Fermion Number Research Articles

Vacuum energy of nonsupersymmetric S˜ heterotic string models

We use the free fermionic formulation of the heterotic string in four dimensions to study the vacuum structure and energy of nonsupersymmetric tachyon free models that correspond to compactifications of tachyonic vacua of the ten-dimensional heterotic string. We explore the class of heterotic SO(10) nonsupersymmetric models constructed from the S˜ model in the free fermionic formalism and investigate the dependence of the potential on the geometric moduli. This paper will explore a sample of 109 string vacua to find the frequency of viable models, classifying these vacua by the following fertility criteria: tachyon presence, number of spinorial 16/16¯ representations, vectorial 10 states, and top quark mass coupling compatibility. Of these we find those that mimic supersymmetric models with equal number of bosons and fermions at the massless level: a00=0. Tachyon free models occur with a frequency of 5.309×10−3. Furthermore, models that fulfil the rest of the phenomenological fertility conditions and the additional condition on a00 occur with probability 4.0×10−9 We analyze the partition functions and study the moduli dependence of such models, finding that almost all fertile models have finite, positive potential at the free fermionic point, with 2 out of 84 of the fertile cores having negative, finite potential. We demonstrate that the free fermionic point is not necessarily a minimum in the potential. This work provides further evidence that supersymmetry may not be a necessary ingredient of phenomenological models, recreating many of the desirable features of such models without employing supersymmetry. Published by the American Physical Society 2024

Black flowers and real forms of higher spin symmetries

Using Chern-Simons formulation, we investigate higher spin (HS) black holes in AdS3 with soft Heisenberg hair and establish linkage with the real forms of the underlying complexified gauge symmetries taken here as SL(N, ℂ)L × SL(N, ℂ)R. We study the various conserved currents characterizing the HS black flowers (HS-BF) and show that they can be formed of layers indexed by the elements of the centre of the gauge symmetry. This feature follows from requiring the holonomy of the asymptotic gauge connection around the thermal cycle to sit in the centre ℤN of the symmetry group. With regard to the compact subgroups of the real forms of the complexified gauge symmetry, we calculate the entropies of the HS-BF and verify that, unless we are considering trivial holonomies, there are no continuous paths joining the HS-BF to the core spin 2 black holes. As explicit illustrations, we give quantum field realisations of the soft Heisenberg hair in terms of bosonic and fermionic primary conformal fields and compute the HS-BF entropy as a function of the number of fermions occupying the ground state of the Heisenberg soft hair.

Time-dependent orbital-optimized coupled-cluster methods families for fermion-mixtures dynamics.

Five time-dependent orbital optimized coupled-cluster methods, of which four can converge to the time-dependent complete active space self-consistent-field method, are presented for fermion-mixtures with arbitrary fermion kinds and numbers. Truncation schemes maintaining the intragroup orbital rotation invariance, as well as equations of motion of coupled-cluster (CC) amplitudes and orbitals, are derived. Present methods are compact CC-parameterization alternatives to the time-dependent multiconfiguration self-consistent-field method for systems consisting of arbitrarily different kinds and numbers of interacting fermions. Theoretical analysis of applications of present methods to various chemical systems is reported.

Free fermions, neutrality and modular transformations

Abstract With a view towards higher-spin applications, we study the partition function of a free complex fermion in 2d conformal field theory, restricted to the neutral (zero fermion number) sector. This restriction leads to a partial theta function with a combinatoric interpretation in terms of Dyson’s crank of a partition. More crucially, this partition function can be expressed in terms of a q-hypergeometric function with quantum modular properties. This allows us to find its high-temperature asymptotics, including subleading terms which agree with, but also go beyond, what one obtains by imposing neutrality thermodynamically through a chemical potential. We evaluate the asymptotic density of states for this neutral partition function, including the first few subleading terms. Our results should be extendable to more fermions, as well as to higher-spin chemical potentials, which would be of relevance to the higher-spin/minimal model correspondence.

Interference of Particles with Fermionic Internal Degrees of Freedom.

The interference of fermionic particles, specifically molecules comprising a small number of fermions, in a Mach-Zehnder interferometer is being investigated under the influence of both classical and non-classical external controls. The aim is to identify control strategies that can elucidate the relationship between the interference pattern and the characteristics of internal fermion-fermion interactions.

