We have developed a concept of parallel existence of the ordinary (O) and mirror (M), or shadow (Sh) worlds. In the first part of the paper we consider a mirror world with broken mirror parity and the breaking $E_6\to SU(3)^3$ in both worlds. We show that in this case the evolutions of coupling constants in the O- and M-worlds are not identical, having different parameters for similar evolutions. $E_6$ unification, inspired by superstring theory, restores the broken mirror parity at the scale $\sim 10^{18}$ GeV. With the aim to explain the tiny cosmological constant, in the second part we consider the breakings: $E_6 \to SO(10)\times U(1)_Z$ -- in the O-world, and $E'_6 \to SU(6)'\times SU(2)'_θ$ -- in the Sh-world. We assume the existence of shadow $θ$-particles and the low energy symmetry group $SU(3)'_C\times SU(2)'_L\times SU(2)'_θ\times U(1)'_Y$ in the shadow world, instead of the Standard Model. The additional non-Abelian $SU(2)'_θ$ group with massless gauge fields, "theton", has a macroscopic confinement radius $1/Λ'_θ$. The assumption that $Λ'_θ\approx 2.3\cdot 10^{-3}$ eV explains the tiny cosmological constant given by recent astrophysical measurements. In this way the present work opens the possibility to specify a grand unification group, such as $E_6$, from Cosmology.
I discuss gauge coupling unification in a class of superstring standard--like models, which are derived in the free fermionic formulation. Recent calculations indicate that the superstring unification scale is at $O(10^{18}GeV)$ while the minimal supersymmetric standard model is consistent with LEP data if the unification scale is at $O(10^{16})GeV$. A generic feature of the superstring standard--like models is the appearance of extra color triplets $(D,{\bar D})$, and electroweak doublets $(\ell,{\bar\ell})$, in vector--like representations, beyond the minimal supersymmetric standard model. I…
We construct a new cosmological model considering the superstring-inspired E_6 unification in the 4-dimensional space at the early stage of the Universe. We develop a concept of parallel existence in Nature of the ordinary and shadow worlds with different cosmological evolutions.
Perturbative gauge coupling unification in realistic superstring models suggests the existence of additional heavy down-type quarks, beyond the minimal supersymmetric standard model. The mass scale of the heavy down-type quarks is constrained by requiring agreement between the measured low energy gauge parameters and the string-scale gauge coupling unification. These additional quarks arise and may be stable due to the gauge symmetry breaking by ``Wilson lines'' in the superstring models. We argue that there is a window in the parameter space within which this down-type quark is a good candida…
We consider the predictions for the hierarchy of mass scales, the fine structure constant, the radii of compactification and the soft SUSY breaking terms which follow if SUSY breaking is triggered by a gaugino condensate.
We have developed a concept of parallel existence of the ordinary (O) and hidden (H) worlds with a superstring-inspired E_6 unification, broken at the early stage of the Universe into SO(10) X U(1) - in the O-world, and SU(6)' X SU(2)' - in the H-world. As a result, we have obtained in the hidden world the low energy symmetry group G'_SM X SU(2)'_θ, instead of the Standard Model group G_SM. The additional non-Abelian SU(2)'_θgroup with massless gauge fields, "thetons", is responsible for the dark energy. We present a baryogenesis mechanism with the B-L asymmetry produced by the conversion of o…
Recently there has been a resurgence of interest in gauge mediated dynamical supersymmetry breaking scenarios. I investigate how low energy dynamical SUSY breaking may arise from superstring models. In a three generation string derived model I propose that the unbroken hidden non--Abelian gauge group at the string scale is $SU(3)_H$ with matter multiplets. Due to the small gauge content of the hidden gauge group the supersymmetry breaking scale may be consistent with the dynamical SUSY breaking scenarios. The messenger states are obtained in the superstring model from sectors which arise due t…
The Minimal superstring unification, assuming orbifold compactification, provides interesting and rather detailed implications on physics at low energy. The interesting feature of this model is that the masses of the spectrum are related since all of them are functions of only two parameters: the goldstino angle theta and the gravitino mass m_{3/2}. This fact will help us in studying the modification of the supersymmetric magnetic moments sum rules which are very sensitive to the supersymmetry breaking. We write these rules in case of exact supersymmetry in a form close to the supersymmetric m…
We study the phenomenological implications of effective supergravities based on string vacua with spontaneously broken N=1 supersymmetry by dilaton and moduli $F$-terms. We further require Minimal String Unification, namely that large string threshold corrections ensure the correct unification of the gauge couplings at the grand unification scale. The whole supersymmetric mass spectrum turns out to be determined in terms of only two independent parameters, the dilaton-moduli mixing angle and the gravitino mass. In particular we discuss the region of the parameter space where at least one super…
