String Scale Research Articles

String landscape and fermion masses

Besides the string scale, string theory has no parameter except some quantized flux values; and the string theory Landscape is generated by scanning over discrete values of all the flux parameters present. We propose that a typical (normalized) probability distribution $P({\cal Q})$ of a physical quantity $\cal Q$ (with nonnegative dimension) tends to peak (diverge) at ${\cal Q}=0$ as a signature of string theory. In the Racetrack K\"ahler uplift model, where $P(\Lambda)$ of the cosmological constant $\Lambda$ peaks sharply at $\Lambda=0$, the electroweak scale (not the electroweak model) naturally emerges when the median $\Lambda$ is matched to the observed value. We check the robustness of this scenario. In a bottom-up approach, we find that the observed quark and charged lepton masses are consistent with the same probabilistic philosophy, with distribution $P(m)$ that diverges at $m=0$, with the same (or almost the same) degree of divergence. This suggests that the Standard Model has an underlying string theory description, and yields relations among the fermion masses, albeit in a probabilistic approach (very different from the usual sense). Along this line of reasoning, the normal hierarchy of neutrino masses is clearly preferred over the inverted hierarchy, and the sum of the neutrino masses is predicted to be $\sum m_{\nu} \simeq 0.0592$ eV, with an upper bound $\sum m_{\nu} <0.066$ eV. This illustrates a novel way string theory can be applied to particle physics phenomenology.

Heterotic − type I dual pairs, rigid branes and broken SUSY

The moduli space of toroidal type I vacua, which are consistent at the non-perturbative level, is composed of independent branches characterized by the number (0, 16 or 32) of rigid branes sitting on top of orientifold planes. This structure persists also when supersymmetry is spontaneously broken à la Scherk–Schwarz. We show that all the components of the moduli space in dimension D≥5 indeed admit heterotic dual components, by explicitly constructing heterotic-type I dual pairs with the rank of the gauge group reduced by 0, 8 or 16 units. In the presence of spontaneous breaking of supersymmetry, the dual pairs we consider are also free of tachyonic instabilities at the one-loop level, provided the scale of supersymmetry breaking is lower than the string scale.

Fractional-Order Memristive Predictor: Arbitrary-Order String Scaling Fracmemristor Based Prediction Model of Trading Price of Future

In this article, inspired by the state-of-the-art research progress of the fractional-order memristor, a fractional-order memristive prediction model of the trading price of future is attempted to be proposed, which can feasibly predict the variation trend of the following unknown trading price data only depending on a small sampling of the given ones in a previous short time. At first, the analogy analysis of the relationship between an actual system of future trading and a physical memristive system of charge transfer is achieved. Second, the achievement of a corresponding capacitive string scaling fracmemristor (LCSF) is mathematically derived and analyzed in detail. Third, a 5-years data from 2015 to 2019 of the 300 exchange traded fund open-end index securities investment fund of Shanghai Stock Exchange is selected to verify the multiscale prediction ability of trading price of future of the LCSF. The theoretical contribution of this article is the first application of the fractional-order memristive electronic system to feasibly achieve an intelligent prediction model of the financial technology.

Cosmological implications of Standard Model criticality and Higgs inflation

The observed Higgs mass indicates that the Standard Model can be valid up to near the Planck scale MP. Within this framework, it is important to examine how little modification is necessary to fit the recent experimental results in particle physics and cosmology. As a minimal extension, we consider the possibility that the Higgs field plays the role of inflaton and that the dark matter is the Higgs-portal scalar field. We assume that the extended Standard Model is valid up to the string scale 1017GeV. (This translates to the assumption that all the non-minimal couplings are not particularly large, ξ≲102, as in the critical Higgs inflation, since MP/102∼1017GeV.) We find a correlated theoretical bound on the tensor-to-scalar ratio r and the dark matter mass mDM. As a result, the Planck bound r<0.09 implies that the dark-matter mass must be smaller than 1.1 TeV, while the PandaX-II bound on the dark-matter mass mDM>0.7±0.2TeV leads to r≳2×10−3. Both are within the range of near-future detection. When we include the right-handed neutrinos of mass MR∼1014 GeV, the allowed region becomes wider, but we still predict r≳10−3 in the most of the parameter space. The most conservative bound becomes r>10−5 if we allow three-parameter tuning of mDM, MR, and the top-quark mass.

