Terms Of Fermions Research Articles

Constraining a general U(1)′ inverse seesaw model from vacuum stability, dark matter, and collider

We consider a class of gauged $U(1)$ extensions of the Standard Model (SM), where the light neutrino masses are generated by an inverse seesaw mechanism. In addition to the three right handed neutrinos, we add three singlet fermions and demand an extra $Z_2$ symmetry under which, the third generations of both of the neutral fermions are odd, which in turn gives us a stable dark matter candidate. We express the $U(1)$ charges of all the fermions in terms of the U(1) charges of the standard model Higgs and the new complex scalar. We study the bounds on the parameters of the model from vacuum stability, perturbative unitarity, dark matter relic density and direct detection constraints. We also obtain the collider constraints on the $Z'$ mass and the $U(1)'$ gauge coupling. Finally we compare all the bounds on the $Z'$ mass versus the $U(1)'$ gauge coupling plane.

Operatorial characterization of Majorana neutrinos

The Majorana neutrino psi _{M}(x) when constructed as a superposition of chiral fermions such as nu _{L} + Coverline{nu _{L}}^{T} is characterized by (mathcal{C}mathcal{P}) psi _{M}(x)(mathcal{C}mathcal{P})^{dagger } =igamma ^{0}psi _{M}(t,-vec {x}), and the CP symmetry describes the entire physics contents of Majorana neutrinos. Further specifications of C and P separately could lead to difficulties depending on the choice of C and P. The conventional mathcal{C} psi _{M}(x) mathcal{C}^{dagger } = psi _{M}(x) with well-defined P is naturally defined when one constructs the Majorana neutrino from the Dirac-type fermion. In the seesaw model of Type I or Type I+II where the same number of left- and right-handed chiral fermions appear, it is possible to use the generalized Pauli–Gursey transformation to rewrite the seesaw Lagrangian in terms of Dirac-type fermions only; the conventional C symmetry then works to define Majorana neutrinos. In contrast, the “pseudo C-symmetry” nu _{L,R}(x)rightarrow Coverline{nu _{L,R}(x)}^{T} (and associated “pseudo P-symmetry”), that has been often used in both the seesaw model and Weinberg’s model to describe Majorana neutrinos, attempts to assign a nontrivial charge conjugation transformation rule to each chiral fermion separately. But this common construction is known to be operatorially ill-defined and, for example, the amplitude of the neutrinoless double beta decay vanishes if the vacuum is assumed to be invariant under the pseudo C-symmetry.

Area-law-like systems with entangled states can preserve ergodicity

We study the ground entangled state of the one-dimensional spin-1/2 Ising ferromagnet at its transverse-field critical point. When this problem is expressed in terms of independent fermions, we show that the usual thermostatistical sums emerging within Fermi-Dirac statistics can, for an L-sized subsystem, be indistinctively taken up to L terms or up to lnL terms, providing a neat understanding of the origin of the logarithmic scaling of the entanglement entropy in the system. This is interpreted as a compact occupancy of the phase-space of the L-subsystem, hence standard Boltzmann-Gibbs thermodynamics quantities with an effective system size V ∝ lnL are appropriate and are explicitly calculated. The calculations are then to be done in a Hilbert space whose effective dimension is 2ln L instead of 2L. In this we can assume ergodicity. Our analysis suggests a scenario where the physical systems are essentially grouped into three classes, in terms of their phase-space occupancy, ergodicity and Lebesgue measure.

Computation of effective front form Hamiltonians for massive Abelian gauge theory

Renormalization group procedure for effective particles (RGPEP) is applied in terms of a second-order perturbative computation to an Abelian gauge theory, as an example of application worth studying on the way toward derivation of a dynamical connection between the spectroscopy of bound states and their parton-model picture in the front form of Hamiltonian dynamics. In addition to the ultraviolet transverse divergences that are handled using the RGPEP in previously known ways, the small-x divergences are handled by introducing a mass parameter and a third polarization state for gauge bosons using a mechanism analogous to spontaneous breaking of global gauge symmetry, in a special limit that simplifies the theory to Soper's front form of massive QED. The resulting orders of magnitude of scales involved in the dynamics of effective constituents or partons in the simplified theory are identified for the fermion and boson mass counter terms, effective masses and self-interactions, as well as for the Coulomb-like effective interactions in bound states of fermions. Computations in orders higher than second are mentioned but not described in this article.