Dyonium induced fermion number violation

Dyonium induced fermion number violation is studied in a SU(2)L×U(1)Y gauge theory with a doublet Higgs field. Dyonium is a generalization of Nambu's monopolium, having finite sized pair of dyon and anti-dyon, connected with a thin string under the linear plus Coulomb force.1This is a follow-up of the author's paper on monopolium induced neutrino mass (including the lepton and baryon number violations), studied with a SO(10) Grand Unified model in 1983. To fulfill the requirement from the chiral anomaly or its index theorem, an electric field should be excited in parallel to the dipole magnetic field. This crucial dynamical problem, not fully answered then, has been solved, by considering not monopolium but dyonium.The fermionic zero modes in the dyonium background fields are necessary in evaluating the transition rate of the fermion number violation processes. Their Dirac equation can be reduced to a single component partial differential equation, similar to the renormalization group equation, which may be useful to estimate the reaction rates.

Classical simulation of non-Gaussian fermionic circuits

We propose efficient algorithms for classically simulating fermionic linear optics operations applied to non-Gaussian initial states. By gadget constructions, this provides algorithms for fermionic linear optics with non-Gaussian operations. We argue that this problem is analogous to that of simulating Clifford circuits with non-stabilizer initial states: Algorithms for the latter problem immediately translate to the fermionic setting. Our construction is based on an extension of the covariance matrix formalism which permits to efficiently track relative phases in superpositions of Gaussian states. It yields simulation algorithms with polynomial complexity in the number of fermions, the desired accuracy, and certain quantities capturing the degree of non-Gaussianity of the initial state. We study one such quantity, the fermionic Gaussian extent, and show that it is multiplicative on tensor products when the so-called fermionic Gaussian fidelity is. We establish this property for the tensor product of two arbitrary pure states of four fermions with positive parity.

The oblique parameters from arbitrary new fermions

We compute the six oblique parameters S, T, U, V, W, X in a New Physics Model with an arbitrary number of new fermions, in arbitrary representations of SU(2) × U(1), and mixing arbitrarily among themselves. We show that S and U are automatically finite, but T is finite only if there is a specific relation between the masses of the new fermions and the representations of SU(2) × U(1) that they sit in. We apply our general computation to two illustrative cases.

On the backreaction of Dirac matter in JT gravity and SYK model

We model backreaction in AdS2 JT gravity via a proposed boundary dual Sachdev-Ye-Kitaev quantum dot coupled to Dirac fermion matter and study it from the perspective of quantum entanglement and chaos. The boundary effective action accounts for the backreaction through a linear coupling of the Dirac fermions to the Gaussian-random two-body Majorana interaction term in the low-energy limit. We calculate the time evolution of the entanglement entropy between graviton and Dirac fermion fields for a separable initial state and find that it initially increases and then saturates to a finite value. Moreover, in the limit of a large number of fermions, we find a maximally entangled state between the Majorana and Dirac fields in the saturation region, implying a transition of the von Neumann algebra of observables from type I to type II. This transition in turn indicates a loss of information in the holographically dual emergent spacetime. We corroborate these observations with a detailed numerical computation of the averaged nearest-neighbor gap ratio of the boundary spectrum and provide a useful complement to quantum entanglement studies of holography.

Entanglement in Interacting Majorana Chains and Transitions of von Neumann Algebras.

We consider Majorana lattices with two-site interactions consisting of a general function of the fermion bilinear. The models are exactly solvable in the limit of a large number of on-site fermions. The four-site chain exhibits a quantum phase transition controlled by the hopping parameters and manifests itself in a discontinuous entanglement entropy, obtained by constraining the one-sided modular Hamiltonian. Inspired by recent work within the AdS/CFT correspondence, we identify transitions between types of von Neumann operator algebras throughout the phase diagram. We find transitions of the form II_{1}↔III↔I_{∞} that reduce to II_{1}↔I_{∞} in the strongly interacting limit, where they connect nonfactorized and factorized ground states. Our results provide novel realizations of such transitions in a controlled many-body model.