A note on string excitations and the Higuchi bound

In this brief note we consider the interaction between high spin excitations in string theory along the Regge trajectory and the Higuchi bound in de Sitter space. There is always a point along the Regge trajectory where the Higuchi bound is violated. However, this point precisely coincides with a string whose length is of order the de Sitter Hubble scale. String theory therefore manifests no immediate inconsistency as long as the string scale Ms is above the Hubble scale H. However, an implication is that the Regge trajectory must be significantly modified at some ultraviolet scale. Insisting that this modification should occur no earlier than the Planck scale would lead to a bound on the string scale of Ms>HMp.

The heavy gluino in natural no-scale [formula omitted]-SU(5)

In light of recent 80–137 fb−1 results at the LHC Run 2 establishing a lower gluino mass limit of 2.25 TeV, we revisit the supersymmetric GUT model Flipped SU(5) with extra vector-like particles, known as F-SU(5), with vanishing No-Scale Supergravity boundary conditions at the string scale of about 2×1017 GeV, including the supersymmetry breaking Bμ parameter which is strictly enforced as Bμ=0. Given the proportional dependence of all model scales on a single parameter M1/2, No-Scale F-SU(5) was shown to possess no electroweak fine-tuning and thus persists as a natural one-parameter model. In this fresh analysis here, we demand consistency with the measured 125 GeV light Higgs boson mass, though we forgo an upper limit on the lightest neutralino relic density. The resulting phenomenology delivers a gluino mass of M(g˜)≲7.5 TeV and a lightest supersymmetric particle (LSP) of M(χ˜10)≲1.6 TeV. In order to dilute the relic density down to the WMAP and Planck measurements, we rely upon a single cosmological master coupling λ6.

Asymptotic safety, string theory and the weak gravity conjecture

We propose a scenario with string theory in the deep ultraviolet, an intermediate asymptotically safe scaling regime for gravity and matter, and the Standard Model in the infrared. This could provide a new perspective to tackle challenges of the two models: For instance, the gravitational Renormalization Group flow could connect a negative microscopic to a positive macroscopic cosmological constant, potentially rendering string theory on an anti-de Sitter background observationally viable. Further, the unitarity of a string-theoretic ultraviolet completion could be inherited by an asymptotically safe fixed point, despite the presence of higher-order interactions. We discuss necessary conditions on the scale of asymptotic safety and the string scale for our scenario to be viable. As a first test, we explore the weak-gravity conjecture in the context of asymptotically safe gravity.

The cosmological constant and the electroweak scale

String theory has no parameter except the string scale, so a dynamically compactified solution to 4 dimensional spacetime should determine both the Planck scale and the cosmological constant Λ. In the racetrack Kähler uplift flux compactification model in Type IIB theory, where the string theory landscape is generated by scanning over discrete values of all the flux parameters, a statistical preference for an exponentially small Λ is found to be natural [1]. Within this framework and matching the median Λ value to the observed Λ, a mass scale m ≃ 100 GeV naturally appears. We explain how the electroweak scale can be identified with this mass scale.

Monopoles, strings, and necklaces in SO(10) and E6

We employ a variety of symmetry breaking patterns in SO(10) and E6 Grand Unified Theories to demonstrate the appearance of topological defects including magnetic monopoles, strings, and necklaces. We show that independent of the symmetry breaking pattern, a topologically stable superheavy monopole carrying a single unit of Dirac charge as well as color magnetic charge is always present. Lighter intermediate mass topologically stable monopoles carrying two or three quanta of Dirac charge can appear in SO(10) and E6 models respectively. These lighter monopoles as well as topologically stable intermediate scale strings can survive an inflationary epoch. We also show the ap­ pearance of a novel necklace configuration in SO(10) broken to the Standard Model via SU(4)c × SU(2)L × SU(2)R. It consists of SU(4)c and SU(2)R monopoles connected by flux tubes. Necklaces consisting of monopoles and antimonopoles joined together by flux tubes are also identified. Even in the absence of topologically stable strings, a monopole-string system can temporarily appear. This system decays by emitting gravity waves and we provide an example in which the spectrum of these waves is strongly peaked around 10−4 Hz with Ωqwh2 ≃10−12. This spectrum should be within the detection capability of LISA.