Superconformal blocks: general theory

In this work we launch a systematic theory of superconformal blocks for four­point functions of arbitrary supermultiplets. Our results apply to a large class of superconformal field theories including 4-dimensional models with any number mathcal{N} of supersymmetries. The central new ingredient is a universal construction of the relevant Casimir differential equations. In order to find these equations, we model superconformal blocks as functions on the supergroup and pick a distinguished set of coordinates. The latter are chosen so that the superconformal Casimir operator can be written as a perturbation of the Casimir operator for spinning bosonic blocks by a fermionic (nilpotent) term. Solu­ tions to the associated eigenvalue problem can be obtained through a quantum mechanical perturbation theory that truncates at some finite order so that all results are exact. We illustrate the general theory at the example of d = 1 dimensional theories with mathcal{N} = 2 supersymmetry for which we recover known superblocks. The paper concludes with an outlook to 4-dimensional blocks with mathcal{N} = 1 supersymmetry.

Critical properties of the Néel–algebraic-spin-liquid transition

The algebraic spin liquid is a long-sought-after phase of matter characterized by the absence of quasiparticle excitations, a low-energy description in terms of emergent Dirac fermions and gauge fields interacting according to (2+1)D quantum electrodynamics (QED$_3$), and power-law correlations with universal exponents. The prototypical algebraic spin liquid is the Affleck-Marston $\pi$-flux phase, originally proposed as a possible ground state of the spin-1/2 Heisenberg model on the 2D square lattice. While the latter model is now known to order antiferromagnetically at zero temperature, recent sign-problem-free quantum Monte Carlo simulations of spin-1/2 fermions coupled to a compact U(1) gauge field on the square lattice have shown that quantum fluctuations can destroy N\'eel order and drive a direct quantum phase transition to the $\pi$-flux phase. We show this transition is in the universality class of the chiral Heisenberg QED$_3$-Gross-Neveu-Yukawa model with a single SU(2) doublet of four-component Dirac fermions (i.e., $N_f=1$), pointing out important differences with the corresponding putative transition on the kagome lattice. Using an $\epsilon$ expansion below four spacetime dimensions to four-loop order, and a large-$N_f$ expansion up to second order, we show the transition is continuous and compute various thermodynamic and susceptibility critical exponents at this transition, setting the stage for future numerical determinations of these quantities. As a byproduct of our analysis, we also obtain charge-density-wave and valence-bond-solid susceptibility exponents at the semimetal-N\'eel transition for interacting fermions on the honeycomb lattice.

Curved spacetime theory of inhomogeneous Weyl materials

We show how the universal low-energy properties of Weyl semimetals with spatially varying time-reversal (TR) or inversion (I) symmetry breaking are described in terms of chiral fermions experiencing curved-\emph{spacetime} geometry and synthetic gauge fields. By employing Clifford representations and Schrieffer-Wolff transformations, we present a systematic derivation of an effective curved-space Weyl theory with rich geometric and gauge structure. To illustrate the utility of the formalism, we give a concrete prescription of how to fabricate nontrivial curved spacetimes and event horizons in topological insulators with magnetic textures. Our theory can also account for strain-induced effects, providing a powerful unified framework for studying and designing inhomogeneous Weyl materials.

Bond particle theory for the pseudogap phase of underdoped cuprates

We present a theory for the lightly doped t-J model which is of possible relevance for the normal state of underdoped cuprates. Starting from an arbitrary dimer covering of the plane an exact representation of the t-J Hamiltonian in terms of bond bosons and fermions can be derived. Since all dimer coverings must give identical results for observable quantities we construct an approximate but translationally invariant Hamiltonian by averaging the bond particle Hamiltonian over all possible dimer coverings. Treating the resulting Hamiltonian in mean-field approximation we find fermi pockets centered near (pi/2,pi/2) with a total area of x/2 (with x the hole concentration) and a gapped spin-wave-like band of triplet excitations.

Dynamical origin of fermion bulk masses in a warped extra dimension

Extensions of the Standard Model featuring a warped extra dimension compactified on an S1/ℤ2 orbifold, in which the fermions and gauge bosons live in the bulk of the fifth dimension, offer one of the most compelling mechanisms for addressing both the hierarchy problem and the flavor puzzle of the Standard Model. However, the five-dimensional mass terms of bulk fermions must be odd functions on the orbifold, and as such they should be described by a field depending on the coordinate of the extra dimension. We demonstrate the feasibility of dynamically generating these fermion bulk masses with a bulk scalar field in warped extra dimensions. The bulk scalar acquires a vacuum expectation value, which is odd under the orbifold symmetry and gives rise to the fermion bulk masses through non-universal Yukawa-like interactions. Like in the conventional Randall-Sundrum setup, the localization of the different fermion zero modes along the extra dimension naturally explains the observed flavor structure and four-dimensional mass hierarchy of the SM fermions. We study the phenomenological implications of the backreaction on the metric and the modified fermion profiles due to the bulk scalar field on electroweak precision and flavor observables. Using up-to-date data, we show that the contributions to the S, T, and ϵK parameters require the mass of the first Kaluza-Klein gluon resonance to be of order 14 and 10 TeV in the minimal and the custodial model, respectively, regardless of the effect of the backreaction. Furthermore, effective flavor-changing interactions among the SM fermions induced by the bulk scalar are discussed. We also comment on the potential impact of the Higgs portal interaction of the bulk scalar on the couplings of the Higgs boson.

