Obtaining non-Abelian field theories via the Faddeev-Jackiw symplectic formalism

In this Letter we construct non-Abelian field theories employing the Faddeev-Jackiw symplectic formalism. The original Abelian fields were modified in order to introduce the non-Abelian algebra. We construct the SU(2) and SU(2)⊗U(1) Yang-Mills theories having as starting point the U(1) Maxwell electromagnetic theory.     

Phase portrait ofSU(5) grand unified model

The one-loop effective potential of theSU(5) model is investigated both in high and low temperature approximation. We find the regions of values of coupling constants and temperatures where theSU(5), theSU(4)×U(1) and theSU(3)×SU(2)×U(1) symmetric states are metastable. A general method of such an investigation is proposed. We observe that the domain structure of the Universe with the simultaneous existence of the gauge symmetriesSU(4)×U(1) andSU(3)×SU(2)×U(1) in different domains could take place.     

The symmetry breaking patternSU(5)→SU(3)×U(1) including one loop radiative corrections

We derive conditions on the Higgs parameters of the minimalSU(5) model under which the phenomenologically desired symmetry breaking patternSU(5)→SU(3)×U(1) persists at the one loop level.     

Nonlinear local supersymmetric SU(5)-model

We construct a realistic nonlinear supersymmetric SU(5) model without superpartner particles in curved space and investigate the Higgs sector in the limit of flat space. We need at least an adjoint-, a quintuplet- and an antiquintuplet-Higgs multiplet. In order to obtain a realistic breakdown of SU(5) to SU(3) × U(1) at tree level we have to modify the vacuum structure of the adjoint representation in comparison to other SU(5)-models. This model requires an “elegant” fine-tuning. We determine the mass spectrum of the electroweak Higgs sector.     

Phenomenology ofSO(10) unified superstring models with intermediate scaleSU R(2) breaking

Electroweak breaking and the supersymmetric particle spectrum are discussed in superstring theories where the gauge group after compactification isSO(10)×E _s ^′ , and where the gauge symmetry after flux breaking isSU(3)×SU(2)×SU(2)×U(1).     

Necessity of intermediate mass scales in grand unified theories with spontaneously brokenCP invariance

It is demonstrated that the spontaneous breakdown ofCP invariance in grand unified theories requires the presence of intermediate mass scales. The simplest realization is provided by weakly broken left-right symmetry in the context ofSU(2)_L×SU(2)_R×U(1) _B?L model embedded in grand unified theories.     

Comparison of lattice gauge theories with gauge groups Z2 and SU(2)

We study a model of a pure Yang Mills theory with gauge group SU(2) on a lattice in Euclidean space. We compare it with the model obtained by restricting variables to $\text{Z}$₂. An inequality relating expectation values of the Wilson loop integral in the two theories is established. It shows that confinement of static quarks is true in our SU(2) model whenever it holds for the corresponding $\text{Z}$₂-model. The SU(2) model is shown to have high and low temperature phases that are distinguished by a qualitatively different behavior of the 't Hooft disorder parameter.     

Phase portrait ofSU(5) model. II intermediate phasesSU(3)×[U(1)]2 and [SU(2)]2×[U(1)]2

The effective potential of the scalar field in theSU(5) model has extrema with symmetry:SU(5),SU(4)×U(1),SU(3)×SU(2)×U(1),SU(3)×[U(1)]², [SU(2)]²×[U(1)]². In our recent paper it was shown that theSU(4)×U(1) phase as well asSU(3)×SU(2)×U(1) phase were stable at the nonzero temperature in a vast region of parameters. In the present paper it is found that the [SU(2)]²×[U(1)]² symmetric vacuum is unstable and theSU(3)×[U(1)]² symmetric vacuum can be metastable in the certain interval of the temperature. Domains of the three phases:SU(4)×U(1),SU(3)×SU(2)×U(1),SU(3)×[U(1)]²-could co-exist in the early. Universe.     

