Stuart Raby, Akin Wingerter
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).
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I discuss the existence of discrete properties in the landscape of free fermionic heterotic-string vacua that were discovered via their classification by SO(10) GUT models and its subgroups such as the Pati-Salam, Flipped SU(5) and SU(4) x SU(2) x U(1) models. The classification is carried out by fixing a set of basis vectors and varying the GGSO projection coefficients entering the one-loop partition function. The analysis of the models is facilitated by deriving algebraic expressions for the GSO projections that enable a computerised analysis of the entire string spectrum and the scanning of…
Unification Scale in String Theory
研究了四维弦论中的统一尺度和规范耦合常数。我们证明了精细结构常数是由隐规范群的维数决定的，只有$SU(6)$和$SO(9)$与极小弦统一一致，而统一尺度可以是$10^{16}\,GeV$量级.
Gauge Coupling Unification due to Large String Threshold Corrections
我们表明，大弦阈值校正可以调和的字符串和MSSM统一尺度在费米子弦。这需要至少三个模量与大VEV是彼此不同的MSSM状态产生的非常规方式从弦谱。前者很容易通过隐藏的高吉诺和物质凝聚的超对称破缺来实现，而后者需要在显式的弦模型中看到。
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…
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.
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.
Implications of Non-universal Soft Masses on Gauge Coupling Unification
研究了具有非普适软标量质量和高吉诺质量的最小超对称标准模型的规范耦合统一。非普适情况下，规范耦合的统一尺度估计。它对非普遍性很敏感。事实证明，这些情况可以与弦统一的假设相结合，这导致$\sin^2 θ_W(M_Z)$和$k_1$的预测，$U(1)_Y$生成器的归一化。弦统一预言了$k_1=1.3 - 1.4$。这些值对字符串模型构建有重要的影响。还计算了双环路校正。其中一些例子显示出实验与弦统一之间的巨大差异。我们计算字符串阈值校正来解释差异。
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…
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…
Gauge Coupling Unification and the Top Mass in String Models with $SU(4)\times O(4)$ Symmetry
考虑到$SU(4) {\times} O(4)$模型中的弦阈值修正，我们讨论了弦尺度规范耦合统一的低能含义。我们表示$sin^2θ_W$和$a_3$作为可计算的字符串阈值差的函数，并讨论简单的例子，保留成功的预测的超对称统一的光谱。进一步利用弦尺度下的低能数据和合理的公共规范耦合值，我们得到了阈值修正的范围。最后，我们研究了在弦尺度下由公共规范耦合确定初始值的顶部汤川耦合（$h_t$）的演化。我们发现$h_t$在弱标度下达到它的（准）红外不动点，并讨论了它对顶质量的影响。
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…
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.
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 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…
Minimal String Unification and Constraint on Hidden Sector
我们研究了是否可以从$Z_4$、$Z_6$和$Z_8$轨道结构中得到一个与MSSM具有相同无质量谱的最小弦模型。利用目标空间对偶对称性的反常抵消条件，通过计算机分析，导出了轨道上最小弦模型U（1）$_Y$的能级$k_1$的允许值.我们研究了SU（3）、SU（2）和U（1）规范耦合常数的阈值修正$_Y$，并检验了模型与LEP实验的一致性。进一步我们研究了什么样的隐藏扇区是符合最小弦模型。并估计了它们的隐群规范耦合常数。我们讨论了模型的汤川耦合。
Gauge Coupling Unification in GUT and String Models
MSSM中压力计联轴器的运行结果通过适当包含所有低尺度效应而得到更新。它们被提出作为预测的方案中的强耦合常数只有两个参数在大统一理论的规模~（$α_{U}$ ~和~ $M_{U}$）~和作为一个失配的规模~ $\sim 3 \times 10^{16}$ GeV ~和~ $4\times10^{17}$ GeV的耦合，当所有三个耦合作为实验输入。
Supersymmetric grand unification based on $SO(10)$ is one of the most attractive paradigms in physics beyond the Standard Model. Inspired by the recent NANOGrav signal, we discuss the implications of detecting a stochastic gravitational wave background emitted by a network of cosmic strings for the $SO(10)$ grand unification. Starting from a minimal model with multiple steps of symmetry breaking, we show that it generally prefers a high intermediate scale above $10^{14}\, \mathrm{GeV}$ that is favored by observable primordial gravitational waves. The observed spectrum can potentially narrow th…