Supersymmetric SU(5)×U(1)χ and the weak gravity conjecture

The gauge symmetry $SU(5) \times U(1)_\chi$ is the unique maximal subgroup of SO(10) which retains manifest unification at $M_{GUT}$ of the Standard Model gauge couplings, especially if low scale supersymmetry is present. The spontaneous breaking of $U(1)_\chi$ at some intermediate scale leaves unbroken a $Z_2$ symmetry which is precisely `matter' parity. This yields a stable supersymmetric dark matter particle as well as topologically stable cosmic strings. Motivated by the weak gravity conjecture we impose unification of $SU(5)$ and $U(1)_\chi$ at an ultraviolet cutoff $\Lambda \sim \alpha_\Lambda ^{1/2} M_{P} \approx 5 \times 10^{17}$ GeV, where $\alpha_\Lambda$ denotes the $SU(5)$ gauge coupling at $\Lambda$ and $M_P \approx 2.4 \times 10^{18}$ GeV is the reduced Planck Scale. The impact of dimension five operators suppressed by $\Lambda$ on gauge coupling unification, proton lifetime estimates and $b-\tau$ Yukawa unification is discussed. In particular, the gauge boson mediated proton decay into $e^+\pi^0$ can lie within the $2-\sigma$ sensitivity of HyperKamiokande. We also discuss how the intermediate scale strings may survive inflation while the $SU(5)$ monopoles are inflated away. The unbroken $Z_2$ symmetry provides an intriguing link between dark matter, black holes carrying `quantum hair' and cosmic strings.

Instantons and infinite distances

We consider geodesics of infinite length and with constant 4d dilaton in the (classical) hypermultiplet moduli space of type II Calabi-Yau compactifications. When approaching such infinite distance points, a large amount of D-instantons develop an exponentially suppressed action, substantially modifying the moduli space metric. We consider a particular large volume/strong coupling trajectory for which, in the corrected metric, the path length becomes finite. The instanton effects also modify the cllassical 4d dilaton such that, in order to keep the 4d Planck mass finite, the string scale has to be lowered. Our results can be related, via the c-map, to the physics around points of infinite distance in the vector multiplet moduli space where the Swampland Distance Conjecture and the Emergence Proposal have been discussed, and provide further evidence for them.

Growing extra dimensions in AdS/CFT

What is the dimension of spacetime? We address this question in the context of the AdS/CFT Correspondence. We give a prescription for computing the number of large bulk dimensions, D, from strongly-coupled CFTd data, where “large” means parametrically of order the AdS scale. The idea is that unitarity of 1-loop AdS amplitudes, dual to non-planar CFT correlators, fixes D in terms of tree-level data. We make this observation rigorous by deriving a positive-definite sum rule for the 1-loop double-discontinuity in the flat space/bulk-point limit. This enables us to prove an array of AdS/CFT folklore, and to infer new properties of large N CFTs at strong coupling that ensure consistency of emergent large extra dimensions with string/M-theory. We discover an OPE universality at the string scale: to leading order in large N, heavy-heavy-light three-point functions, with heavy operators that are parametrically lighter than a power of N, are linear in the heavy conformal dimension. We explore its consequences for supersymmetric CFTs and explain how emergent large extra dimensions relate to a Sublattice Weak Gravity Conjecture for CFTs. Lastly, we conjecture, building on a claim of [1], that any CFT with large higher-spin gap and no global symmetries has a holographic hierarchy: D = d + 1.

