The classification of emergent spinor fields according to modified bilinear covariants is scrutinized, in spacetimes with nontrivial topology, which induce inequivalent spin structures. Extended Clifford algebras, constructed by equipping the underlying spacetime with an extended bilinear form with additional terms coming from the nontrivial topology, naturally yield emergent extended algebraic spinor fields and their subsequent extended bilinear covariants, which are contrasted to the classical spinor classification. An unexpected duality between the standard and the exotic spinor field classes is therefore established, showing that a complementary fusion process among the spinor field classes sets in, when extended Clifford bundles are addressed in multiply-connected spacetimes.
Exotic spinors arise in non-simply connected base manifolds due to the nonequivalent spinor structure. The dynamics of exotic spinors are endowed with an additional differential factor. In this work, we merge the exotic spinor scenario with Cartan's spinor viewpoint, according to which a given spacetime point is understood as a kind of composition of spinor entries. As a result, we arrive at a geometrical setup in which the Minkowski metric is perturbed by elements reflecting the nontrivial topology. Such corrections shall be felt by any physical system studied with the resulting bilinear form…
Exotic dark spinor fields are introduced and investigated in the context of inequivalent spin structures on arbitrary curved spacetimes, which induces an additional term on the associated Dirac operator, related to a Cech cohomology class. For the most kinds of spinor fields, any exotic term in the Dirac operator can be absorbed and encoded as a shift of the electromagnetic vector potential representing an element of the cohomology group H^1(M, Z_2). The possibility of concealing such an exotic term does not exist in case of dark (ELKO) spinor fields, as they cannot carry electromagnetic charg…
A topological interpretation of the electron--electron interaction under FQHE conditions gives rise to the existence of some kind of composite fermions. The interaction term is similar to the Coulomb interaction and produces punctures in the configuration space which change its topology. Now the relevant configuration space is not simply connected and as a consequence, ``new'' fermions, so called ``exotic spinors'', appear. We argue that composite fermions may be interpreted as exotic spinors. The denominator of the filling factor is calculated to be an odd number. We point out further possibl…
We investigate the effective Dirac equation, corrected by merging two scenarios that are expected to emerge towards the quantum gravity scale. Namely, the existence of a minimal length, implemented by the generalized uncertainty principle, and exotic spinors, associated with any non-trivial topology equipping the spacetime manifold. We show that the free fermionic dynamical equations, within the context of a minimal length, just allow for trivial solutions, a feature that is not shared by dynamical equations for exotic spinors. In fact, in this coalescing setup, the exoticity is shown to preve…
In this paper we construct a coordinate atlas in an exotic $\mathbb{R}^{4}$ using Bizaca's construction. The main source for such an atlas is the handle body decomposition of a Casson handle, which of course is an infinite, but periodic, process. The immersion of the end-periodic manifold into $\mathbb{R}^{4}$ is directly related to the exoticness of the $\mathbb{R}^{4}$ and also gives rise naturally to a spinor field. Thus we obtain the interesting result that the simplest exotic $\mathbb{R}^{4}$ generates an extra spinor field by exoticness.