We present a six-dimensional T^2/Z_2 orbifold model which arises as an intermediate step in the compactification of the heterotic string to the MSSM. The orbifold contains two pairs of inequivalent fixed points, with unbroken local gauge groups SU(5) and SU(2)xSU(4), respectively, the intersection of which gives the standard model gauge group. All bulk and brane anomalies are cancelled by the Green--Schwarz mechanism. At each SU(5) fixed point, there is a localised \bar{5}+10 standard model generation, while the third generation and the Higgs fields come in split bulk multiplets due to the bre…
We estimate the effect of threshold corrections coming from Wilson lines to gauge coupling unification in the weakly coupled heterotic string with orbifold compactification. By expressing the corrections in terms of an effective field theory calculation we are able to estimate the minimal threshold corrections in a realistic model without constructing the full string theory. Using this we show that the effect of the gauge boson Kaluza Klein excitations is systematically to reduce the string prediction for the unification scale. In the case of discrete Wilson lines the effect of the Wilson line…
Gauge Coupling Unification due to Non-universal Soft Supersymmetry Breaking
在具有非普适软超对称破缺项的MSSM中研究规范耦合统一。如果Gaugino质量比标量软质量小得多，并且标量软质量也具有某种非普适性，那么即使在MSSM的范围内，规范耦合统一尺度也可以大于$3\times 10^{16}$ ~GeV。串统一可能不需要大的阈值校正或大的模值。我们还讨论了与弦模型建立的关系。
We briefly discuss the status of three-family grand unified string models.
Analysis of Running Coupling Constant Unification in String Theory
利用最近得到的双圈弦耦合常数，分析了一类基于轨道紧化的弦模型。假设在弦尺度和单尺度统一下的弱耦合导致了对大质量（弦尺度和弱尺度之间）物质超多重态的谱和/或对卡茨-穆迪代数水平的限制。
The minimal supersymmetric standard model (MSSM), is perhaps the leading candidate for new physics beyond the standard model, but it encounters difficulties with string gauge unification and in addition does not shed any light on the question of fermion masses. We consider a scenario in which the MSSM is valid up to an energy scale of 10^16 GeV, but that above this scale the theory is supplemented by extra vector-like representations of the gauge group, plus a gauged U(1)_X family symmetry. In our approach the extra heavy matter above the scale 10^16 GeV is used in two different ways: (1) to a…
In this talk, gauge coupling evolution is analyzed in D-brane inspired models with two Higgs doublets and a U(3)xU(2)xU(1)^N gauge symmetry. In particular, we focus on D-brane configurations with two or three abelian factors. We find that the correct hypercharge assignment of the Standard Model particles is reproduced for six viable models distinguished by different brane configurations. We also investigate the bottom tau quark mass relation and find that the correct low energy m_b / m_τratio is obtained for equal b-τYukawa couplings at a string scale around 10^3 TeV.
