I review our recent attempts toward obtaining the MSSM from string orbifold compactification. The required constraints are the existence of three families and R parity, vectorlike exotics, one pair of Higgs doublets, and the SU(5)$'$ hidden sector for dynamical breaking of SUSY toward a GMSB scenario. We also comment on the threshold correction which are influenced by a power law evolution of gauge couplings through the KK radius in non-prime orbifolds and can be used to fit the couplings.
We discuss a muon anomalous magnetic moment in a five dimensional SU (3) gauge- Higgs unification compactified on M^4 \times S^1 /Z_2 space-time including Z_2 -odd bulk mass for a fermion. We calculate one-loop corrections to the anomalous magnetic moment of muon and find a lower bound for the compactification scale to be around 5 \sim 6 TeV by comparing nonzero Kaluza-Klein mode contributions with the muon (g - 2) experiment at BNL.
A Z_2 orbifold compactification of the heterotic string is considered. The resulting 6D GUT groups can be SO(16) or E_7 times SU(2) plus some hidden sector groups. The N=4 supersymmetry is reduced to N=2. In particular, the SO(16) 6D model with one spinor representation 128 can reduce to the previous 5D SO(16) or SO(14) family unification models after compactifying the sixth dimension. To obtain one spinor, we have to take into account the left-over center of SO(16). We also comment on the E_7 times SU(2) model.
We make a detailed study of the unification of gauge couplings in the MSSM with large extra dimensions. We find some scenarios where unification can be achieved (with the strong coupling constant at the Z mass within one standard deviation of the experimental value) with both the compactification scale and the SUSY breaking scale in the few TeV range. No enlargement of the gauge group or particle content is needed. One particularly interesting scenario is when the SUSY breaking scale is larger than the compactification scale, but both are small enough to be probed at the CERN LHC. Unification …
It is well-known that heterotic string compactifications have, in spite of their conceptual simplicity and aesthetic appeal, a serious problem with precision gauge coupling unification in the perturbative regime of string theory. Using both a duality-based and a field-theoretic definition of the boundary of the perturbative regime, we reevaluate the situation in a quantitative manner. We conclude that the simplest and most promising situations are those where some of the compactification radii are exceptionally large, corresponding to highly anisotropic orbifold models. Thus, one is led to con…
We study a gauge coupling unification scenario based on a non-supersymmetric 5-dimensional model. Through an orbifold compactification, we obtain the Standard Model with split multiplets on a 4-dimensional wall, which is compatible with a grand unification.
We consider a 5-dimensional SU(5) model wherein the symmetry is broken to the 4-dimensional Standard Model by compactification of the 5th dimension on an S^1/(Z_2 \times Z^\prime_2) orbifold. We identify the members of all SU(5) representations upto 75 which have zero modes. We examine how these light scalars affect gauge coupling unification assuming a single intermediate scale and present several acceptable solutions. The 5-D compactification scale coincides with the unification scale of gauge couplings and is determined via this renormalization group analysis. When SO(10) is considered as t…
We analyze gauge coupling unification in the context of heterotic strings on anisotropic orbifolds. This construction is very much analogous to effective 5 dimensional orbifold GUT field theories. Our analysis assumes three fundamental scales, the string scale, $\mstring$, a compactification scale, $\mc$, and a mass scale for some of the vector-like exotics, $\mex$; the other exotics are assumed to get mass at $\mstring$. In the particular models analyzed, we show that gauge coupling unification is not possible with $\mex = \mc$ and in fact we require $\mex \ll \mc \sim 3 \times 10^{16}$ GeV. …
We consider the renormalization group approach to the SUSY flavor problem in the supersymmetric SU(5) model with one extra dimension. In higher dimensional SUSY gauge theories, it has been recently shown that power corrections due to the Kaluza-Klein states of gauge fields run the soft masses generated at the orbifold fixed point to flavor conserving values in the infra-red limit. In models with GUT breaking at the brane where the GUT scale can be larger than the compactification scale, we show that the addition of a bulk Higgs multiplet, which is necessary for the successful unification, is c…
We apply the standard approach of RG flow for the gauge couplings in N=1 D=4 Supergravity to show how to match its results with the heterotic $Z_3$ orbifold and Type IIB ${Z_3}$ orientifold-based models. Using only supergravity, anomaly cancellation and the requirement of unification we determine the part of the Kähler potential of the model invariant under the symmetries of the model. For heterotic orbifolds/type IIB orientifolds, this shows that the lowest order Kähler term of the dilaton has the structure $-\ln(S+{\bar S})$ in agreement with string calculations. The structure of the holomor…
We summarize recent developments in the prediction for $α_s(M_Z)$, self-consistent string unification and the dynamical determination of mass scales, and leptophobic $Z'$ gauge bosons in the context of stringy flipped SU(5). [To appear in Proceedings of Fourth International Conference on Supersymmetry (SUSY96), University of Maryland (May 1996).]