The Swampland Distance Conjecture and towers of tensionless branes

The Swampland Distance Conjecture states that at infinite distance in the scalar moduli space an infinite tower of particles become exponentially massless. We study this issue in the context of 4d type IIA and type IIB Calabi-Yau compactifications. We find that for large moduli not only towers of particles but also domain walls and strings become tensionless. We study in detail the case of type IIA and IIB \U0001d4a9 = 1 CY orientifolds and show how for infinite Kähler and/or complex structure moduli towers of domain walls and strings become tensionless, depending on the particular direction in moduli space. For the type IIA case we construct the monodromy orbits of domain walls in detail. We study the structure of mass scales in these limits and find that these towers may occur at the same scale as the fundamental string scale or the KK scale making sometimes difficult an effective field theory description. The structure of IIA and IIB towers are consistent with mirror symmetry, as long as towers of exotic domain walls associated to non-geometric fluxes also appear. We briefly discuss the issue of emergence within this context and the possible implications for 4d vacua.

Hagedorn-like transition at high supersymmetry breaking scale

We consider phase transitions occurring in four-dimensional heterotic orbifold models, when the scale of spontaneous breaking of mathcal{N} = 1 supersymmetry is of the order of the string scale. The super-Higgs mechanism is implemented by imposing distinct boundary conditions for bosons and fermions along an internal circle of radius R. Depending on the orbifold action, the usual scalars becoming tachyonic when R falls below the Hagedorn radius may or may not be projected out of the spectrum. In all cases, infinitely many other scalars, which are pure Kaluza-Klein or pure winding states along other internal directions, become tachyonic in subregions in moduli space. We derive the off-shell tree level effective potential that takes into account these potentially tachyonic modes. We show that when a combination of the usual tachyons survives the orbifold action, it is the only degree of freedom that actually condenses.

Weak Gravity Conjecture from Unitarity and Causality.

The weak gravity conjecture states that quantum gravity theories have to contain a charged state with a charge-to-mass ratio bigger than unity. By studying unitarity and causality constraints on higher derivative corrections to the charge-to-mass ratio of extremal back holes, we demonstrate that heavy extremal black holes can play the role of the required charged state under several assumptions. In particular, our argument is applicable when the higher-spin states Reggeizing graviton exchange are subdominant in the photon scattering. It covers (1)theories with light neutral bosons such as dilaton and moduli, and (2)UV completion where the photon and the graviton are accompanied by different sets of Regge states just like open string theory. Our result provides an existence proof of the weak gravity conjecture in a wide class of theories, including generic string theory setups with the dilaton or other moduli stabilized below the string scale.

Open-string singlet interaction as pomeron in elastic pp, pbar{p} scattering

We consider contributions of the open-string singlet (OSS) interaction to the proton–proton scattering. Modelling baryon and meson as instanton and open string in the effective QCD string model, the typical pomeron is identified with a massive spin-2 closed string. According to the open-closed string duality, the massive spin-2 closed string is accompanied by the open-string singlet interaction with universal coupling. The flat space 4-point open-string singlet amplitudes and cross sections are computed in the Regge limit. Including both the open and closed string pomerons, we fit the differential cross-section with experimental data of the proton–proton and proton–antiproton scattering from the CDF, E-710, D0, LHC-ATLAS and LHC-TOTEM collaborations. The fitting results show the universality of the string mass scale (or string tension) and consistency of the string model between the open and closed string parameters in describing the pp and pbar{p} scattering in the Regge limit. The fitting of the string model to experimental data gives the string scale M_{S}simeq 1.7–1.8 GeV and the corresponding glueball pole mass m_{g}simeq 1.6–1.7 GeV. This lies within experimental values of the observed 2^{++}, I=0 “meson” masses.

Bimetric, conformal supergravity and its superstring embedding

We discuss the connection between Weyl2 supergravity and superstrings and further discuss holography between 4-dimensional, mathcal{N} = 4 superconformal Weyl2 supergravity and mathcal{N} = 8, higher spin-four theory on AdS5. The Weyl2 plus Einstein supergravity theory is a special kind of a bimetric gravity theory and consists of a massless graviton multiplet plus an additional massive spin-two supermultiplet. Here, we argue that the additional spin-two field and its superpartners originate from massive excitations in the open string sector; just like the mathcal{N} = 4 super Yang-Mills gauge fields, they are localized on the world volume of D3-branes. The ghost structure of the Weyl action should be considered as an artifact of the truncation of the infinitely many higher derivative terms underlying the massive spin 2 action. In field theory, mathcal{N} = 4 Weyl2 supergravity exhibits superconformal invariance in the limit of vanishing Planck mass. In string theory the additional spin-two fields become massless in the tensionless limit. Therefore low string scale scenarios with large extra dimensions provide (almost) superconformal field theories with almost massless open string spin-two fields. The full mathcal{N} = 4 scalar potential including the Yang-Mills matter multiplets is presented and the supersymmetric vacua of Einstein Supergravity are shown, as expected, to be vacua of massive Weyl supergravity. Other vacua are expected to exist which are not vacua of Einstein supergravity. Finally, we identify certain spin-four operators on the 4-dimensional boundary theory that could be the holographic duals of spin-four fields in the bulk.