Minimal String Unification and Yukawa Couplings in Orbifold Models
研究了由$Z_N \times Z_M$轨道模型导出的极小超对称标准模型。研究了规范耦合的模量依赖的阈值修正，解释了耦合常数的测量值。此外，我们还研究了模型的汤川耦合。我们发现，$Z_2 \times Z_6'$，$Z_2\times Z_6$，$Z_3 \times Z_6$和$Z_6 \times Z_6$轨道模型有可能导出第二代和第三代Yukawa耦合以及测量的规范耦合常数.允许的模型显示明确的组合模块权重的物质领域。
A new scenario for string unification
本文提出了一种新的翻转SU（5）弦模型中规范耦合统一的方案，它将SU（3）和SU（2）统一的$M_{32}$标度与经验$M_{\rm LEP}\sim10^{15-16}$ ~GeV标度相一致，将SU（5）和U（1）统一的$M_{51}$标度与理论$M_{\rm string}\sim5\times10^{17}$ ~GeV弦统一标度相一致。真空位移是消除反常$\rm U_A(1)$和SU（4）部分带电粒子隐藏扇区所必需的，在这种情况下，所有中间质量尺度的动力学确定中起着至关重要的作用。
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…
We study the path from the string scale physics to the low-energy physics in the $SU(6) \times SU(2)_R$ string-inspired model with the flavor symmetry ${\bf Z}_M \times {\bf Z}_N \times \tilde{D}_4$. The flavor symmetry controls the mass spectra of heavy particles as well as those of quarks and leptons in the intermediate energy region ranging from the string scale ($\sim 10^{18} {\rm GeV}$) to the electroweak scale. In this paper we examine the mass spectra of heavy particles in detail in our model. The renormalization group evolution of the gauge couplings is studied up to two-loop order. A …
We investigate the phase space of parameters in the Pati-Salam model derived in the context of D-branes scenarios, requiring low energy string scale. We find that a non-supersymmetric version complies with a string scale as low as 10 TeV, while in the supersymmetric version the string scale raises up to ~2 x 10^7 TeV. The limited energy region for RGE running demands a large tan(beta) in order to have experimentally acceptable masses for the top and bottom quarks.
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.
We consider the sparticle and higgs spectroscopy in a class of superstring inspired models in which the string threshold corrections ensure the consistency of the string unification scale with the low energy data. The lightest neutralino is almost a pure bino and it is predicted to be the lightest sparticle (LSP). Requiring that $Ω_{LSP}\leq 0.9$, we find an upper bound on its mass which, in the case of dilaton supersymmetry breaking, turns out to be 160 GeV. The LEP 1.5 experimental lower bound on the chargino mass, $m_{χ^{\pm}} > 65$ GeV, implies that the lower bound on the LSP mass is $m_{L…
Low Energy Implications of Minimal Superstring Unification
本文利用声子项和模$F$项研究了N=1超对称性自发破缺弦真空中有效超引力的唯象意义。我们进一步要求最小弦统一，即大弦阈值修正确保规范耦合在大统一尺度下的正确统一。整个超对称质量谱原来是确定在只有两个独立的参数，介子模混合角和引力子质量。特别是，我们讨论的区域的参数空间中，至少有一个superpartner是"可见”在LEP2。我们发现最有可能的候选者是右手电子和最轻电荷子的标量伙伴，它们的质量与最轻希格斯粒子的质量之间有着有趣的相关性。我们展示了如何发现超对称粒子在LEP2可能会相当尖锐的区别与纯超对称破坏和混合超对称模量破坏的情况。
Natural gauge-coupling unification at the string scale
我们认为，在标准模型规范群的伴随表示中的模是超弦模型的一个自然特征，并且它们可以解释弦标度和统一标度之间的明显差异。
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.
We briefly review the status of three-family grand unified string models.