Exotic Spinor Deformation of a Schwarzschild Black Hole: Perturbations and Stability
Faculty of Engineering and Science of Guaratinguetá, UNESP（圣保罗州立大学瓜拉廷格塔工程与科学学院）；São Paulo State Department of Education (SEDUC-SP)（圣保罗州教育部）；Engineering School of Lorena - University of Sao Paulo (EEL-USP)（圣保罗大学洛雷达纳工程学院）
Starting with a classical action whose matter variables are a d=10 spacetime vector $x^m$ and a pure spinor $λ^α$, the pure spinor formalism for the superstring is obtained by gauge-fixing the twistor-like constraint $\partial x^m (γ_m λ)_α=0$. The fermionic variables $θ^α$ are Faddeev-Popov ghosts coming from this gauge-fixing and replace the usual (b,c) ghosts coming from gauge-fixing the Virasoro constraint. After twisting the ghost-number such that $θ^α$ has ghost-number zero and $λ^α$ has ghost-number one, the BRST cohomology describes the usual spacetime supersymmetric states of the supe…
A nonsingular emergent universe cosmology can be realized by a nonconventional spinor field as first developed in \cite{Cai:2012yf}. We study the mechanisms of generating scale-invariant primordial power spectrum of curvature perturbation in the frame of spinor emergent universe cosmology. Particularly, we introduce a light scalar field of which the kinetic term couples to the bilinear of the spinor field. This kinetic coupling can give rise to an effective "Hubble radius" for primordial fluctuations from the scalar field to squeeze at large length scales as well as to form a nearly scale-inva…
An intrinsic mass generation mechanism for exotic ELKO dark matter fields is scrutinized, in the context of the very special relativity (VSR). Our results are reported on unraveling inequivalent spin structures that educe an additional term on the associated Dirac operator. Contrary to the spinor fields of mass dimension 3/2, this term is precluded to be absorbed as a shift of some gauge vector potential, regarding the equations for the dark spinor fields. It leads to some dynamical constraints that can be intrinsically converted into a dark spinor mass generation mechanism, with the encoded s…
In this paper we will discuss Brans conjecture that exotic smoothness serves as an additional gravitational source naturally arising from the handlebody construction of the exotic $\mathbb{R}^{4}$. We will consider the two possible classes, the large and the small exotic $\mathbb{R}^{4}$. Then we calculate the Einstein-Hilbert action for both exotic $\mathbb{R}^{4}$ to show the apearance of spinor fields. Then we discuss the physical properties of these spinor fields to relate them to fermions. Finally we identify the corresponding 3-manifolds as knot complements of hyperbolic knots, i.e. the …
We perform an exotic dualization of the Ramond-Ramond fields in type II double field theory, in which they are encoded in a Majorana-Weyl spinor of O(D,D). Starting from a first-order master action, the dual theory in terms of a tensor-spinor of O(D,D) is determined. This tensor-spinor is subject to an exotic version of the (self-)duality constraint needed for a democratic formulation. We show that in components, reducing O(D,D) to GL(D), one obtains the expected exotically dual theory in terms of mixed Young tableaux fields. To this end, we generalize exotic dualizations to self-dual fields, …
In Ref. \cite{Horava2005} Hořava suggested, that the multi - fermion many-body system with topologically stable Fermi surfaces may effectively be described (in a vicinity of the Fermi surface) by the theory with coarse-grained fermions. The number of the components of these coarse-grained fermions is reduced compared to the original system. Here we consider the $3+1$ D system and concentrate on the particular case when the Fermi surface has co-dimension $p=3$, i.e. it represents the Fermi point in momentum space. First we demonstrate explicitly that in agreement with Hořava conjecture, in the …
Exotic spinor fields arise from inequivalent spin structures on non-trivial topological manifolds, $M$. This induces an additional term in the Dirac operator, defined by the cohomology group $H^1(M,\mathbb{Z}_2)$ that rules a Cech cohomology class. This formalism is extended for manifolds of any finite dimension, endowed with a metric of arbitrary signature. The exotic corrections to heat kernel coefficients, relating spectral properties of exotic Dirac operators to the geometric invariants of $M$, are derived and scrutinized.