Constraints on <Emphasis Type="Italic">SU</Emphasis>(2) ⊗ <Emphasis Type="Italic">SU</Emphasis>(2) invariant polynomials for a pair of entangled qubits

We discuss the entanglement properties of two qubits in terms of polynomial invariants of the adjoint action of SU(2) ⊕ SU(2) group on the space of density matrices \(\mathfrak{P}_ +\). Since elements of \(\mathfrak{P}_ +\) are Hermitian, non-negative fourth-order matrices with unit trace, the space of density matrices represents a semi-algebraic subset, \(\mathfrak{P}_ + \in \mathbb{R}^{15}\). We define \(\mathfrak{P}_ +\) explicitly with the aid of polynomial inequalities in the Casimir operators of the enveloping algebra of SU(4) group. Using this result the optimal integrity basis for polynomial SU(2) ⊕ SU(2) invariants is proposed and the well-known Peres-Horodecki separability criterion for 2-qubit density matrices is given in the form of polynomial inequalities in three SU(4) Casimir invariants and two SU(2) ⊕ SU(2) scalars; namely, determinants of the so-called correlation and the Schlienz-Mahler entanglement matrices.     

Quaternion Octonion Reformulation of Grand Unified Theories

In this paper, Grand Unified theories are discussed in terms of quaternions and octonions by using the relation between quaternion basis elements with Pauli matrices and Octonions with Gell Mann λ matrices. Connection between the unitary groups of GUTs and the normed division algebra has been established to re-describe the SU(5) gauge group. We have thus described the SU(5) gauge group and its subgroup SU(3) _C ×SU(2) _L ×U(1) by using quaternion and octonion basis elements. As such the connection between U(1) gauge group and complex number, SU(2) gauge group and quaternions and SU(3) and octonions is established. It is concluded that the division algebra approach to the theory of unification of fundamental interactions as the case of GUTs leads to the consequences towards the new understanding of these theories which incorporate the existence of magnetic monopole and dyon.     

Origin and phenomenology of weak-doublet spin-1 bosons

We study phenomenological consequences of the Standard Model extension by the new spin-1 fields with the internal quantum numbers of the electroweak Higgs doublets. We show, that there are at least three different classes of theories, all motivated by the hierarchy problem, which predict appearance of such vector weak-doublets not far from the weak scale. The common feature for all the models is the existence of an SUW(3) gauge extension of the weak SUW(2) group, which is broken down to the latter at some energy scale around TeV. The Higgs doublet then emerges as either a pseudo-Nambu-Goldstone boson of a global remnant of SUW(3), or as a symmetry partner of the true eaten-up Goldstone boson. In the third class, the Higgs is a scalar component of a high-dimensional SUW(3) gauge field. The common phenomenological feature of these theories is the existence of the electroweak doublet vectors (Z^?,W^?), which in contrast to well-known Z^′ and W^′ bosons posses only anomalous (magnetic moment type) couplings with ordinary light fermions. This fact leads to some unique signatures for their detection at the hadron colliders.     

Flavored surface defects in 4d $$\mathcal{N}=1$$ N = 1 SCFTs

We discuss supersymmetric surface defects in compactifications of six-dimensional minimal conformal matter of types SU(3) and SO(8) to four dimensions. The relevant field theories in four dimensions are \(\mathcal{N}=1\) quiver gauge theories with SU(3) and SU(4) gauge groups, respectively. The defects are engineered by giving space-time-dependent vacuum expectation values to baryonic operators. We find evidence that in the case of SU(3) minimal conformal matter, the defects carry SU(2) flavor symmetry which is not a symmetry of the four-dimensional model. The simplest case of a model in this class is SU(3) SQCD with nine flavors, and thus the results suggest that this admits natural surface defects with SU(2) flavor symmetry. We analyze the defects using the superconformal index and derive analytic difference operators introducing the defects into the index computation. The duality properties of the four-dimensional theories imply that the index of the models is a kernel function for such difference operators. In turn, checking the kernel property constitutes an independent check of the dualities and the dictionary between six- dimensional compactifications and four-dimensional models.

     

A Chern-Simons effective field theory for the Pfaffian quantum Hall state

We present a low-energy effective field theory describing the universality class of the Pfaffian quantum Hall state. To arrive at this theory, we observe that the edge theory of the Pfaffian state of bosons at v = 1 is an SU(2)₂ Kac-Moody algebra. It follows that the corresponding bulk effective field theory is an SU(2) Chem-Simons theory with coupling constant k = 2. The effective field theories for other Pfaffian states, such as the fermionic one at v = 1/2 are obtained by a flux-attachment procedure. We discuss the non-Abelian statistics of quasiparticles in the context of this effective field theory.     