Creation of bound half-fermion pairs by solitons

In the presence of topologically nontrivial bosonic field configurations, the fermion number operator may take on fractional eigenvalues, because of the existence of zero-energy fermion modes. The simplest examples of this occur in 1+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1+1$$\\end{document} dimensions, with zero modes attached to kink-type solitons. In the presence of a kink-antikink pair, the two associated zero modes bifurcate into positive and negative energy levels with energies ±ge-gΔ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm ge^{-g\\Delta }$$\\end{document}, in terms of the Yukawa coupling g≪1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g\\ll 1$$\\end{document} and the distance Δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta $$\\end{document} between the kink and antikink centers. When the kink and antikink are moving, it seems that there could be Landau–Zener-like transitions between these two fermionic modes, which would be interpretable as the creation or annihilation of fermion-antifermion pairs; however, with only two solitons in relative motion, this does not occur. If a third solitary wave is introduced farther away to perturb the kink-antikink system, a movement of the faraway kink can induce transitions between the discrete fermion modes bound to the solitons. These state changes can be interpreted globally as creation or destruction of a novel type of pair: a half-fermion and a half-antifermion. The production of the half-integral pairs will dominate over other particle production channels as long as the solitary waves remain well separated, so that there is a manifold of discrete fermion states whose energies are either zero or exponentially close to zero.

Radiative Majorana neutrino masses in a parity solution to the strong CP problem

The strong CP problem is solved in Parity symmetric theories, with the electroweak gauge group containing SU(2)L × SU(2)R broken by the minimal set of Higgs fields. Neutrino masses may be explained by adding the same number of gauge singlet fermions as the number of generations. The neutrino masses vanish at tree-level and are only radiatively generated, leading to larger couplings of right-handed neutrinos to Standard Model particles than with the tree-level seesaw mechanism. We compute these radiative corrections and the mixing angles between left- and right-handed neutrinos. We discuss sensitivities to these right-handed neutrinos from a variety of future experiments that search for heavy neutral leptons with masses from tens of MeV to the multi-TeV scale.

QCD with an infrared fixed point: The pion sector

The possibility that gauge theories with chiral symmetry breaking below the conformal window exhibit an infrared fixed point is explored. With this assumption three aspects of pion physics are reproduced if the quark mass anomalous dimension at the infrared fixed point is γ*=1. First, by matching the long-distance scalar adjoint correlation function. Second, by perturbing the fixed point by a small quark mass, the mq-dependence of the pion mass is reproduced by renormalization group arguments. Third, consistency of the trace anomaly and the Feynman-Hellmann theorem, for small mq, imply the same result once more. This suggests the following picture for the conformal window; close to its upper boundary γ* is zero and grows as the number of fermions is reduced until its lower boundary γ*=1 is reached, where chiral symmetry breaking sets in. Below, the strongly coupled gauge theory with γ*=1 is infrared dual to the free theory of pions. A possible dilaton sector of the scenario will be addressed in a companion paper. Published by the American Physical Society 2024

Explorations in scalar fermion theories: β-functions, supersymmetry and fixed points

Results for β-functions and anomalous dimensions in general scalar fermion theories are presented to three loops. Various constraints on the individual coefficients for each diagram following from supersymmetry are analysed. The results are used to discuss potential fixed points in the ε-expansion for scalar fermion theories, with arbitrary numbers of scalar fields, and where there are just two scalar couplings and one Yukawa coupling. For different examples the fixed points follow a similar pattern as the numbers of fermions is varied. For diagrams with subdivergences there are extensive consistency constraints arising from the existence of a perturbative a-function and these are analysed in detail. Further arbitrary scheme variations which preserve the form of β functions and anomalous dimensions in terms of 1PI diagrams are also discussed. The existence of linear and quadratic scheme invariants is demonstrated and the consistency condition are shown to be expressible in terms of these invariants.

Radiation from a gluon-gluino colour-singlet dipole at N3LO

We compute the quantum chromodynamics (QCD) corrections to the decay of a neutralino to gluinos and partons at next-to-next-to-next-to-leading order (N3LO) in the strong coupling constant αs, integrated separately over the phase-space of two, three, four or five particles in the final state. The resulting matrix elements are related to the quark-gluon antenna functions, completing the set of integrated antenna functions in final-final kinematics required for the extension of the antenna subtraction scheme to N3LO. For a model with massless partons (quarks and gluons) and an arbitrary number of adjoint fermions, we obtained the following new results to Oαs3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left({\\alpha}_s^3\\right) $$\\end{document}: the inclusive cross section for the decay of a neutralino, the renormalization of the effective coupling of a neutralino to a gluino and gluon(s), the gluino collinear anomalous dimension, the gluino contribution to the parton collinear anomalous dimensions and the neutralino-gluino-gluon(s) vertex form factors. A special case of this model is the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 super Yang-Mills theory, where we can relate some of our findings to known results.

