In a six dimensional brane world model with multiple $S_1/Z_2$ warping, two of the 4-branes at the boundaries have coordinate dependent brane tensions in order to implement the orbifolded boundary conditions consistently. Such brane tension is shown to be equivalent to a scalar field distribution on the brane [1]. We show that in such a scenario a masslesss left chiral fermion on the 4-brane localizes naturally on the standard model 3-brane located at one edge of the compact manifold while the massless right chiral fermion wave function as well as the wave functions for the massive fermion modes peak away from this brane. This offers a mechanism of obtaining massless chiral fermion with only one of its chiral component present in our brane.
The Randall-Sundrum warped braneworld model is generalised to six and higher dimensions such that the warping has a non-trivial dependence on more than one dimension. This naturally leads to a brane-box like configuration alongwith scalar fields with possibly interesting cosmological roles. Also obtained naturally are two towers of 3 branes with mass scales clustered around either of Planck scale and TeV scale. Such a scenario has interesting phenomenological consequences including an explanation for the observed hierarchy in the masses of standard model fermions.
The absence, so far, of any graviton signatures at the LHC imposes severe constraints on the Randall-Sundrum scenario. Although a generalization to higher dimensions with nested warpings has been shown to avoid these constraints, apart from incorporating several other phenomenologically interesting features, moduli stabilization in such models has been an open question. We demonstrate here how both the moduli involved can be stabilized, employing slightly different mechanisms for the two branches of the theory. This also offers a dynamical mechanism to generate and stabilize the scale for the …
We analyze the wavefunctions for open strings stretching between intersecting 7-branes in type IIB/F-theory warped compactifications, as a first step in understanding the warped effective field theory of 4d chiral fermions. While in general the equations of motion do not seem to admit a simple analytic solution, we provide a method for solving the wavefunctions in the case of weak warping. The method describes warped zero modes as a perturbative expansion in the unwarped spectrum, the coefficients of the expansion depending on the warping. We perform our analysis with and without the presence …
We study the properties of chiral anomalies in a wide class of spacetimes which possess a principal Killing-Yano tensor. This class includes metrics of charged rotating black holes as a special physically important case. The spacetimes which admit a principal Killing-Yano tensor possess a number of remarkable properties. In particular, such spacetimes have two commuting Killing vectors and a Killing tensor responsible for their hidden symmetries. We calculate the gravitational and electromagnetic contributions to the axial anomaly currents in the spacetime of a charged rotating black hole, and…
Underlying a general noncommutative algebra with both noncommutative coordinates and noncommutative momenta in a (1+1)-dimensional spacetime, a chiral boson Lagrangian with manifest Lorentz covariance is proposed by linearly imposing a generalized self-duality condition on a noncommutative generalization of massless real scalar fields. A significant property uncovered for noncommutative chiral bosons is that the left- and right-moving chiral scalars cannot be distinguished from each other, which originates from the noncommutativity of coordinates and momenta. An interesting result is that Dira…
Using the renormalization group (RG) approach and the equivalency between the class of gauge-Higgs-Yukawa models and the gauged Nambu-Jona-Lasinio (NJL) model, we study the gauged NJL model in curved space-time. The behaviour of the scalar-gravitational coupling constant $ξ(t)$ in both theories is discussed. The RG improved effective potential of gauged NJL model in curved spacetime is found. The curvature at which chiral symmetry in the gauged NJL model is broken is obtained explicitly in a remarkably simple form. The powerful RG improved effective potential formalizm leads to the same result…
We show how wormholes in three spacetime dimensions can be customizably warped using pressureless matter. In particular, we exhibit a large new class of solutions in (2+1)-dimensional general relativity with energy-momentum tensor describing a negative cosmological constant and positive-energy dust. From this class of solutions, we construct wormhole geometries and study their geometric and holographic properties, including Ryu-Takayanagi surfaces, entanglement wedge cross sections, mutual information, and outer entropy. Finally, we construct a Python's Lunch geometry: a wormhole in asymptotic…
The phase structure of the $d=3$ Nambu-Jona-Lasinio model in curved spacetime is considered to leading order in the $1/N$--expansion and in the linear curvature approximation. The possibility of a curvature-induced first-order phase transition is investigated numerically. The dynamically generated fermionic mass is calculated for some values of the curvature.