The string theory predicts the unification of the gauge couplings and gravity. The minimal supersymmetric Standard Model, however, gives the unification scale $\sim 2\times 10^{16}$ GeV which is significantly smaller than the string scale $\sim 5\times 10^{17}$ GeV of the weak coupling heterotic string theory. We study the unification scale of the non-supersymmetric minimal Standard Model quantitatively at the two-loop level. We find that the unification scale should be at most $\sim 4\times 10^{16}$ GeV and the desired Kac-Moody level of the hyper-charge coupling should be $1.33 \lsim \ky \ls…
The grand unification of flavor(GUF) in extra dimensions is discussed. After reviewing the old GUF, I present a GUF model SU(7) in 5D with the recently popular field theoretic orbifold compactification.
In this letter we consider the consequences for the LHC of light vector-like exotica with fractional electric charge. It is shown that such states are found in orbifold constructions of the heterotic string. Moreover, these exotica are consistent with gauge coupling unification at one loop, even though they do not come in complete multiplets of SU(5).
We point out that in (open) string compactifications with non-zero NS-NS B-field we can have large Kaluza-Klein thresholds even in the small volume limit. In this limit the corresponding gauge theory description is in terms of a compactification on a non-commutative space (e.g., a torus or an orbifold thereof). Based on this observation we discuss a brane world scenario of non-commutative unification via Kaluza-Klein thresholds. In this scenario, the unification scale can be lowered down to the TeV-range, yet the corresponding compactification radii are smaller than the string length. We discu…
In orbifold models, gauge, Higgs and the matter fields can be unified in one multiplet from the compactification of higher dimensional supersymmetric gauge theory. We study how three families of chiral fermions can be unified in the gauge multiplet. The bulk gauge interaction includes the Yukawa interactions to generate masses for quarks and leptons after the electroweak symmetry is broken. The bulk Yukawa interaction has global or gauged flavor symmetry originating from the R symmetry or bulk gauge symmetry, and the Yukawa structure is restricted. When the global and gauged flavor symmetries …
Motivated by the fact that the string scale can be many orders of magnitude lower than the Planck mass, we investigate the required modifications in the MSSM $β$--functions in order to achieve intermediate ($10^{10-13}$GeV) scale unification, keeping the traditional logarithmic running of the gauge couplings. We present examples of string unified models with the required extra matter for such a unification while we also check whether other MSSM properties (such as radiative symmetry breaking) are still applicable.
String unification at a scale of a few tens of TeV explains the existence of cosmic ray interactions beyond the Greisen-Zatsepin-Kuzmin (GZK) cutoff. Trans-GZK cosmic rays are neutrinos which can penetrate the cosmic microwave background. In interactions with atmospheric nuclei they have sufficient energy for exciting string modes. We present a model for the description of such interactions and discuss the properties of the resulting extensive air showers. Presently available data on trans-GZK cosmic rays suggest a string scale around 80 TeV.
It has recently been proposed that gravity-localized compactifications can generate the required gauge hierarchy without the need for hierarchically large extra spacetime dimensions. In this paper, we show that gauge coupling unification arises naturally in such scenarios as a result of the anomaly induced by the rescaling of the wavefunctions of the brane fields. Thus, ``anomaly-induced'' gauge coupling unification can easily explain the apparent low-energy gauge couplings in gravity-localized compactifications. However, we also point out a number of phenomenological difficulties with such co…
In certain five dimensional gauge theories compactified on the orbifold $S^1/Z_2$ the Standard Model Higgs doublet is identified with the zero mode of the fifth component of the gauge field. This gauge-Higgs unification scenario is realized at high energies, and the Standard Model as an effective theory below the compactification scale satisfies the boundary condition that the Higgs quartic coupling vanishes at the compactification scale (gauge-Higgs condition). This is because at energies above the compactification scale, the five dimensional gauge invariance is restored and the Higgs potenti…
In the context of the minimal supersymmetric standard model (MSSM), we discuss the introduction of exotic matter below the string scale $M_X$ in order to achieve gauge unification at $M_X$ (a constraint of a large class of string models). The possible types of exotic matter that can realise this are investigated and its effect on the top quark mass $m_t$ is presented. The implementation of a theory of fermion masses which utilises the exotic matter is briefly discussed.
