similarity transformations H′=e ω ̂ † He ω ̂ , the latter invariance plays the role of gauge symmetry group of the model. In the framework of the perturbative decomposition, the Hermitian part of ω gauges away the trace parts of the symmetric tensors parameterizing the fluctuation, while the anti-Hermitian one provides standard linearized gauge transformations of conformal higher spin fields. The action can be calculated as a semiclassical series in ℏ which counts the number of space–time derivatives and thereby exhibits itself as a parameter of low-energy expansion, like α′ in string theory, in so doing the classical term is given by the volume of the domain H( x, p)>0 (where H( x, p) is the Weyl symbol of H ), it does not contain derivatives and is interpreted as a cosmological term. At the same time, further terms of the ℏ-expansion are given by integrals of distributions localized on the constraint surface H( x, p)=0, and the conformal higher spin- s action arises from the ℏ d−4+2 s -correction. The full gauge invariance of the model is interpreted as covariance algebra of generalized Klein–Gordon equation H|ψ〉=0 for complex scalar field ψ.

Enhanced Gauge Symmetry and Braid Group Actions

Enhanced gauge symmetry appears in Type II string theory (as well as F- and M-theory) compactified on Calabi--Yau manifolds containing exceptional divisors meeting in Dynkin configurations. It is shown that in many such cases, at enhanced symmetry points in moduli a braid group acts on the derived category of sheaves of the variety. This braid group covers the Weyl group of the enhanced symmetry algebra, which itself acts on the deformation space of the variety in a compatible fashion. Extensions of this result are given for nontrivial $B$-fields on K3 surfaces, explaining physical restrictions on the $B$-field, as well as for elliptic fibrations. The present point of view also gives new evidence for the enhanced gauge symmetry content in the case of a local $A_{2n}$-configuration in a threefold having global $\Z/2$ monodromy.

William Edward Caswell

William Edward Caswell

NoncommutativeSp(2,R)gauge theories: A field theory approach to two-time physics

Phase-space and its relativistic extension is a natural space for realizing Sp(2,R) symmetry through canonical transformations. On a Dx2 dimensional covariant phase-space, we formulate noncommutative field theories, where Sp(2,R) plays a role as either a global or a gauge symmetry group. In both cases these field theories have potential applications, including certain aspects of string theories, M-theory, as well as quantum field theories. If interpreted as living in lower dimensions, these theories realize Poincare' symmetry linearly in a way consistent with causality and unitarity. In case Sp(2,R) is a gauge symmetry, we show that the spacetime signature is determined dynamically as (D-2,2). The resulting noncommutative Sp(2,R) gauge theory is proposed as a field theoretical formulation of two-time physics: classical field dynamics contains all known results of `two-time physics', including the reduction of physical spacetime from D to (D-2) dimensions, with the associated `holography' and `duality' properties. In particular, we show that the solution space of classical noncommutative field equations put all massless scalar, gauge, gravitational, and higher-spin fields in (D-2) dimensions on equal-footing, reminiscent of string excitations at zero and infinite tension limits.

Gauge symmetryand gravito-electromagnetism

A tensor description of perturbative Einsteinian gravity about anarbitrary background spacetime is developed. By analogy with thecovariant laws of electromagnetism in spacetime, gravito-electromagnetic potentials and fields are definedto emulate electromagnetic gauge transformations undersubstitutions belonging to the gauge symmetry group ofperturbative gravitation. These definitions have the advantagethat on a flat background, with the aid of a covariantly constanttimelike vector field, a subset of the linearized gravitationalfield equations can be written in a form that is fully analogousto Maxwell's equations (without awkward factors of four andextraneous tensor fields). It is shown how the remainingequations in the perturbed gravitational system restrict the timedependence of solutions to these equations and thereby prohibitthe existence of propagating vector fields. The induced gravito-electromagnetic Lorentz force on a test particle is evaluated interms ofthese fields together with the torque on a small gyroscope. It isconcluded that the analogy of perturbative gravity to Maxwell'sdescription of electromagnetism can be valuable for(quasi-)stationary gravitational phenomena but that the analogyhas its limitations.