The construction of vector-like supersymmetric gauge models of weak and electromagnetic interactions

Despite great efforts and partial successes the situation with respect to spontaneously broken supersymmetric unified gauge models of weak, electromagnetic and strong interactions has remained quite unsatisfactory up to now. Starting from the most simple SU(2) × U(1) cases we exploit possible extensions. This naturally leads to a consideration of vector-like models with—in the first instance—a larger number of multiplets. Although the later can be made massive without spoiling the conservation of fermion number, the additional massive fermions only show parity conserving interactions with all the intermediate vector fields. Therefore models with larger gauge groups are considered: SU(2) × SU(2) × U(1) with two quartets, SU(3) × U(1) with four triplets, and finally SU(3) × SU(2) × U(1) with two sextets of matter fields. None of these can be accepted yet as a true model for physical particles, but it is shown how different negative features in the simple theories may be avoided in the more complicated ones. Thus our results may be considered as an encouraging starting point for investigations of larger gauge groups in supersymmetric models.     

Construction of grand unified models under maximal subalgebras

A construction of grand unified models of the strong, weak and electromagnetic interactions is described based on the transformation properties of the group generators under a maximal subgroup decomposition without recourse to large representation matrices or to the specific algebraic structures of some classical Lie-groups, such as the Clifford algebra associated with the orthogonal groups or the octonionic structure of the exceptional groups. To illustrate the procedure an explicit construction is given of the SU(5) model useful in the discussion of higher rank groups, of SO(10) under the maximal subalgebras SU(2)_L × SU(2)_R × SU(4)_c and SU(5) × U(1)_r and of the exceptional group E₆ under SU(3)_L × SU(3)_R × SU(3)_c and SO(10) × U(1)_t. The construction procedure can be used as well with any classical Lie-group.     

Monopole classical solutions and the vacuum structure in lattice gauge theories

Classical solutions corresponding to monopole-antimonopole pairs are found in 3d and 4d SU(2) and U(1) lattice gauge theories. The stability of these solutions in various theories is studied.     

Flat directions in flipped SU(5). I: All-order analysis

We present a systematic classification of field directions for the string-derived flipped SU(5) model that are D- and F-flat to all orders. Properties of the flipped SU(5) model with field values in these directions are compared to those associated with other flat directions that have been shown to be F-flat to specific finite orders in the superpotential. We discuss the phenomenological Higgs spectrum, and quark and charged-lepton mass textures.     

Proton decay in theSU(4) c ×SU(2) L ×SU(2) R model

Possible proton decays in theSU(4) _C ×SU(2) _L ×SU(2) _R unification model are discussed. There are some characteristics in the decay products, which are different from those in the standardSU(5) orSO (10) model, in certain cases.     

Alternative scaling hypothesis forSU(2) andSU(3) lattice gauge theories

High precision data from a variety of sources forSU(2) andSU(3) Wilson action lattice gauge theory are analyzed with respect to the hypothesis of the possible existence of a zero temperature deconfining phase transition, in analogy with theU(1) theory. The internal energy, specific heat, string tension, and Wilson line, fit well to correlation length scaling laws associated with a finite order transition occurring at the weak coupling end of the crossover region for both theories. TheSU(2) theory is consistent with a correlation length exponent ν=2/3 and critical pointβ _c ≈2.47. ForSU(3) the data fit well to ν=1 andβ _c ≈6.69. Additional indirect evidence for the existence of such phase transitions is discussed, as is the possible crucial role of light dynamical fermions in the confinement mechanism.     

E6 breaking in (0,2) string compactifications

The existence of a duality in (0,2) compactifications which is present at the Landau-Ginzburg point allows us to connect in a smooth manner theories with different gauge groups with the same base manifold and same number of effective generations. As we move along the Kahler moduli space of the theories with E₆ gauge group, the VEV's of SO(10) singlets are turned on and break the gauge group to SO(10). We generalize this result and break E₆ down to SU(5).