We consider the phenomenological implications of a class of compactified string theories which naturally reproduces the flavour multiplet structure of the Standard Model. The implications for gauge unification depends on which of three possibilities is realised for obtaining light Higgs multiplets. The more conventional one leads to predictions for the gauge couplings close to that of the MSSM but with an increased value of the unification scale. The other two cases offer a mechanism for bringing the prediction for the strong coupling into agreement with the measured value while still increasi…
We use a new approach to study string scale gauge coupling unification systematically, allowing both the possibility of non-canonical U(1)_Y normalization and the existence of vector-like particles whose quantum numbers are the same as those of the Standard Model (SM) fermions and their Hermitian conjugates and the SM adjoint particles. We first give all the independent sets (Yi) of particles that can be employed to achieve SU(3)_C and SU(2)_L string scale gauge coupling unification and calculate their masses. Second, for a non-canonical U(1)_Y normalization, we obtain string scale SU(3)_C x S…
Unified theories based on an extended left-right symmetric group, $SU(4) \times SU(2)^4$, are constructed in five dimensions. The compactification scale is assumed to be only a loop factor above the weak scale, so that the weak mixing angle is predicted to be close to its tree level value of 0.239. Boundary conditions in the 5th dimension break $SU(4) \to SU(3) \times U(1)_{B-L}$, removing powerful constraints from $K_L \to μe$ while allowing a reliable calculation of the leading logarithm corrections to $\sin^2 θ$. The compactification scale is expected in the 1--5 TeV region, depending on ho…
We provide what we believe is the minimal three family ${\cal N} = 1$ SUSY and conformal Pati-Salam Model from type IIB superstring theory. This $Z_3$ orbifolded AdS$\otimes S^5$ model has long lived protons and has potential phenomenological consequences for LHC.
One cannot yet point to any firm string prediction. While many approximate string ground states are known with interesting properties, we do not have any argument that one or another describes what we observe around us, and for reasons which appear fundamental we do not know how to systematically determine even any rough quantitative properties. I argue here that we should examine large classes of string ground states, trying to determine whether features such as low energy supersymmetry, the pattern of supersymmetry breaking, the presence of axions, large dimensions, or others might be generi…
Grand unified theories (GUTs) and extra dimensions are potential ingredients of the new physics that may resolve various outstanding problems of the Standard Model. If the inverse size of (one of) the extra dimension(s) is smaller than the GUT scale and standard gauge bosons are allowed to propagate in the bulk then, among other consequences, the evolution of the gauge couplings deviates from the usual logarithmic running somewhat below and between these two scales. In this work, we show that if the compactification scale is the order of 10 TeV, then this modified running may be observable at …
The problem of families, "Why are there three families of fermions?", is a long awaited question to be answered within a reasonable framework. We propose anti-SU($N$) groups for the unification of families in grand unification (GUT) groups, where the separation of color and weak gauge groups in the GUT is achieved by antisymmetric tensor Brout-Englert-Higgs boson instead of an adjoint representation. Theories of anti-SU($N$)'s are proposed for the unification of families. The minimal model is found as \antiSD \, GUT with the fermion representation [3]+2[2]+8[\bar-1]. We present an example in a…
We look for the minimal particle content which is necessary to add to the standard model in order to have a complete unification of gauge couplings and gravity at the weakly coupled heterotic string scale. Using the current precision electroweak data, we find that the presence of a vector-like fermion at an intermediate scale and a non-standard hypercharge normalization are in general sufficient to achieve this goal at two-loop level. If one requires the extra matter scale to be below the TeV scale, then it is found that the addition of three vector-like fermion doublets with a mass around 700…
We discuss whether the (MSSM) unification of gauge couplings can be accommodated in string theories with a low (TeV) string scale. This requires either power law running of the couplings or logarithmic running extremely far above the string scale. In both cases it is difficult to arrange for the multiplet structure to give the MSSM result. For the case of power law running there is also enhanced sensitivity to the spectrum at the unification scale. For the case of logarithmic running there is a fine tuning problem associated with the light closed string Kaluza Klein spectrum which requires gau…
Here we ask if it is possible to have string unification in $\mathsf{SU(5)\times SU(5)}$ gauge group. We specifically investigate the weakly coupled heterotic string unification for the four couplings in this framework. We show that only a limited versions of $\mathsf{SU(5)\times SU(5)}$ with adjoint representation components at intermediated scales, between $M_Z$ and $Λ$ (unification), are allowed. This is essentially due to the limitation in the parameter space to the gauge coupling constant $α_1^{-1}$ related to hypercharge. Indeed, only the vanishing hypercharge decompositions of $\mathsf{…
We consider gauge coupling unification in models with TeV scale strings and large compact dimensions realized as type IIB string orientifolds. Following an observation by Ibanez we show that the gauge couplings at low energies can behave as if they effectively unify at $M_U \sim 2 \times 10^{16} GeV$ with $α_U \sim 1/24$. This requires the $σ$ model anomaly coefficients $b_a^{i'}$ not to be all equal and their ratio to the $β$-functions of minimally supersymmetric Standard Model $β_a$ to be a constant independent of the gauge group. If, in addition, $b_a^{i'}$ have a gauge group independent co…
In this talk I discuss the problems and virtues of SUSY GUTs in four dimensions. I then show how to solve some of these problems, without foregoing the virtues, by considering an SO(10) SUSY GUT in five dimensions. I discuss gauge coupling unification and neutrino masses. In particular, it is shown that the 5D compactification scale and cutoff scale are determined by fitting the low energy values of the three standard model gauge couplings. Neutrino masses can be accommodated.