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 …
We construct and analyze an $SU(6)\times SU(2)$ GUT. The model is k=1 string embedable in the sense that we employ only chiral representations allowed at the k=1 level of the associated Kač-Moody Algebra. Both cases $SU(6)\times SU(2)_{L}$ and $SU(6)\times SU(2)_{R}$ are realized. The model is characterized by the $SU(6)\times SU(2) \to SU(4)\times SU(2)\times SU(2)$ breaking scale $M_X$, and the $SU(4)\times SU(2)\times SU(2) \to SU(3)_{C}\times SU(2)_{L}\times U(1)_{Y}$ breaking scale $M_{R}$ . The spectrum bellow $M_R$ includes an extra pair of charge-1/3 colour-triplets of mass $M_{I}\leq …
This is a pedagogical review article surveying the various approaches towards understanding gauge coupling unification within string theory. As is well known, one of the major problems confronting string phenomenology has been an apparent discrepancy between the scale of gauge coupling unification predicted within string theory, and the unification scale expected within the framework of the Minimal Supersymmetric Standard Model (MSSM). In this article, I provide an overview of the different approaches that have been taken in recent years towards reconciling these two scales, and outline some o…
Gauge Coupling Unification: Strings versus SUSY-GUTs
具有标准模型规范组的标准（一级）杂种优势弦模型预测$SU(3)$和$SU(2)$规范耦合的统一，而$U(1)$因子统一模未知的归一化因子$k_1$。另一方面，统一质量已知。我认为，这种情况是非常类似的（虽然相反），在超对称大统一理论中，$U(1)$规范化是已知的（$k_1=5/3$），但统一质量$M_X$是未知的。我强调，在字符串方法中，$k_1$应被视为自由参数（与在SUSY-GUT中将$M_X$视为自由参数的方式完全相同）。如果这样做了，弦方法在规范耦合统一方面的成功可以与超对称大统一理论相媲美
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.
Making Ends Meet: String Unification and Low-Energy Data
弦现象学中一个长期存在的问题是，弦统一尺度与通过在最小超对称标准模型（MSSM）框架内外推低能数据得到的大统一尺度不一致。在本文中，我们研究了几种影响，可能会修改最小弦的预测，从而使弦尺度统一到协议与低能量的数据。这些包括重弦阈值校正，非标准超荷归一化，轻超对称阈值，中间规范结构，以及超出MSSM的额外物质产生的阈值。我们在各种实际的自由费米子弦模型中明确地评估了这些贡献，包括翻转的SU（5）、SO（6）x SO（4）和各种SU（3）x SU（2）x U（1）模型，并发现这些来源中的大多数基本上不会改变最小弦预测。事实上，我们发现，要使弦统一与低能数据相一致，唯一的方法就是通过某种类型的额外物质。然而，值得注意的是，许多现实的弦模型在它们的低能谱中恰恰包含了这种必需的物质。
We study strong coupling effects in four-dimensional heterotic string models where supersymmetry is spontaneously broken with large internal dimensions, consistently with perturbative unification of gauge couplings. These effects give rise to thresholds associated to the dual theories: type I superstring or M-theory. In the case of one large dimension, we find that these thresholds appear close to the field-theoretical unification scale $\sim 10^{16}$ GeV, offering an appealing scenario for unification of gravitational and gauge interactions. We also identify the inverse size of the eleventh d…
Gauge Coupling Unification in Realistic Free-Fermionic String Models
我们在文献中出现的广泛的自由费米子弦模型的框架内讨论规范耦合的统一，包括翻转的SU（5），SO（6）xSO（4）和各种SU（3）xSU（2）xU（1）模型。如果弦尺度下的物质谱是最小超对称标准模型的谱，那么弦统一理论就与实验不符。因此，我们研究了几种可能修改最小字符串预测的效果。首先，我们开发了一个系统的程序，用于评估一个循环的重弦阈值修正的自由费米子弦模型，我们明确评估这些修正的每个现实的模型。我们发现，这些字符串的阈值校正是小的，我们提供了一般的参数解释为什么这样的阈值校正被抑制在弦论。因此，高阈值不能解决与实验的分歧。我们还研究了非标准超荷归一化，轻超对称阈值，和中间尺度规范结构的影响，同样得出结论，这些影响不能解决与低能量数据的分歧。最后，我们研究的影响，额外的颜色三重态和电弱双峰超出MSSM。虽然在普通的大统一场景中不需要，但这种状态通常出现在某些现实的自由费米子弦模型中。我们表明，如果这些状态存在于适当的阈值，那么规范耦合将确实统一在弦尺度。因此，在这些弦模型中，弦统一可以与低能数据相一致。
We look for minimal chiral sets of fermions beyond the standard model that are anomaly free and, simultaneously, vectorlike particles with respect to colour SU(3) and electromagnetic U(1). We then study whether the addition of such particles to the standard model particle content allows for the unification of gauge couplings at a high energy scale, above $5.0 \times 10^{15}$ GeV so as to be safely consistent with proton decay bounds. The possibility to have unification at the string scale is also considered. Inspired in grand unified theories, we also search for minimal chiral fermion sets tha…