Superstring phenomenology aims at achieving two goals. The first is to reproduce the observed physics of the Standard Model. The second is to identify experimental signatures of superstring unification which, if observed, will provide further evidence for the validity of superstring theory. I discuss such potential signatures of superstring unification. I propose that proton lifetime constraints imply that the Standard Model gauge group must be obtained directly at the string level. In this case the unifying gauge group, for example $SO(10)$, is broken to the Standard Model gauge group by ``Wi…
Utilizing the idea of extra large dimensions, it has been suggested that the gauge and gravity couplings unification can happen at a scale as low as 1 TeV. In this paper, we explore this phenomenological possibility within string theory. In particular, we discuss how the proton decay bound can be satisfied in Type I string theory. The string picture also suggests different scenarios of gauge and gravitational couplings unification. The various scenarios are explicitly illustrated with a specific 4-dimensional N=1 supersymmetric chiral Type I string model with Pati-Salam-like gauge symmetry. We…
We argue that moduli in the adjoint representation of the standard- model gauge group are a natural feature of superstring models, and that they can account for the apparent discrepancy between the string and unification scales.
The recent measurements of the solar neutrino mixing angle theta_{sol} and the Cabibbo mixing angle theta_C reveal a surprising relation, theta_{sol}+theta_C ~ pi/4. Interpreting this empirical relation as a support of the quark-lepton unification, we find that the PMNS mixing matrix can be decomposed into a CKM-like matrix and maximal mixing matrices, which can give profound implications on the quark-lepton unification. We explore a possibility to probe the implication of quark-lepton unification by considering the relative sizes of branching ratios for the lepton flavor violating radiative d…
We have developed a concept of parallel existence of the ordinary (O) and mirror (M), or shadow (Sh) worlds. E_6 unification, inspired by superstring theory, restores the broken mirror parity at the scale ~ 10^18 GeV. With the aim to explain the tiny cosmological constant, we consider the breakings: E_6 -> SO(10) X U(1)_Z - in the O-world, and E'_6 -> SU(6)' X SU(2)'_θ- in the Sh-world. We assume the existence of shadow θ-particles and the low energy symmetry group SU(3)'_C X SU(2)'_L X SU(2)'_θX U(1)'_Y in the shadow world, instead of the Standard Model. The additional non-Abelian SU(2)'_θgro…
We argue that a high precision measurement of the neutrino mixing parameter $θ_{13}$, within a three neutrino seesaw framework can throw important light on the question of whether the quarks and leptons unify into a single matter at high scales. Based on a number of examples, we conclude that a value of $θ_{13} \leq {\frac{Δm^2_{\odot}}{Δm^2_A}}\simeq 0.04$ would require at the minimum a pure leptonic interchange symmetry between $μ$ and $τ$ generations for its natural theoretical understanding and will disfavor a quark-lepton unification type theory such as those based on $SU(4)_c$ or SO(10) …
String theory and supersymmetry are theoretical ideas that go beyond the standard model of particle physics and show promise for unifying all forces. After a brief introduction to supersymmetry, we discuss the prospects for its experimental discovery in the near future. We then show how the magic of supersymmetry allows us to solve certain quantum field theories exactly, thus leading to new insights about field theory dynamics related to electric-magnetic duality. The discussion of superstring theory starts with its perturbation expansion, which exhibits new features including ``stringy geomet…
We argue that there exists simple relation between the quark and lepton mixings which supports the idea of grand unification and probes the underlying robust bi-maximal fermion mixing structure of still unknown flavor physics. In this framework the quark mixing matrix is a parameter matrix describing the deviation of neutrino mixing from exactly bi-maximal, predicting theta_{sol}+theta_C=pi/4, where theta_C is the Cabibbo angle, theta_{atm}+theta_{23}^{CKM}=pi/4 and theta_{13}^{MNS} ~ theta_{13}^{CKM} ~ O(lambda^3), in a perfect agreement with experimental data. Both non-Abelian and Abelian fl…
Recent measurements of the values of gauge coupling constants as well as neutrino properties support the idea of a grand unified (GUT) description of particle physics at a large scale of $M_{GUT}\sim 10^{16}$ GeV. We discuss a strategy to incorporate this picture in the framework of superstring theory. In such a scheme successful predictions of GUTs can be realized while some of the more problematic aspects of grand unification might be avoided. The most promising models are expected in the framework of the heterotic $E_8\times E_8$ string theory.
