I describe how superstring theory may violate spin-statistics in an experimentally observable manner. Reviewing the basics of superstring interactions and how to utilize these to produce a statistical phase, I then apply these ideas to two specific examples. The first is the case of heterotic worldsheet linkings, whereby one small closed string momentarily enlarges sufficiently to pass over another, producing such a statistical phase. The second is the braneworld model with noncommutative geometry, whereby matter composed of open strings may couple to a background in which spacetime coordinates do not commute, modifying the field (anti)commutator algebra. I conclude with ways to sharpen and experimentally test these exciting avenues to possibly verify superstring theory.
The ALEPH collaboration has recently reported a significant excess of four-jet events at the LEP 1.5 and LEP 2. While not yet confirmed by the other collaborations, it was recently proposed that this excess may be explained by certain R-parity violating operators in supersymmetric models. R-parity violating operators introduce the danger of inducing rapid proton decay. I discuss how the operators required to explain the ALEPH four jet events may arise from superstring derived models without inducing rapid proton decay.
Fractional superstrings in the tensor-product formulation experience ``internal projections'' which reduce their effective central charges. Simple expressions for the characters of the resulting effective worldsheet theory are found. All states in the effective theory can be consistently assigned definite spacetime statistics. The projection to the effective theory is shown to be described by the action of a dimension-three current in the original tensor-product theory.
Rolling tachyon backgrounds, arising from open strings on unstable branes in bosonic string theory, can be related to a simple statistical mechanical model - Coulomb gas of point charges in two dimensions confined to a circle, the Dyson gas. In this letter we describe a statistical system that is dual to non-BPS branes in superstring theory. We argue that even though the concept of time is absent in the statistical dual sitting at equilibrium, the notion of time can emerge at the large number of particles $N \to \infty$ limit.
In perturbative amplitudes in quantum field theory and string field theory, Cutkosky rule expresses the anti-hermitian part of a Feynman diagram in terms of sum over all its cut diagrams, and this in turn is used to prove unitarity of the theory. For D-instanton contribution to a string theory amplitude, the cutting rule needed for the proof of unitarity is somewhat different; we need to sum over only those cut diagrams for which all the world-sheet boundaries ending on some particular D-instanton lie on the same side of the cut. By working with the closed string effective action, obtained aft…
Recently it was argued that proton lifetime limits impose that the scale of quantum gravity must be above 10^{16} GeV. By studying the proton stability in the context of realistic heterotic-string models, I propose that proton longevity necessitates the existence of an additional U(1)_{Z'} symmetry, which is of non-GUT origin and remains unbroken down to intermediate, or low, energies. It is shown that the realistic string models frequently give rise to U(1) symmetries, which suppress the proton decay mediating operators, with, or without, the possibility of R-parity violation. By studying the…
The supercoherent states of the RNS string are constructed using the covariant quantization and analogously the light cone quantization formalisms. Keeping intact the original definition of coherent states of harmonic oscillators, we extend the bosonic annihalation operator into the superspace by inclusion of fermionic contribution to oscillator modes thus construct the supercoherent states with supersymetric harmonic oscillator. We analyse the statistics of these states by explicitly calculating the Mandel parameter and obtained interesting results about the nature of distribution of the stat…
We discuss the possibility that CPT violation may appear as a consequence of microscopic decoherence due to quantum-gravity effects, that we describe using a density-matrix formalism motivated by our studies of non-critical string theory. The maximum possible order of magnitude of such decohering CPT-violating effects is not far from the sensitivity of present experiments on the neutral kaon system, and we review a simple parametrization for them. We also review a recent data analysis carried out together with the CPLEAR collaboration, which bounds any such decohering CPT-violating parameters …
A well known problem in supersymmetric models is the presence of, lepton and baryon number violating, dimension four operators. The traditional R parity solution may not be suitable if one tries to incorporate supersymmetry into a Planck scale theory. I propose a different solution in the context of realistic string models. I show that realistic string models can give rise to custodial nonabelian gauge symmetries under which only the leptons or quarks transform. I explain how such symmetries arise in a class of free fermionic models that are based on $Z_2\times Z_2$ orbifold with standard embe…
Semi-classical soliton solutions for superstrings in $AdS_5\times S^5$ are used to predict the dimension of gauge theory operators in $\N=4 $ SU(N) SYM theory. We discuss the possible origin of scaling violations on the gauge theory side.