We renormalize models with scalar chiral superfields with an odd superpotential to several orders in perturbation theory. These extensions of the cubic Wess-Zumino model are renormalizable in spacetime dimensions which are rational. When endowed with an $O(N)$ symmetry it is shown that they share the same property as their non-supersymmetric counterparts in that at a particular fixed point there is an emergent $OSp(1|n-1)$ symmetry, where $n$ is the power of the superpotential. This is shown at a loop order beyond that for which it was established in the parallel non-supersymmetric theory.
Chiral symmetry breaking in the Nambu-Jona-Lasinio model in a constant magnetic field is studied in spacetimes of dimension D > 4. It is shown that a constant magnetic field can be characterized by [(D-1)/2] parameters. For the maximal number of nonzero field parameters, we show that there is an effective reduction of the spacetime dimension for fermions in the infrared region D $\to$ 1 + 1 for even-dimensional spacetimes and D $\to$ 0 + 1 for odd-dimensional spacetimes. Explicit solutions of the gap equation confirm our conclusions.
We consider a holographic model of strongly interacting plasma with a gravitational anomaly. In this model, we compute parity-odd responses of the system at finite temperature and chemical potential to external electromagnetic and gravitational fields. Working within the linearized fluid/gravity duality, we performed the calculation up to the third order in gradient expansion. Besides reproducing the chiral magnetic(CME) and vortical (CVE) effects we also obtain gradient corrections to the CME and CVE due to the gravitational anomaly. Additionally, we find energy-momentum and current responses…
In this paper we have analyzed the $κ$-deformed Minkowski spacetime through the light of the interference phenomena in QFT where two opposite chiral fields are put together in the same multiplet and its consequences are discussed. The chiral models analyzed here are the chiral Schwinger model, its generalized version and its gauge invariant version, where a Wess-Zumino term were added. We will see that the final actions obtained here are in fact related to the original ones via duality transformations.
We discuss the phase structure (in the $1/N$-expansion) of the Nambu-Jona-Lasinio model in curved spacetime with non-trivial topology ${\cal M}^3 \times {\rm S}^1$. The evaluation of the effective potential of the composite field $\barψ ψ$ is presented in the linear curvature approximation (topology is treated exactly) and in the leading order of the $1/N$-expansion. The combined influence of topology and curvature to the phase transitions is investigated. It is shown, in particular, that at zero curvature and for small radius of the torus there is a second order phase transition from the chir…
A Siegel-type chiral p-form action is proposed in D=2(p+1) spacetime dimensions. The approach we adopt is to realize the symmetric second-rank Lagrange-multiplier field, introduced in Siegel's action, in terms of a normalized multiplication of two (q+1)-form fields with q indices of each field contracted in the even p case, or of two pairs of (q+1)-form fields with q indices of each pair of fields contracted in the odd p case, where the (q+1)-form fields are of external derivatives of one auxiliary q-form field for the former, or a pair of auxiliary q-form fields for the latter. Using this act…
We investigate the recently proposed Kerr/CFT correspondence in the context of rotating spacetimes with a NUT twist. The Kerr/CFT correspondence states that the near-horizon states of an extremal four (or higher) dimensional black hole could be identified with a certain chiral conformal field theory. The corresponding Virasoro algebra is generated with a class of diffeomorphism which preserves an appropriate boundary condition on the near-horizon geometry. We try to understand the analog of singularities in the context of dual chiral CFT. Explicitly, we use Kerr/CFT correspondence to show that…
A toy model for the electroweak interactions(without chirality) is proposed in a six dimensional spacetime with 3 timelike and 3 spacelike coordinates. The spacetime interval $ds^2=dx_μdx^μ$ is left invariant under the symmetry group SO(3,3). We obtain the six-dimensional version of the Dirac gamma matrices, $Γ_μ$, and write down a Dirac-like lagrangian density, ${\cal L}=i \barψ Γ^μ\nabla_μψ$. The spinor $ψ$ is decomposed into two Dirac spinors, $ψ_1$ and $ψ_2$, which we interpret as the electron and neutrino fields, respectively. In six-dimensional spacetime the electron and neutrino fields …