Next-level composite fermions

A rich pattern of fractional quantum Hall states in graphene double layers can be naturally explained in terms of two-component composite fermions carrying both intra- and inter-layer vortices.

From quantum wires to the Chern-Simons description of the fractional quantum Hall effect

We show the explicit connection between two distinct and complementary approaches to the fractional quantum Hall system (FQHS): the quantum wires formalism and the topological low-energy effective description given in terms of an Abelian Chern-Simons theory. The quantum wires approach provides a description of the FQHS directly in terms of fermions arranged in an array of one-dimensional coupled wires. In this sense it is usually referred to as a microscopic description. On the other hand, the effective theory has no connection with the microscopic modes, involving only the emergent topological degrees of freedom embodied in an Abelian Chern-Simons gauge field, which somehow encodes the collective motion of the strongly correlated electrons. The basic strategy pursued in this work is to bosonize the quantum wires system and then consider the continuum limit. By examining the algebra of the bosonic operators of the Hamiltonian, we are able to identify the bosonized microscopic fields with the components of the field strength (electric and magnetic fields) of the emergent gauge field. Thus our study provides a bridge between the microscopic physical degrees of freedom and the emergent topological ones, without relying on the bulk-edge correspondence.

Vestiges of Topological Phase Transitions in Kitaev Quantum Spin Liquids.

We investigate signatures of topological quantum phase transitions (TQPTs) between the Z_{2} quantum spin liquids (QSLs). In two spatial dimensions, Z_{2} QSLs and their TQPTs are only well defined at zero temperature (T=0), and it is imperative to clarify their observable signatures under nonzero temperatures. Here, we present the vestiges of TQPTs between Z_{2} QSLs with Majorana fermions in terms of thermal Hall conductivity κ_{xy} at nonzero temperatures. The κ_{xy}/T shows characteristic temperature dependences around TQPTs. We argue that an exponential upturn near T=0 and the peak of κ_{xy}/T around massive excitation energy are observable smoking-gun signals of the TQPTs. Quantum critical fan-shape temperature dependences are uncovered across TQPTs. We also perform the parton mean-field analysis on a modified Kitaev model with next-nearest neighbor interactions finding TQPTs between the phases with different Chern numbers and their vestiges self-consistently. We discuss the implication of our results to the recent experiments in α-RuCl_{3}.

A new scheme for heavy nuclei: proxy-SU(3)

The SU(3) symmetry realized by J. P. Elliott in the sd nuclear shell is destroyed in heavier shells by the strong spin-orbit interaction. However, the SU(3) symmetry has been used for the description of heavy nuclei in terms of bosons in the framework of the Interacting Boson Approximation, as well as in terms of fermions using the pseudo-SU(3) approximation. We introduce a new fermionic approximation, called the proxy-SU(3), and we discuss how some of its novel predictions come out as a consequence of the short range of the nucleon-nucleon interaction and the Pauli principle.

Braided fermions from Hurwitz algebras

Some curious structural similarities between a recent braid - and Hurwitz algebraic description of the unbroken internal symmetries for a single generations of Standard Model fermions were recently identified. The non-trivial braid groups that can be represented using the four normed division algebras are B2 and , exactly those required to represent a single generation of fermions in terms of simple three strand ribbon braids. These braided fermion states can be identified with the basis states of the minimal left ideals of the Clifford algebra Cℓ(6), generated from the nested left actions of the complex octonions on itself. That is, the ribbon spectrum can be related to octonion algebras. Some speculative ideas relating to ongoing research that attempts to construct a unified theory based on braid groups and Hurwitz algebras are discussed.