In this paper we consider the role that worldsheet instantons in the heterotic string could play in spin-statistics violations. Such violations are nonperturbative in the string tension and so would not appear in the spacetime effective action, producing a unique signature of string theory and the details of compactification. By performing a Bogomol'nyi transformation it is shown that there are no instanton solutions in the simplest model proposed by Harvey and Liu, but it is conjectured that more sophisticated models may yield solutions. If such instantons do exist, their effect might be meas…
A review of the soft supersymmetry-breaking parameters and the $μ$ term arising in superstring models is performed paying special attention to their phenomenological implications. In particular, the violation of the scalar mass universality which may lead to dangerous flavor changing neutral current phenomena and the existence of charge and color breaking minima are discussed. Finally, quadratically-divergent loop effects by pure supergravity interactions on soft parameters and the $μ$ term are also reviewed and applied to superstring models. They provide several new sources of the $μ$ term, n…
We derive general formulae for computing the average spectrum for Bosonic or Fermionic massless emission from generic or particular sets of closed superstring quantum states, among the many occurring at a given large value of the number operator. In particular we look for states that can produce a Bosonic spectrum resembling the classical spectrum expected for peculiar cusp-like or kink-like classical configurations, and we perform a statistical counting of their average number. The results can be relevant in the framework of possible observations of the radiation emitted by cosmic strings.
We investigate the Hagedorn transitions of string networks with Y-junctions as may occur, for example, with (p,q) cosmic superstrings. In a simplified model with three different types of string, the partition function reduces to three generalised coupled XY models. We calculate the phase diagram and show that, as the system is heated, the lightest strings first undergo the Hagedorn transition despite the junctions. There is then a second, higher, critical temperature above which infinite strings of all tensions, and junctions, exist. Conversely, on cooling to low temperatures, only the lightes…
In string bit models, the superstring emerges as a very long chain of "bits", in which s fermionic degrees of freedom contribute positively to the ground state energy in a way to exactly cancel the destabilizing negative contributions of d=s bosonic degrees of freedom. We propose that the physics of string formation be studied nonperturbatively in the class of string bit models in which s>d, so that a long chain is stable, in contrast to the marginally stable (s=d=8) superstring chain. We focus on the simplest of these models with s=1 and d=0, in which the string bits live in zero space dimens…
We study the gravitational emission, in Superstring Theory, from fundamental strings exhibiting cusps. The classical computation of the gravitational radiation signal from cuspy strings features strong bursts in the special null directions associated to the cusps. We perform a quantum computation of the gravitational radiation signal from a cuspy string, as measured in a gravitational wave detector using matched filtering and located in the special null direction associated to the cusp. We study the quantum statistics (expectation value and variance) of the measured filtered signal and find th…
Some general features of the scattering of boson-based anyons with an added non-statistical interaction are discussed. Periodicity requirements of the phase shifts are derived, and used to illustrate the danger inherent in separating these phase shifts into the well-known pure Aharanov-Bohm phase shifts, and an additional set which arise due to the interaction. It is proven that the added phase shifts, although due to the non-statistical interaction, necessarily change as the statistical parameter is varied, keeping the interaction fixed. A hard-disk interaction provides a concrete illustratio…
I discuss theories of violations of statistics, including intermediate statistics, parastatistics, parons, and quons. I emphasize quons, which allow small violations of statistics. I analyze the quon algebra and its representations, implications of the algebra including the observables allowed by the superselection rule separating inequivalent representations of the symmetric group, the conservation of statistics rules, and the rule for composite systems of quons. I conclude by raising the question of possible origins of violations of statistics and of the level at which violations should be e…
From the "top-down" approach we investigate physics implications of the class of D- and F- flat directions formed from non-Abelian singlets which are proven flat to all orders in the nonrenormalizable superpotential, for a prototype quasi-realistic free fermionic string model with the standard model gauge group and three families (CHL5). These flat directions have at least an additional U(1)' unbroken at the string scale. For each flat direction, the complete set of effective mass terms and effective trilinear superpotential terms in the observable sector are computed to all orders in the VEV'…
After some general comments about statistics and the TCP theorem, I discuss experimental searches for violations of the exclusion principle and theories which allow for such violations.