We consider chiral fermion confinement in scalar thick branes, which are known to localize gravity, coupled through a Yukawa term. The conditions for the confinement and their behavior in the thin-wall limit are found for various different BPS branes, including double walls and branes interpolating between different AdS_5 spacetimes. We show that only one massless chiral mode is localized in all these walls, whenever the wall thickness is keep finite. We also show that, independently of wall's thickness, chiral fermionic modes cannot be localized in dS_4 walls embedded in a M_5 spacetime. Fina…
We study the hydrodynamics of a gas of noninteracting Weyl fermions coupled to the electromagnetic field in $(2N + 1) + 1$ spacetime dimensions using the chiral kinetic theory, which encodes the gauge anomaly in the Chern character of the nonabelian Berry connection over the Fermi surface. We derive the anomalous contributions to the relativistic hydrodynamic currents in equilibrium and at a finite temperature, which agree with and provides an approach complementary to the results derived previously using thermodynamic constraints.
The Dirac equation with chiral symmetry is derived using the irreducible representations of the Poincaré group, the Lagrangian formalism, and a novel method of projection operators that takes as its starting point the minimal assumption of four linearly independent physical states. We thereby demonstrate the fundamental nature of this form of the Dirac equation. The resulting equation is then examined within the context of spacetime and CPT symmetries with a discussion of the implications for the general formulation of physical theories.
We develop the necessary ingredients for the construction of realistic models with warped universal extra dimensions. Our investigations are based on the seven dimensional (7D) spacetime AdS_5 x T^2 and we derive the Kaluza-Klein (KK) spectra for gravitons, bulk vectors and the TeV brane localized Higgs boson. We show that, starting with a massive 7D fermion, one may obtain a single chiral massless mode whose profile is readily localized towards the Planck or TeV brane. This allows one to place the standard model fermions in the bulk and construct models of flavor as in Randall-Sundrum models.…
Renormalization of chiral perturbation theory with spinless matter field in curved spacetime
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
Assuming $\mathbf{O}(D,D)$ covariant fields as the `fundamental' variables, Double Field Theory can accommodate novel geometries where a Riemannian metric cannot be defined, even locally. Here we present a complete classification of such non-Riemannian spacetimes in terms of two non-negative integers, $(n,\bar{n})$, $0\leq n+\bar{n}\leq D$. Upon these backgrounds, strings become chiral and anti-chiral over $n$ and $\bar{n}$ directions respectively, while particles and strings are frozen over the $n+\bar{n}$ directions. In particular, we identify $(0,0)$ as Riemannian manifolds, $(1,0)$ as non-…
We study the applicability of the covariant holographic entanglement entropy proposal to asymptotically warped AdS$_3$ spacetimes with an SL(2,R) x U(1) isometry. We begin by applying the proposal to locally AdS$_3$ backgrounds which are written as a real-line fibration over AdS$_2$. We then perturb away from this geometry by considering a warping parameter $a=1+δ$ to get an asymptotically warped AdS$_3$ spacetime and compute the dual entanglement entropy perturbatively in $δ$. We find that for large separation in the fiber coordinate, the entanglement entropy can be computed to all orders in …
We have considered gravity in a five-dimensional warped product space-time, with a time-dependent warp factor and a time-dependent extra dimension. The five-dimensional field equations are derived for a spatially flat FRW brane and the energy conditions and the nature of bulk geometry have been examined. It is found that the expansion of the four-dimensional universe depends on its location along the extra dimension and will be different at different locations in the bulk spacetime. At low energies, the trapping of fields within the brane implies a specific correlation between the warp factor …
Scalar kinks propagating along the bulk in warped spacetimes provide a thick brane realisation of the braneworld. We consider here, a class of such exact solutions of the full Einstein-scalar system with a sine-Gordon potential and a negative cosmological constant. In the background of the kink and the corresponding warped geometry, we discuss the issue of localisation of spin half fermions (with emphasis on massive ones) on the brane in the presence of different types of kink-fermion Yukawa couplings. We analyse the possibility of quasi-bound states for large values of the Yukawa coupling par…