Gravity can be regarded as a consequence of local Lorentz (LL) symmetry, which is essential in defining a spinor field in curved spacetime. The gravitational action may admit a zero-field limit of the metric and vierbein at a certain ultraviolet cutoff scale such that the action becomes a linear realization of the LL symmetry. Consequently, only three types of term are allowed in the four-dimensional gravitational action at the cutoff scale: a cosmological constant, a linear term of the LL field strength, and spinor kinetic terms, whose coefficients are in general arbitrary functions of LL and…
We study a composition of normal and exotic matter which is required for a flat Emergent Universe scenario permitted by the equation of state (EOS)($p=Aρ-Bρ^{1/2}$) and predict the range of the permissible values for the parameters $A$ and $B$ to explore a physically viable cosmological model. The permitted values of the parameters are determined taking into account the $H(z)-z$ data obtained from observations, a model independent BAO peak parameter and CMB shift parameter (WMAP7 data). It is found that although $A$ can be very close to zero, most of the observations favours a small and negati…
We analyse the trapping of eigenspinors of the charge conjugation operator with dual helicity (Elko), in thin and thick string-like models with codimension-2. Elko spinor fields describe mass dimension one fermions in four dimensions (and, correspondingly, mass dimension two fermions in six dimensions), that represent natural dark matter prime candidates. This dark spinor has many applications, from particle physics to cosmology. On the other hand, six-dimensional brane-world models have, among other prominent features, the spontaneous confinement of free spin 1 fields and a mechanism that exp…
A classification of spinor fields according to the associated bilinear covariants is constructed in arbitrary dimensions and metric signatures, generalizing Lounesto's 4D spinor field classification. In such a generalized classification a basic role is played by the geometric Fierz identities. In 4D Minkowski spacetime the standard bilinear covariants can be either null or non-null -- with the exception of the current density which is invariably different from zero for physical reasons -- and sweep all types of spinor fields, including Dirac, Weyl, Majorana and more generally flagpoles, flag-d…
Emergent Einstein-Cartan gravity from a spinor loop
Center for Theoretical Physics and College of Physics, Jilin University（吉林大学理论物理中心及物理学院）；Department of Information and Mathematical Sciences, Tokyo Woman’s Christian University（东京女子基督教大学信息数学科学系）；Institute of Particle Physics and Key Laboratory of Quark and Lepton Physics (MOE), Central China Normal University（华中师范大学粒子物理研究所及夸克与轻子物理教育部重点实验室）；State Key Laboratory of Nuclear Physics and Technology, Institute of Quantum Matter, South China Normal University（华南师范大学量子物质研究院及核物理与技术国家重点实验室）；Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, Guangdong Provincial Key Laboratory of Nuclear Science（广东省物质结构与基本相互作用卓越基础研究中心及广东省核科学重点实验室）；Department of Physics and Astronomy, Kwansei Gakuin University（关西学院大学物理天文学系）
We provide a linearised superfield description of the exotic non-metric $N=(4,0)$ supergravity in $D=6$, by using a pure spinor superfield formalism. The basic field $Ψ$ is a ghost number 2 scalar, transforming in the same R-symmetry module as the tensor fields. Partial results for the $N=(3,1)$ model are presented.
We demonstrate the existence of entanglement between the spatial degrees of freedom of a system of harmonic oscillators placed in the noncommutative Moyal plane ("exotic oscillators") by computing the entanglement entropy as measured by the von Neumann entropy of the reduced density matrix. It is explicitly verified that the entanglement arises from the noncommutativity, which controls the coupling strength between the spatial modes. This can easily be generalised to the case where the momentum components also satisfy noncommutative relations, so that the entire phase space becomes noncommutat…
Relativistic spin-1/2 particles in curved spacetime are naturally described by Dirac theory, which is a dynamical and Lorentz-invariant field theory. In this work, we propose a non-dynamical fermion theory in 3+1 dimensions dubbed spinor topological field theory, built in terms of a spinor field and a Cartan connection related to de Sitter group. We show that our model gives rise to the Dirac theory in curved spacetime when the local de Sitter gauge invariance of the model breaks down to the Lorentz gauge invariance, providing also a geometric origin to the fermion mass. Finally, we show that …
The geometric Fierz identities are here employed to generate new emergent fermionic fields on the parallelizable (curvatureless, torsionfull) 7-sphere ($S^7$). Employing recently found new classes of spinor fields on the $S^7$ spin bundle, new classes of fermionic fields are obtained from their bilinear covariants by a generalized reconstruction theorem, on the parallelizable $S^7$. Using a generalized non-associative product on the octonionic bundle on the parallelizable $S^7$, these new classes of algebraic spinor fields, lifted onto the parallelizable $S^7$, are shown to correctly transform…
Two forms of anomalies for chiral spinors living on submanifolds of the spacetime are obtained from the integrality theorem for immersions. The first form of the chiral anomaly is the usual for chiral spinors living on D-brane and O-plane intersections, the second form is exotic.