We revisit the issue of the vacuum angle theta dependence in weakly coupled (Higgsed) Yang-Mills theories. Two most popular mechanisms for eliminating physical theta dependence are massless quarks and axions. Anselm and Johansen noted that the vacuum angle theta(EW), associated with the electroweak SU(2) in the Glashow-Weinberg-Salam model, is unobservable although all fermion fields obtain masses through Higgsing and there is no axion. We generalize this idea to a broad class of Higgsed Yang-Mills theories. In the second part we consider consequences of Grand Unification. We start from a unif…
In this talk, I present a family unification in $Z_3$ orbifolded $E_8\times E_8^\prime$ heterotic strings. It is argued that trinification is a plausible candidate toward supersymmetric standard model at low energy.
Assuming that the Standard Model of particle physics arises from the $E_8\times E_8$ Heterotic String Theory, we try to solve the discrepancy between the unification scale predicted by this theory ($\approx g_{GUT}\times 5.27\cdot 10^{17}$ GeV) and the value deduced from LEP experiments ($\approx 2\cdot 10^{16}$ GeV). A crucial ingredient in our solution is the presence at low energies of three generations of supersymmetric Higgses and vector-like colour triplets. As a by-product our analysis gives rise to a strategy which might be useful when constructing realistic models.
The possibility that non-supersymmetric conformal field theories softly broken below 100 TeV may provide an alternative to conventional grand unification is explored. We consider a low energy theory presumed to be of this type arising from the Type IIB superstring compactified on a $AdS_5 \times S_5/Γ$ space whose gauge group and the particle content are severely restricted by the compactification process. We present an example of a resulting $SU(4)_c\times SU(2)_L\times SU(2)_R$ with three generations, which leads to coupling unification and a prediction for $sin^2θ_W\simeq .227$ and other ph…
The first part of this talk presents the general complexion of baryon and lepton number non-conservation that may arise in the context of quark-lepton unification. The second part presents the status of grand unification with and without supersymmetry and spells out the characteristic proton decay modes, which if seen, will clearly show supersymmetry. The main theme of this talk, that follows next, pertains to two issues: (i) the need to remove the mismatch between MSSM and string-unifications; and especially (ii) the need to resolve naturally the problem of rapid proton decay, that genericall…
A talk presents a new cosmological model with superstring-inspired $E_6$ unification, broken at the early stage of the Universe into $SO(10)\times U(1)_Z$ -- into the ordinary world, and $SU(6)'\times SU(2)'_θ$ -- into the hidden world.
In the framework of the four dimensional heterotic superstring with free fermions we discuss the rank eight and/or sixteen Grand Unified String Theories (GUST) which contain the SU(3)_H - gauge family symmetry. We explicitly investigate the paths of the unification in the GUST with gauge symmetry G x G = [SU(5) x U(1) x (SU(3) x U(1))_H]^2. We show that the GUSTs with the G x G gauge group allow to make the scale of unification to be consistent with the string scale M_SU = g_{string} * 5 * 10^17 GeV.