When identical particles cease to be indistinguishable: violation of statistics in quantum spacetime
Centro Ricerche Enrico Fermi - Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”（恩里科·费米研究中心 - 物理历史博物馆及恩里科·费米中心研究与学习）；Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare（弗拉斯卡蒂国家实验室，意大利国家核物理研究所）；IFIN-HH, Institutul National pentru Fizica si Inginerie Nucleara Horia Hulubei（霍里亚·胡卢贝伊国家核物理与核工程研究所）；Center for Field Theory and Particle Physics & Department of Physics Fudan University（复旦大学物理系与场论粒子物理中心）；INFN sezione Roma Tor Vergata（意大利国家核物理研究所罗马托维尔加塔分部）
There are two motivations to consider statistics that are neither Bose nor Fermi: (1) to extend the framework of quantum theory and of quantum field theory, and (2) to provide a quantitative measure of possible violations of statistics. After reviewing tests of statistics for various particles, and types of statistics that are neither Bose nor Fermi, I discuss quons, particles characterized by the parameter $q$, which permit a smooth interpolation between Bose and Fermi statistics; $q=1$ gives bosons, $q=-1$ gives fermions. The new result of this talk is work by Robert C. Hilborn and myself th…
The statistical expectation values of the temperature fluctuations of cosmic microwave background (CMB) are assumed to be preserved under rotations of the sky. This assumption of {\em statistical isotropy} (SI) of the CMB anisotropy should be observationally verified since detection of violation of SI could have profound implications for cosmology. We propose a set of measures, $κ_\ell$ ($\ell=1,2,3, ...$) for detecting violation of statistical isotropy in an observed CMB anisotropy sky map indicated by non zero $κ_\ell$. We define an estimator for the $κ_\ell$ spectrum and analytically comput…
The quon algebra gives a description of particles, ``quons,'' that are neither fermions nor bosons. The parameter $q$ attached to a quon labels a smooth interpolation between bosons, for which $q = +1$, and fermions, for which $q = -1$. Wigner and Ehrenfest and Oppenheimer showed that a composite system of identical bosons and fermions is a fermion if it contains an odd number of fermions and is a boson otherwise. Here we generalize this result to composite systems of identical quons. We find $q_{composite}=q_{constituent}^{n^2}$ for a system of $n$ identical quons. This result reduces to the …
Quantum theories constructed on the noncommutative spacetime called the Groenewold-Moyal plane exhibit many interesting properties such as Lorentz and CPT noninvariance, causality violation and twisted statistics. We show that such violations lead to many striking features that may be tested experimentally. These theories predict Pauli forbidden transitions due to twisted statistics, anisotropies in the cosmic microwave background radiation due to correlations of observables in spacelike regions and Lorentz and CPT violations in scattering amplitudes.
We present the different consistency relations that can be seen as variations of the well known Suyama-Yamaguchi (SY) consistency relation τ_{NL} \geqslant ((6/5) f_{NL})^2. It has been claimed that the following variation: τ_{NL} ({\bf k}_1, {\bf k_3}) \geqslant (6/5)^2 f_{NL} ({\bf k}_1) f_{NL} ({\bf k}_3), which we call "the fourth variety", in the collapsed (for τ_{NL}) and squeezed (for f_{NL}) limits is always satisfied independently of any physics; however, the proof depends sensitively on the assumption of scale-invariance which only applies for cosmological models involving Lorentz-in…
In this note we expose some surprising connections between string theory and statistical inference. We consider a large collective of agents sweeping out a family of nearby statistical models for an M-dimensional manifold of statistical fitting parameters. When the agents making nearby inferences align along a d-dimensional grid, we find that the pooled probability that the collective reaches a correct inference is the partition function of a non-linear sigma model in d dimensions. Stability under perturbations to the original inference scheme requires the agents of the collective to distribut…
We investigate a statistical anisotropy on the Cosmic Microwave Background (CMB) bispectrum, which can be generated from the primordial non-Gaussianity induced by quantum fluctuations of a vector field. We find new configurations in the multipole space of the CMB bispectrum given by $\ell_1 = \ell_2 + \ell_3 + 2, |\ell_2 - \ell_3| - 2$ and their permutations, which violate the rotational invariance, such as an off-diagonal configuration in the CMB power spectrum. We also find that in a model presented by Yokoyama and Soda (2008), the amplitude of the statistically anisotropic bispectrum in the…
Many years ago Friedman and Sorkin [1] established the existence of certain topological solitonic excitations in quantum gravity called (topological) geons. Geons can have quantum numbers like charge and can be tensorial or spinorial having integer or half-odd integer spin. A striking result is that geons can violate the canonical spin-statistics connection [2,3]. Such violation induces novel physical effects at low energies. The latter will be small since the geon mass is expected to be of the order of Plank mass. Nevertheless, these effects are very striking and include CPT and causality vio…