The main purpose of this work is to show that massless Dirac equation formulated for non-interacting Majorana-Weyl spinors in higher dimensions, particularly in D=1+9 and D=5+5, can lead to an interpretation of massive Majorana and Dirac spinors in D=1+3. By adopting suitable representations of the Dirac matrices in higher dimensions, we pursue the investigation of which higher dimensional space-times and which mass-shell relation concerning massless Dirac equations in higher dimensions may induce massive spinors in D=1+3. The mixing of the chiral fermions in higher dimensions may induce a mec…
There are many examples where geometry and gravity are concepts that emerge from a theory of quantum mechanics without gravity. This suggests thinking of gravity as an exotic phase of matter. Quantifying this phase in the Landau paradigm requires some sort of symmetry principle or order parameter that captures its appearance. In this essay we propose higher-form symmetries as a symmetry principle underlying emergent spacetime. We explore higher-form symmetries in gauge-gravity duality and explain how their breaking describes features of a gravitational theory. Such symmetries imply the existen…
In this paper we discuss the question how matter may emerge from space. For that purpose we consider the smoothness structure of spacetime as underlying structure for a geometrical model of matter. For a large class of compact 4-manifolds, the elliptic surfaces, one is able to apply the knot surgery of Fintushel and Stern to change the smoothness structure. The influence of this surgery to the Einstein-Hilbert action is discussed. Using the Weierstrass representation, we are able to show that the knotted torus used in knot surgery is represented by a spinor fulfilling the Dirac equation and le…
Strongly interacting arrays of Rydberg atoms provide versatile platforms for exploring exotic many-body phases and dynamics of correlated quantum systems. Motivated by recent experimental advances, we show that the combination of Rydberg interactions and appropriate lattice geometries naturally leads to emergent $\mathbb{Z}_2$ gauge theories endowed with matter fields. Based on this mapping, we describe how Rydberg platforms could realize two distinct classes of topological $\mathbb{Z}_2$ quantum spin liquids, which differ in their patterns of translational symmetry fractionalization. We also …
We study a six matrix model with global $SO(3)\times SO(3)$ symmetry containing at most quartic powers of the matrices. This theory exhibits a phase transition from a geometrical phase at low temperature to a Yang-Mills matrix phase with no background geometrical structure at high temperature. This is an exotic phase transition in the same universality class as the three matrix model but with important differences. The geometrical phase is determined dynamically, as the system cools, and is given by a fuzzy four-sphere background ${\bf S}^2_N\times{\bf S}^2_N$, with an Abelian gauge field whic…
Quantum spin liquids (QSL) are exotic phases of matter that host fractionalized excitations. It is difficult for local probes to characterize QSL, whereas quantum entanglement can serve as a powerful diagnostic tool due to its non-locality. The kagome antiferromagnetic Heisenberg model is one of the most studied and experimentally relevant models for QSL, but its solution remains under debate. Here, we perform a numerical Aharonov-Bohm experiment on this model and uncover universal features of the entanglement entropy. By means of the density-matrix renormalization group, we reveal the entangl…
We present a systematic attempt at classification of supersymmetric M-theory vacua with zero flux; that is, eleven-dimensional lorentzian manifolds with vanishing Ricci curvature and admitting covariantly constant spinors. We show that there are two distinct classes of solutions: static spacetimes generalising the Kaluza-Klein monopole, and non-static spacetimes generalising the supersymmetric wave. The classification can be further refined by the holonomy group of the spacetime. The static solutions are organised according to the holonomy group of the spacelike hypersurface, whereas the non-s…
Condensed matter systems provide alternative `vacua' exhibiting emergent low-energy properties drastically different from those of the standard model. A case in point is the emergent quantum electrodynamics (QED) in the fractionalized topological magnet known as quantum spin ice, whose magnetic monopoles set it apart from the familiar QED of the world we live in. Here, we show that the two greatly differ in their fine-structure constant $α$, which parametrizes how strongly matter couples to light: $α_{\mathrm{QSI}}$ is more than an order of magnitude greater than $α_{\mathrm{QED}} \approx 1/13…
Many quantum lattice models have an emergent relativistic description in their continuum limit. The celebrated example is graphene, whose continuum limit is described by the Dirac equation on a Minkowski spacetime. Not only does the continuum limit provide us with a dictionary of geometric observables to describe the models with, but it also allows one to solve models that were otherwise analytically intractable. In this thesis, we investigate novel features of this relativistic description for a range of quantum lattice models. In particular, we demonstrate how to generate emergent curved spa…