Symmetry breaking and reheating after inflation in no-scale flipped SU(5)

No-scale supergravity and the flipped SU(5)×U(1) gauge group provide an ambitious prototype string-inspired scenario for physics below the string scale, which can accommodate the Starobinsky-like inflation favoured by observation when the inflaton is associated with one of the singlet fields associated with neutrino mass generation. During inflation, the vacuum remains in the unbroken GUT phase, and GUT symmetry breaking occurs later when a field with a flat direction (the flaton) acquires a vacuum expectation value. Inflaton decay and the reheating process depend crucially on GUT symmetry breaking, as decay channels open and close, depending on the value of the flaton vacuum expectation value. Here, we consider the simultaneous cosmological evolution of both the inflaton and flaton fields after inflation. We distinguish weak, moderate and strong reheating regimes, and calculate in each case the entropy produced as all fields settle to their global minima. These three reheating scenarios differ in the value of a Yukawa coupling that introduces mass mixing between the singlets and the 10s of SU(5). The dynamics of the GUT transition has an important impact on the production of gravitinos, and we also discuss the pattern of neutrino masses we expect in each of the three cases. Finally, we use recent CMB limits on neutrino masses to constrain the reheating models, finding that neutrino masses and the cosmological baryon asymmetry can both be explained if the reheating is strong.

Inspiration from intersecting D-branes: general supersymmetry breaking soft terms in no-scale mathcal{F}-SU(5)

Motivated by D-brane model building, we evaluate the mathcal {F}-SU(5) model with additional vector-like particle multiplets, referred to as flippons, within the framework of No-Scale Supergravity with non-vanishing general supersymmetry breaking soft terms at the string scale. The viable phenomenology is uncovered by applying all current experimental constraints, including but not limited to the correct light Higgs boson mass, WMAP and Planck relic density measurements, and several LHC constraints on supersymmetric particle spectra. Four interesting regions of the parameter space arise, as well as mixed scenarios, given by: (1) light stop coannihilation; (2) pure Higgsino dark matter; (3) Higgs funnel; and (4) light stau coannihilation. All regions can generate the observed value of the relic density commensurate with a 125 GeV light Higgs boson mass, with the exception of the relatively small relic density value for the pure Higgsino lightest supersymmetric particle. This work is concluded by gauging the model against present LHC search constraints and derivation of the final states observable at the LHC for each of these scenarios.

Supersymmetric embedding of antibrane polarization

We study the supersymmetry breaking induced by probe anti-D3-branes at the tip of the Klebanov-Strassler throat geometry. Antibranes inside this geometry polarize and can be described by an NS5-brane wrapping an $S^2$. When the number of antibranes is small compared to the background flux a metastable state exists that breaks supersymmetry. We present a manifestly supersymmetric effective model that realizes the polarized metastable state as a solution, spontaneously breaking the supersymmetry. The supersymmetric model relies crucially on the inclusion of Kaluza-Klein (matrix) degrees of freedom on the $S^2$ and two supersymmetric irrelevant deformations of ${\cal N}=4$ super-Yang-Mills (SYM), describing a large number of supersymmetric D3-branes in the IR. We explicitly identify the massless Goldstino and compute the spectrum of massive fluctuations around the metastable supersymmetry-breaking minimum, finding a Kaluza-Klein tower with masses warped down from the string scale. Below the Kaluza-Klein scale the massive tower can be integrated out and supersymmetry is realized nonlinearly. We comment on the effect of the Kaluza-Klein modes on the effective description of de Sitter vacua in string theory and inflationary model building.