Intrinsic and extrinsic geometries of correlated many-body states

We explore two approaches to characterise the quantum geometry of the ground state of correlated fermions in terms of the distance matrix in the spectral parameter space. (a) An intrinsic geometry approach, in which we study the intrinsic curvature defined in terms of the distance matrix. (b) An extrinsic geometry approach, in which we investigate how the distance matrix can be approximately embedded in finite dimensional Euclidean spaces. We implement these approaches for the ground state of a system of one-dimensional fermions on a 18-site lattice with nearest neighbour repulsion. The intrinsic curvature sharply changes around the Fermi points in the metallic regime but is more or less uniform in the insulating regime. In the metallic regime, the embedded points clump into two well seperated sets, one corresponding to modes in the Fermi sea and the other to the modes outside it. In the insulating regime, the two sets tend to merge.

The action of long strings in supersymmetric field theories

Long strings emerge in many Quantum Field Theories, for example as vortices in Abelian Higgs theories, or flux tubes in Yang-Mills theories. The actions of such objects can be expanded in the number of derivatives, around a long straight string solution. This corresponds to the expansion of energy levels in powers of 1/L, with L the length of the string. Doing so reveals that the first few terms in the expansions are universal, and only from a certain term do they become dependent on the originating field theory. Such classifications have been made before for bosonic strings. In this work we expand upon that and classify also strings with fermionic degrees of freedom, where the string breaks D = 4, N = 1 SUSY completely. An example is the confining string in N = 1 SYM theory. We find a general method for generating supersymmetric action terms from their bosonic counterparts, as well as new fermionic terms which do not exist in the non-supersymmetric case. These terms lead to energy corrections at a lower order in 1/L than in the bosonic case.

Phase structure and surface tension in quark meson model

In a mean-field approximation, we study the in-medium effective potential of the two-flavor quark meson model in the presence of a fermionic vacuum term at a finite temperature and density. There exists a crossover phase transition in the low-density region, and also there is a first-order phase transition in the high-density region accompanied by a critical end point. For the first-order phase transition, when the temperature is close to the critical temperature, the values of surface tension are calculated at various chemical potentials and we find that our results are very close to the results recently found in other chiral models with two flavors. Some consequences and possible applications of our results are also pointed out for the experiments on heavy ion collisions and the evolutions of the compact stars in their early stages.

Out-of-time-ordered correlators in short-range and long-range hard-core boson models and in the Luttinger-liquid model

We study out-of-time-ordered correlators (OTOC) in hard-core boson models with short-range and long-range hopping and compare the results to the OTOC in the Luttinger liquid model. For the density operator, a related `commutator function' starts at zero and decays back to zero after the passage of the wavefront in all three models, while the wavefront broadens as $t^{1/3}$ in the short-range model and shows no broadening in the long-range model and the Luttinger liquid model. For the boson creation operator, the corresponding commutator function shows saturation inside the light cone in all three models, with similar wavefront behavior as in the density-density commutator function, despite the presence of a nonlocal string in terms of Jordan-Wigner fermions. For the long-range model and the Luttinger liquid model, the commutator function decays as power law outside the light cone in the long time regime when following different fixed-velocity rays. In all cases, the OTOCs approach their long-time values in a power-law fashion, with different exponents for different observables and short-range vs long-range cases. Our long-range model appears to capture exponents in the Luttinger liquid model (which are found to be independent of the Luttinger parameter in the model). This conclusion also bears on the OTOC calculations in conformal field theories, which we propose correspond to long-ranged models.

Interplay between chiral magnetic and Kondo effects in Weyl metal phase

We investigate the Kondo effect in a Weyl metal state, which occurs from a spin-orbit coupled Dirac metal phase under magnetic fields. We start from an effective field theory in terms of low-energy fermions on a pair of chiral Fermi surfaces, which takes into account both the Berry curvature and chiral anomaly. Resorting to the U(1) slave-boson mean-field theory, we find that the effective Kondo temperature increases monotonically as a function of the external magnetic field due to enhancement of the density of states. The enhancement is originated from the chiral magnetic effect which is novel feature of Weyl metals. This leads to the prediction of the magnetic-field dependence in the logarithmic temperature dependence of the longitudinal magnetoconductivity.

Topology and strong four fermion interactions in four dimensions

We study massless fermions interacting through a particular four fermion term in four dimensions. Exact symmetries prevent the generation of bilinear fermion mass terms. We determine the structure of the low energy effective action for the auxiliary field needed to generate the four fermion term and find it has an novel structure that admits topologically non-trivial defects with non-zero Hopf invariant. We show that fermions propagating in such a background pick up a mass without breaking symmetries. Furthermore pairs of such defects experience a logarithmic interaction. We argue that a phase transition separates a phase where these defects proliferate from a broken phase where they are bound tightly. We conjecture that by tuning one additional operator the broken phase can be eliminated with a single BKT-like phase transition separating the massless from massive phases.