超弦理论中的非对称速动tachyon弦：现象学真空新视角

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本文《从世界表的角度看字符串现象学》由Alon E. Faraggia撰写，发表于2019年的《欧洲物理杂志C》(Eur.Phys.J.C)，卷79，文章编号703，DOI为10.1140/epjc/s10052-019-7222-5。该研究属于理论物理学领域，主要探讨的是非超对称速动超弦在构建可行的弦理论现象学真空中的作用。作者认为，在高维（例如十维）下，非超对称的tachyonicsuperstrings（tachyon是弦理论中的一种不稳定粒子）可能成为解决弦现象学中一些悬而未决问题的关键。tachyonicsuperstrings由于其独特的性质，为构建具有现实意义的物理真空提供了新的可能性，从而拓宽了解决现有问题的理论空间。作者提出了一种自由的、满足六个标准的tachyon模型，这个模型可以被看作是$$ SO(16) \times E_8 $$ 的一个扭折（orbifold），这是一种通过固定点操作来构造新理论的技术。这一模型试图模拟Standard-like Model（类似标准模型的模型），它包含六个代的标准模型特征，这在解决粒子物理学标准模型与弦理论之间的连接问题上具有重要意义。作者进一步探讨了从(2,0)异构型弦理论到四维(2,2)理论的可能转变。他提出，任何四维的(2,0)异构型弦理论可以通过扭折或积分变换与(2,2)理论相联系，这提供了一种理论框架来理解那些不能归结为(2,2)理论的有效场论模型的局限性。这些模型可能会陷入所谓的"沼泽地"，暗示它们可能存在内在的不可持续性或者与实验观测不符。这篇文章对于理解弦理论的结构、模型构建以及与现实世界的关联性有重要贡献，尤其是在处理超弦理论中的tachyon现象及其在构建物理现象学模型中的潜在作用方面。通过世界表（worldsheet）的视角，作者提出了新的思考路径，挑战了现有的理论框架，并为进一步探索弦现象学的实证性进展铺平了道路。

Eur. Phys. J. C (2019) 79:703

https://doi.org/10.1140/epjc/s10052-019-7222-5

Regular Article - Theoretical Physics

String phenomenology from a worldsheet perspective

Alon E. Faraggi

Dept. of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK

Received: 19 July 2019 / Accepted: 8 August 2019 / Published online: 21 August 2019

Abstract I argue that the ten dimensional non-supersym-

metric tachyonic superstrings may serve as good start-

ing points for the construction of viable phenomenological

vacua. Thus, enlarging the space of possible solutions that

may address some of the outstanding problems in string phe-

nomenology. A tachyon free six generation Standard–like

Model is presented, which can be regarded as an orbifold of

the SO(16) × E

heterotic–string in ten dimensions. I pro-

pose that any (2, 0) heterotic–string in four dimensions can

be connected to a (2, 2) one via an orbifold or by interpola-

tions and provide some evidence for this conjecture. It sug-

gests that any Effective Field Theory (EFT) model that cannot

be connected to a (2, 2) theory is necessarily in the swamp-

land, and will simplify the analysis of the moduli spaces of

(2, 0) string compactiﬁcations.

1 Introduction

String theory provides a viable framework to explore the

uniﬁcation of all the fundamental matter and interactions.

While string theory produces a consistent theory of perturba-

tive quantum gravity, it accommodates consistently the gauge

and matter structures of the subatomic regime, including the

chirality property of the electroweak interactions. No other

contemporary theory achieves this feat. Yet it is expected that

the string character of this basic theory is only exhibited at

energy scales that are far removed from those accessible to

present day experiments. In that respect one would have to

rely on the effective, point-like, ﬁeld theory limit of the string

construction in order to confront the theory with experiment.

For that purpose it is vital to be able to identify the smooth

effective ﬁeld theory (EFT) limit corresponding to partic-

ular string theory vacua. To date this identiﬁcation is only

possible in limited cases [1], and entail mostly the analysis

of various supergravity theories that are EFT limits of the

e-mail: alon.faraggi@liv.ac.uk

corresponding string theories. The picture is murky in both

directions, as for the most part one does not know whether

an actual supergravity theory has an origin in a string con-

struction. Furthermore, while supersymmetry is a beautiful

theoretical construction, it is not clear whether nature makes

use of it. It is therefore important to explore alternatives from

the point of view of the worldsheet string theory.

To date investigation of non-supersymmetric string mod-

els were primarily conducted in the context of the tachyon

free SO(16) × SO(16) ten dimensional heterotic string the-

ory [2–21]. This construction can be obtained as an orbifold

of the ten dimensional supersymmetric E

× E

heterotic–

string, and can be connected to it by interpolations in a com-

pactiﬁed dimension [4,5]. It is well known that string theory

gives rise to additional vacua in ten dimensions that are tachy-

onic [2–4,6]. However, the tachyonic modes may be pro-

jected out by Generalised GSO projections. Therefore, from

the point of view of the worldsheet string theory, these string

vacua may serve as viable starting points for the construction

of phenomenological string models and offer novel perspec-

tives on some outstanding issues in string phenomenology.

Furthermore, they may reveal alternative symmetries to those

provided by spacetime supersymmetry. An example is the

Massive Boson–Fermion Degeneracy of [22–24].

In this paper I explore this possibility. For general refer-

ence I ﬁrst examine the constructions of such models in ten

dimensions. The discussion then reverts to the construction

of phenomenological models in four dimensions that can be

regarded as compactiﬁcations of the ten dimensional vacua.

I present a six generation tachyon free model with standard–

like gauge group, as well as a three generation model that

does, however, contain two tachyonic states. I discuss the

reduction of the number of generations to three generations

and the prospect of generating such tachyon free models.

Additionally, the moduli spaces of (2, 0) heterotic–string

vacua is discussed. This class of compactiﬁcations is vast

with little understanding of the relation between the world-

sheet constructions and their smooth effective ﬁeld theory

123

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