Dynamical electroweak symmetry breaking by the Hosotani mechanism in the Randall-Sundrum warped spacetime is examined, relations among the W-boson mass (m_W), the Kaluza-Klein mass scale (M_{KK}), and the Higgs boson mass (m_H) being derived. It is shown that M_{KK}/m_W = (2 pi kR)^{1/2} (pi/theta_W) and m_H /m_W = 0.058 kR (pi/theta_W), where k^2, R, and theta_W are the curvature and size of the extra-dimensional space and the Wilson line phase determined dynamically. For typical values kR = 12 and theta_W = (0.2 to 0.4) pi, one finds that M_{KK} = (1.7 to 3.5) TeV, k = (1.3 to 2.6) x 10^{19}…
We show that contrary to first expectations realistic three generation supersymmetric intersecting brane world models give rise to phenomenologically interesting predictions about gauge coupling unification. Assuming the most economical way of realizing the matter content of the MSSM via intersecting branes we obtain a model independent relation among the three gauge coupling constants at the string scale. In order to correctly reproduce the experimentally known values of sin^2[theta_W(M_z)] and alpha_s(M_z) this relation leads to natural gauge coupling unification at a string scale close to t…
Quantum weakdynamics (QWD) as an SU(3)_I gauge theory with the Theta vacuum term is considered to be the unification of the electroweak interaction as an SU(2)_L x U(1)_Y gauge theory. The grand unification of SU(3)_I x SU(3)_C beyond the standard model SU(3)_C x SU(2)_L x U(1)_Y is established by the group SU(3)_I. The grand unified interactions break down to weak and strong interactions at a new grand unification scale 10^{3} GeV, through dynamical spontaneous symmetry breaking (DSSB); the weak and strong coupling constants are the same, alpha_i = alpha_s ~ 0.12, at this scale. DSSB is reali…
We consider corrections to the unification of down-quark and charged-lepton Yukawa couplings in supersymmetric GUTs, which links the large nu_tau-nu_mu mixing angle to b -> s transitions. These corrections generically occur in simple grand-unified models with small Higgs representations and affect s -> d and b -> d transitions via the mixing of the corresponding right-handed superpartners. On the basis of a specific SUSY-SO(10) model, we analyze the constraints from K-Kbar and B-Bbar mixing on the additional \tilde{d}_R-\tilde{s}_R rotation angle theta. We find that epsilon_K already sets a st…
Going beyond the theta function approximation we discuss supersymmetric unification of gauge couplings with exact decoupling of light and heavy particles at energy scales below their masses. We find that the Minimal SUSY model is strongly disfavored while the Missing Doublet Model survives with GUT scale masses rising into the $10^{18}$ GeV region.
The superstring-inspired E_6 model is reduced to the supersymmetric standard model extended by a specific U(1) factor. This choice allows for the existence of naturally light singlet neutrinos which also mix with the known three doublet neutrinos, thus making it possible to accommodate all present neutrino data. Other consequences of this model are also discussed: oblique corrections from Z-Z' mixing, phenomenology of the two-Higgs-doublet sector, and possible scenarios of gauge-coupling unification.
Recently in connection with Superstring theory E_8 and E_6 unifications became very promising. In the present paper we have investigated a number of available paths from the Standard Model (SM) to the E_6 unification, considering a chain of flipped models following the extension of the SM: SU(3)_C\times SU(2)_L\times U(1)_Y \to SU(3)_C\times SU(2)_L\times U(1)_X \times U(1)_Z \to SU(5)\times U(1)_X \to SU(5)\times U(1)_{Z1} \times U(1)_{X1} \to SO(10) \times U(1)_{X1} \to SO(10) \times U(1)_{Z2}\times U(1)_{X2} \to E_6\times U(1)_{X2} or E_6, Also we have considered a chain with a left-right s…
A new supersymmetric grand unified model based on the gauge group $SU(5)\times SU(5)$ is discussed. The model has the feature that the conventional seesaw mechanism for neutrino masses is implemented using the $(15, 1)+(1,\bar{15)}$ representation. This multiplet may have a better chance of arising from level two compactification of superstring theories than the the ${bf \bar{126}}$ representation used in the SO(10) model. The model also naturally suppresses all R-parity violating interactions.
It is argued that a phenomenologically viable grand unification model from superstring is $SU(3)^3$, the simplest gauge group among the grand unifications of the electroweak hypercharge embedded in semi-simple groups. We construct a realistic 4D $SU(3)^3$ model with the GUT scale $\sin^2θ_W^0= \frac38$ in a $Z_3$ orbifold with Wilson line(s). By two GUT scale vacuum expectation values, we obtain a rank 4 supersymmetric standard model below the GUT scale, and predict three more strange families.