We consider a class of non-unitary Toda theories based on the Lie superalgebras $A^{(1)}(n,n)$ in two-dimensional Minkowski spacetime, which can be twisted into a topological sector. In particular we study the simplest example with $n=1$ and real fields, and show how this theory can be treated as an integrable perturbation of the $A(1,0)$ superconformal model. We construct the conserved currents and the vertex operators which are chiral primary fields in the conformal theory. We then define the chiral ring of the $A^{(1)}(1,1)$ Toda theory and compute topological correlation functions in the t…
We discuss the phase structure of the NJL model in curved spacetime with magnetic field using $1/N$-expansion and linear curvature approximation. The effective potential for composite fields $\barψψ$ is calculated using the proper-time cut-off in the following cases: a) at non-zero curvature, b) at non-zero curvature and non-zero magnetic field, and c) at non-zero curvature and non-zero covariantly constant gauge field. Chiral symmetry breaking is studied numerically. We show that the gravitational field may compensate the effect of the magnetic field what leads to restoration of chiral symmet…
In the framework of N=2 conformal supergravity in four dimensions, we introduce a nilpotent chiral superfield suitable for the description of partial supersymmetry breaking in maximally supersymmetric spacetimes. As an application, we construct Maxwell-Goldstone multiplet actions for partial N=2 --> N=1 supersymmetry breaking on R x S^3, AdS_3 x S^1 (or its covering AdS_3 x R), and a pp-wave spacetime. In each of these cases, the action coincides with a unique curved-superspace extension of the N=1 supersymmetric Born-Infeld action, which is singled out by the requirement of U(1) duality invar…
Several interacting models of chiral bosons and gauge fields are investigated on the noncommutative extended Minkowski spacetime which was recently proposed from a new point of view of disposing noncommutativity. The models include the bosonized chiral Schwinger model, the generalized chiral Schwinger model (GCSM) and its gauge invariant formulation. We establish the Lagrangian theories of the models, and then derive the Hamilton's equations in accordance with the Dirac's method and solve the equations of motion, and further analyze the self-duality of the Lagrangian theories in terms of the p…
The theory of free Majorana-Weyl spinors is the prototype of conformal field theory in two dimensions in which the gravitational anomaly and the Weyl anomaly obstruct extending the flat spacetime results to curved backgrounds. In this paper, we investigate a quantization scheme in which the short distance singularity in the two-point function of chiral fermions on a two dimensional curved spacetime is given by the Green's function corresponding to the classical field equation. We compute the singular term in the Green's function explicitly and observe that the short distance limit is not well-…
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.
Bosonization of the Schwinger model with noncommutative chiral bosons is considered on a spacetime of cylinder topology. Using point splitting regularization, manifest gauge invariance is maintained throughout. Physical consequences are discussed.
Many-body systems with chiral fermions exhibit anomalous transport phenomena originated from quantum anomalies. Based on quantum field theory, we derive the kinetic theory for chiral fermions interacting with an external electromagnetic field and a background curved geometry. The resultant framework respects the covariance under the U(1) gauge, local Lorentz, and diffeomorphic transformations. It is particularly useful to study the gravitational or non-inertial effects for chiral systems. As the first application, we study the chiral dynamics in a rotating coordinate and clarify the roles of t…
We consider intersecting D-brane models which have two dimensional chiral fermions localized at the intersections. At weak coupling, the interactions of these fermions are described by generalized Gross-Neveu models. At strong coupling, these configurations are described by the dynamics of probe D-branes in a curved background spacetime. We study patterns of dynamical chiral symmetry breaking in these models at weak and strong coupling, and also discuss relationships between these two descriptions.