We discuss the unification of gauge coupling constants in non-supersymmetric open string vacua that possess the properties of Split Supersymmetry, namely the Standard Model with Higgsinos at low energies and where the Standard model spectrum is always accompanied by right handed neutrinos. These vacua achieve partial unification of two out of three (namely SU(3)$_c$, SU(2), U(1)) running gauge couplings, possess massive gauginos and light Higgsinos at low energies and also satisfy $sin^2θ_w (M_s) = 3/8$. These vacua are based on four dimensional orbifold $Z_3 \times Z_3$ compactifications of s…
We calculate the weak scale MSSM spectrum starting from a heterotic string theory compactified on an anisotropic orbifold. Supersymmetry breaking is mediated by vector-like exotics that arise naturally in heterotic string theories. The messengers that mediate SUSY breaking come in incomplete GUT multiplets and give rise to non-universal gaugino masses at the GUT scale. Models with non-universal gaugino masses at the GUT scale have the attractive feature of allowing for precision gauge coupling unification at the GUT scale with negligible contributions from threshold corrections near the unific…
Recently J. Giedt discussed a mechanism, entitled optical unification, whereby string scale unification is facilitated via exotic matter with intermediate scale mass. This mechanism guarantees that a virtual MSSM unification below the string scale is extrapolated from the running of gauge couplings upward from M_Z^o when an intermediate scale desert is assumed. In this letter we explore the possibility of optical unification within the context of weakly coupled heterotic strings. In particular, we investigate this for models of free fermionic construction containing the NAHE set of basis vecto…
The significant heavy threshold effect is found in the supersymmetric SU(5) model with two adjoint scalars, one of which is interpreted as a massive string mode decoupled from the lower-energy particle spectra. This threshold related with the generic mass splitting of the basic adjoint moduli is shown to alter properly the running of gauge couplings, thus giving a natural solution to the string-scale grand unification as prescribed at low energies by LEP precision measurements and minimal particle content. The further symmetry condition of the (top-bottom) Yukawa and gauge coupling superunific…
Effective dimension-5 operators which modify the gauge kinetic term in Grand Unified Theories may arise as a consequence of quantum gravity or string compactification. We exhaustively calculate the modification of the gauge unification condition due to such operators for all viable rank-preserving symmetry breakings of SO(10) and E(6) grand unified models.
We consider states in the adjoint representation of the Standard Model gauge group as messengers for mediation of supersymmetry (SUSY) breaking. These new messengers can shift the gauge coupling unification to the string scale at O(5x10^{17} GeV) if their masses are at O(10^{14} GeV). The predicted SUSY mass spectrum at the electroweak scale is significantly different from those in other gauge-mediated or supergravity models, resulting in robust mass relations. The gravitino mass is predicted to be about 1-10 GeV. The heavy messenger sector could provide a superheavy dark matter candidate.
The idea of grand unification in a minimal supersymmetric SU(5)xSU(5) framework is revisited. It is shown that the unification of gauge couplings into a unique coupling constant can be achieved at a high-energy scale compatible with proton decay constraints. This requires the addition of a minimal particle content at intermediate energy scales. In particular, the introduction of the SU(2)_L triplets belonging to the (15,1)+(\bar{15},1) representations, as well as of the scalar triplet Σ_3 and octet Σ_8 in the (24,1) representation, turns out to be crucial for unification. The masses of these i…
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