We develop a concept of parallel existence of the ordinary (O) and hidden (H) worlds. We compare two cases: 1) when the hidden sector of the Universe is a mirror counterpart of the ordinary world, and 2) when it is a superstring-inspired shadow world described, in contrast to the mirror world, by a symmetry group (or by a chain of groups), which does not coincide with the ordinary world symmetry group. We construct a cosmological model assuming the existence of the superstring-inspired E_6 unification, broken at the early stage of the Universe to SO(10)\times U(1)_Z - in the O-world, and to SU…
In the extra U(1) superstring inspired model, we examine the electroweak and U(1)-prime symmetry breaking with the singlet and exotic quark D, D+{\c}along with the study of heavy Z-prime boson in accordance with the top quark mass region. For this, we have done the analysis of complete renormalization group equations (RGEs)pertaining to the anomaly free E-{\6}-Eta model of rank 5. The Z-prime is found to the order of TeV or above with allowed small Z-Zprime mixing angle, for which the large singlet VEV is required. This is done by considering the only non-universality of Yukawa couplings at GU…
The weakly-coupled heterotic string is known to have problems of dilaton/moduli stabilization, supersymmetry breaking (by hidden-sector gaugino condensation), gauge coupling unification (or the Newton's constant), QCD axion, as well as cosmological problems. We study these problems by adopting the viewpoint that they arise mostly due to our limited calculational power, little knowledge of the vacuum structure, and an inappropriate treatment of gaugino condensation. It turns out that these problems can be solved or are much less severe after a more consistent and complete treatment. There are t…
Type IIB superstring models with the standard model gauge group on D3-branes and with massless matter associated with open strings joining D3-branes to D3-branes or D3-branes to ${\rm D}7_3$-branes are studied. Models with gauge coupling constant unification at an intermediate scale between about $10^{10}$ and $10^{12}$GeV and consistency with the observed value of $\sin^2 θ_W (M_Z)$ are obtained. Extra vector-like states and extra pairs of Higgs doublets play a crucial role.
We investigate more generally the possible unification Yang-Mills groups $G_{YM}$ and representations with CP as a gauge symmetry. Besides the possible Yang-Mills groups $E_8$, $E_7$, $SO(2n+1)$, $SO(4n)$, $SP(2n)$, $G_2$ or $F_4$ (or a product of them) which only allow self-contragredient representations, we present other unification groups $G_{YM}$ and representations which may allow CP as a gauge symmetry. These include especially $SU(N)$ containing Weyl fermions and their CP-conjugates from low-energy spectra in a basic irreducible representation (IR). Such an example is the 496-dimensiona…
In the present paper we have developed a concept of parallel ordinary (O) and mirror (M) worlds. We have shown that in the case of a broken mirror parity (MP), the evolutions of fine structure constants in the O- and M-worlds are not identical. It is assumed that E_6-unification inspired by superstring theory restores the broken MP at the scale \sim 10^{18} GeV, what unavoidably leads to the different E_6-breakdowns at this scale: E_6 \to SO(10)\times U(1)_Z - in the O-world, and E'_6 \to SU(6)'\times SU(2)'_Z - in the M-world. Considering only asymptotically free theories, we have presented t…
In the present talk we have developed a concept of parallel ordinary (O) and mirror (M) worlds. We have shown that in the case of a broken mirror parity (MP), the evolutions of fine structure constants in the O- and M-worlds are not identical. It is assumed that E_6-unification inspired by superstring theory restores the broken MP at the scale \sim 10^{18} GeV, what unavoidably leads to the different E_6-breakdowns at this scale: E_6 \to SO(10)\times U(1)_Z - in the O-world, and E'_6 \to SU(6)'\times SU(2)'_Z - in the M-world. Considering only asymptotically free theories, we have presented th…
We discuss various aspects of the early petite unification (PUT) of quarks and leptons based on the gauge group G_PUT=SU(4)_PS x SU(2)_L x SU(2)_R x SU(2)_H. This unification takes place at the scale M= O(1-2 TeV) and gives the correct value of sin^2 theta_W(M_Z^2) without the violation of the upper bound on the K_L -> mu e rate and the limits on FCNC processes. These properties require the existence of three new generations of unconventional quarks and leptons with charges up to 4/3 (for quarks) and 2 (for leptons) and masses O(250 GeV) in addition to the standard three generations of quarks …
We study more extensively and completely for global gauge anomalies with some semisimple gauge groups as initiated in ref.1. A detailed and complete proof or derivation is provided for the Z_2 global gauge anomaly given in ref.1 for a gauge theory with the semisimple gauge group SU(2)\times SU(2)\times SU(2) in D=4 dimensions and Weyl fermions in the irreducible representation (IR) ω=(2,2,2) with 2 denoting the corresponding dimensions. This Z_2 anomaly was used in the discussions related to generic SO(10) and supersymmetric SO(10) unification theories^1 for the total generation numbers of fer…
Recently type II seesaw dominance in a supersymmetric SO(10) framework has been found useful in explaining large solar and atmospheric mixing angles as well as larger values of $theta_{13}$ while unifying quark and lepton masses. An important question in these models is whether there exists consistency between coupling unification and type II seesaw dominance. Scenarios where this consistency can be demonstrated have been given in a SUSY framework. In this paper we give examples where type II dominance occurs in SO(10) models without supersymmetry but with additional TeV scale particles and al…