We exploit the measured branching ratio for $b \rightarrow sγ$ to derive lower limits on the sparticle and Higgs masses in the minimal string unification models. For the LSP('bino'), chargino and the lightest Higgs, these turn out to be 50, 90 and 75 GeV respectively. Taking account of the upper bounds on the mass spectrum from the LSP relic abundance, we estimate the direct detection rate for the latter to vary from 10^{-1} to 10^{-4} events/kg/day. The muon flux, produced by neutrinos from the annihilating LSP's, varies in the range 10^{-2} - 10^{-9} muons/m^2/day.
In certain five dimensional gauge theories the Standard Model Higgs doublet is identified, after compactification on the orbifold S^1/Z_2, with the zero mode of the fifth component of the gauge field. An effective potential for the Higgs field is generated via quantum corrections, triggered by the breaking of the underlying gauge symmetry through boundary conditions. The quartic Higgs coupling can be estimated at low energies by employing the boundary condition that it vanishes at the compactification scale Λ, as required by five dimensional gauge invariance. For Λ\gtrsim 10^{13}-10^{14} GeV, …
We analyze the implications of electroweak and strong coupling unification in a very general class of models extending the minimal supersymmetric standard model in $4+p$ dimensions $(p\geq 0)$. In general, electroweak precision data require the presence of large extra dimensions (low compactification scales, $M_c$) and/or low unification scale, $M_U$. In particular, the actual experimental value of the strong coupling at $M_Z$ imposes an upper bound on the compactification and unification scales. In four dimensional theories ($M_c\simeq M_U$) with canonical hypercharge assignment we find $M_U\…
We explicitly test the asymptotic grand unification of a minimal 5-dimensional model with SO(10) gauge theory compactified on an $S^{1}/Z_{2}\times Z^{\prime}_{2}$ orbifold. We consider all matter fields as propagating in the bulk and show that the gauge couplings asymptotically run to a fixed point in the UV. However, the Yukawa couplings will typically hit a Landau pole right above the compactification scale in this class of SO(10) models.