A symmetry algebra in double-scaled SYK

The double-scaled limit of the Sachdev-Ye-Kitaev (SYK) model takes the number of fermions and their interaction number to infinity in a coordinated way. In this limit, two entangled copies of the SYK model have a bulk description of sorts known as the “chord Hilbert space”. We analyze a symmetry algebra acting on this Hilbert space, generated by the two Hamiltonians together with a two-sided operator known as the chord number. This algebra is a deformation of the JT gravitational algebra, and it contains a subalgebra that is a deformation of the \mathfrak{sl}_2𝔰𝔩2 near-horizon symmetries. The subalgebra has finite-dimensional unitary representations corresponding to matter moving around in a discrete Einstein-Rosen bridge. In a semiclassical limit the discreteness disappears and the subalgebra simplifies to \mathfrak{sl}_2𝔰𝔩2, but with a non-standard action on the boundary time coordinate. One can make the action of \mathfrak{sl}_2𝔰𝔩2 algebra more standard at the cost of extending the boundary circle to include some “fake” portions. Such fake portions also accommodate certain subtle states that survive the semi-classical limit, despite oscillating on the scale of discreteness. We discuss applications of this algebra, including sub-maximal chaos, the traversable wormhole protocol, and a two-sided OPE.

Scattering amplitudes of fermions on monopoles

We consider scattering processes involving massless fermions and ’t Hooft-Polyakov magnetic monopoles in a minimal SU(2) model and in the Grand Unified SU(5) theory. We construct expressions for on-shell amplitudes for these processes in the J = 0 partial wave using the spinor helicity basis consisting of single-particle and pairwise helicities. These processes are unsuppressed and are relevant for the monopole catalysis of proton decay. The amplitudes for the minimal processes involving a single fermion scattering on a monopole in the initial state and half-fermion solitons in the final state are presented for the first time and are used to obtain the amplitudes for processes involving more fermions in the initial state and integer fermion numbers in the final state. A number of such anomalous and non-anomalous processes, along with their amplitude expressions, are written down for the SU(5) GUT model.

The parastatistics of braided Majorana fermions

This paper presents the parastatistics of braided Majorana fermions obtained in the framework of a graded Hopf algebra endowed with a braided tensor product. The braiding property is encoded in a t-dependent 4×4 braiding matrix B_tBt related to the Alexander-Conway polynomial. The nonvanishing complex parameter t defines the braided parastatistics. At t=1 ordinary fermions are recovered. The values of t at roots of unity are organized into levels which specify the maximal number of braided Majorana fermions in a multiparticle sector. Generic values of t and the t=-1 root of unity mimick the behaviour of ordinary bosons.

Finiteness of quantum gravity with matter on a PL spacetime

We study the convergence of the path integral (PI) for general relativity with matter on a picewise linear (PL) spacetime that corresponds to a triangulation of a smooth manifold by using a PI measure that renders the pure gravity PI finite. This measure depends on a parameter p, and in the case when the matter content is just scalar fields, we show that the PI is absolutely convergent for 0,5 and not more than two scalar fields. In the case of Yang–Mills (YM) fields, we show that the PI is absolutely convergent for the U(1) group and 0,5. In the case of Dirac fermions, we show that the PI is absolutely convergent for any number of fermions and a sufficiently large p. When the matter content is given by scalars, YM fields and fermions, as in the case of the standard model (SM), we show that the PI is absolutely convergent for 52,5. Hence one can construct a finite quantum gravity theory on a PL spacetime such that the classical limit is general relativity coupled to the SM.

Fermion mass hierarchy and mixing in simplified grand gauge–Higgs unification

Grand gauge–Higgs unification of five-dimensional SU(6) gauge theory on an orbifold S 1/Z 2 with localized gauge kinetic terms is discussed. The Standard Model (SM) fermions on the boundaries and some massive bulk fermions coupling to the SM fermions are introduced. Compared to the previous model, the number of bulk fermions is reduced, which reproduces the generation mixing of SM fermions and SM fermion mass hierarchy by mildly tuning the bulk masses and parameters of the localized gauge kinetic terms.