The supersymmetry breaking parameters and the resulting supersymmetric particle spectrum are studied in orbifold compactifications of string theory under the assumption that unification of gauge coupling constants at about $10^{16}$ GeV is a consequence of large moduli dependent string loop threshold corrections. The effect on the spectrum of various assumptions as to the modular weights of the states, the values of the Green-Schwarz parameter, $δ_{GS}$, the origin of the $μ$ parameter and the moduli dependence of Yukawa couplings is discussed. The effect of radiative corrections to the effect…
We point out that models where gauge and charged matter fields live on the world volume of D3 branes can provide a weak string coupling description of the gauge coupling unification in the supersymmetric standard model at a scale of order $10^{16}$ GeV. In the D3 brane picture, the string and unification scales coincide, while the size of the extra dimensions is somewhat larger than the string length. We then construct a quasirealistic "three generation" model with D3 branes at orbifold fixed points. We point out that placing D3 branes at different orbifold fixed points provides a geometric de…
Following the suggestion of Bachas, Fabre and Yanagida (BFY), we analyze the gauge coupling unification at the two-loop order, in a supersymmetric scenario where scalars belonging to the adjoint representations contribute to the evolution of the couplings from intermediate scales onward, and the unification scale is pushed towards the string scale. Thereafter, we compare the masses of these adjoint scalars to the scale at which the hidden sector gauge coupling reaches the non-perturbative limit at the two-loop order for various possible hidden sector gauge groups motivated by the the conjectur…
Higher-dimensional models of grand unification allow us to relate the top Yukawa coupling y_t to the gauge coupling g. The tree level relation y_t=g at the scale of grand unification implies, in the framework of the MSSM, a rather small ratio of Higgs expectation values tan beta. We find that, in the presence of localized Fayet-Iliopoulos terms, y_t is suppressed against g because the bulk fields acquire non-trivial profiles whose overlap is smaller than in the case of flat profiles. This increases the prediction for tan beta to moderately large values. Thus tan beta is related to the geometry…
We derive the universal threshold corrections in heterotic string theory including a continuous Wilson line. Unification of gauge and gravitational couplings is shown to be possible even within perturbative string theory. The relative importance of gauge group dependent and independent thresholds on unification is clarified. Equipped with these results we can then attempt an extrapolation to the strongly coupled heterotic string -- M-theory. We argue that such an extrapolation might be meaningful because of the holomorphic structure of the gauge coupling function and the close connection of th…
For the weakly coupled heterotic string (WCHS) there is a well-known factor of twenty conflict between the minimum string coupling unification scale, Lambda_H ~5x10^(17) GeV, and the projected MSSM unification scale, Lambda_U ~ 2.5x10^(16) GeV, assuming an intermediate scale desert (ISD). Renormalization effects of intermediate scale MSSM-charged exotics (ISME) (endemic to quasi-realistic string models) can resolve this issue, pushing the MSSM scale up to the string scale. However, for a generic string model, this implies that the projected Lambda_U unification under ISD is accidental. If the …
We discuss string scale unification facilitated by exotic matter with masses at intermediate scales, between the observable sector supersymmetry breaking scale and the string scale. We point out a mechanism by which string scale unification may occur while producing a (lower) virtual unification scale independent of the location of the intermediate scale and the value of the string coupling. The apparent unification obtained by extrapolating low energy gauge couplings is not accidental when this mechanism is invoked; virtual unification is robust.
A general prediction of string unification is the existence of exotic states with fractional charges under the free unbroken Abelian generators of the underlying GUT symmetry. Such states may be long-lived due to the existence of weakly broken gauge, or local discrete, symmetries, and may serve as experimental probes of string theory in forthcoming cosmic ray and dark matter experiments.
The lower limit to string coupling unification in weakly coupled heterotic strings was shown by Kaplunovsky to be around Lambda_H ~ 5 x 10^{17} GeV. In contrast, under the scenario of an intermediate scale desert, the SU(3)_C x SU(2)_L x U(1)_Y ([321]) Minimal Supersymmetric Standard Model (MSSM) unification scale is Lambda_U ~ 2.5 x 10^{16} GeV. Optical unification was proposed by Giedt as a robust mechanism for relating these two scales. In this mechanism, intermediate scale MSSM-charged exotic particles effect running couplings like a diverging lens, always producing a ``virtual'' image of …
This is a pedagogical review article surveying the various approaches towards understanding gauge coupling unification within string theory. As is well known, one of the major problems confronting string phenomenology has been an apparent discrepancy between the scale of gauge coupling unification predicted within string theory, and the unification scale expected within the framework of the Minimal Supersymmetric Standard Model (MSSM). In this article, I provide an overview of the different approaches that have been taken in recent years towards reconciling these two scales, and outline some o…
I argue that in open-string theory with hierarchically small (or large) extra dimensions, gauge groups can unify naturally with logarithmically-running coupling constants at the high Kaluza-Klein (or string-winding) scale. This opens up the possibility of rescuing the standard logarithmic unification at $M_U\sim 10^{15-18}$ GeV even if the fundamental-string scale is much lower, at intermediate or possibly even electroweak scales. I also explain, however, why a low type-I string scale may not suffice to obliterate the ultraviolet problems usually associated with the gauge hierarchy.
One of the drawbacks of conventional grand unification scenarios has been that the unification scale is too high to permit direct exploration. In this paper, we show that the unification scale can be significantly lowered (perhaps even to the TeV scale) through the appearance of extra spacetime dimensions. Such extra dimensions are a natural consequence of string theories with large-radius compactifications. We show that extra spacetime dimensions naturally lead to gauge coupling unification at intermediate mass scales, and moreover may provide a natural mechanism for explaining the fermion ma…