We propose a classical action for the motion of massless Weyl fermions in a background gauge field in (2N+1)+1 spacetime dimensions. We use this action to derive the collisionless Boltzmann equation for a gas of such particles, and show how classical versions of the gauge and Abelian chiral anomalies arise from the Chern character of the non-Abelian Berry connection that parallel transports the spin degree of freedom in momentum space.
We find exact D-brane configurations in the Nappi-Witten background using the boundary state approach and describe how they are related by T-duality transformations. We also show that the classical boundary conditions of the associated sigma model correspond to a field dependent automorphism relating the chiral currents and discuss the correspondence between the boundary state approach and the sigma model approach.
We study the spacetime-reduced (Eguchi-Kawai) version of large-N QCD with nonzero chemical potential. We explore a method to suppress the sign fluctuations of the Dirac determinant in the hadronic phase; the method employs a re-summation of gauge configurations that are related to each other by center transformations. We numerically test this method in two dimensions, and find that it successfully solves the silver-blaze problem. We analyze the system further, and measure its free energy F, the average phase theta of its Dirac determinant, and its chiral condensate <psi-bar-psi>. We show that …
Semiclassical chiral kinetic theories in the presence of electromagnetic fields as well as vorticity can be constructed by means of some different relativistic or nonrelativistic approaches. To cover the noninertial features of rotating frames one can start from the modified quantum kinetic equation of Wigner function in Minkowski spacetime. It provides a relativistic chiral transport equation whose nonrelativistic limit yields a consistent three-dimensional kinetic theory which does not depend explicitly on spatial coordinates. Recently a chiral transport equation in curved spacetime has been…
Starting from the recent action proposed by Sen [1,2], we evaluate the partition function of the compact chiral boson on a two-dimensional torus using a path-integral formulation. Crucially, we use a Wick-rotation procedure obtained from a complex deformation of the physical spacetime metric. This directly reproduces the expected result including general characteristics for the theta functions. We also present results for the chiral 2-form potential in six dimensions which can be readily extended to 4k+2 dimensions.
We investigate the trace anomaly of a chiral fermion in dimensional regularization, considering in detail the simplest case of coupling to an abelian gauge field. We apply the Breitenlohner-Maison/'t Hooft-Veltman prescription for dealing with the chiral matrix $γ^5$ and verify that no parity-odd term arises in the trace anomaly. The issue treated here is analogous to that of a chiral fermion in curved spacetime, discussed in recent literature. The advantage of having a simplified background minimizes the amount of algebraic calculations and allows pinpointing better the subtle points carried …
Momentum transport is anomalous in chiral $p+ip$ superfluids and superconductors in the presence of textures and superflow. Using the gradient expansion of the semi-classical approximation, we show how gauge and Galilean symmetries induce an emergent curved spacetime with torsion and curvature for the quasirelativistic low-energy Majorana-Weyl quasiparticles. We explicitly show the emergence of the spin-connection and curvature, in addition to torsion, using the superfluid hydrodynamics. The background constitutes an emergent quasirelativistic Riemann-Cartan spacetime for the Weyl quasiparticl…
Four-fermion interaction models are often used as simplified models of interacting fermion fields with the chiral symmetry. The chiral symmetry is dynamically broken for a larger four-fermion coupling. It is expected that the broken symmetry is restored under extreme conditions. In this paper, the finite size effect on the chiral symmetry breaking is investigated in the four-fermion interaction model. We consider the model on a flat spacetime with a compactified spatial coordinate, $\mathcal{M}^{D-1} \otimes S^1$ and obtain explicit expressions of the effective potential for arbitrary spacetim…
We calculate some extremal and non-extremal four-point functions on the sphere of certain chiral primary operators for strings on AdS_3 x S^3 x T^4. The computation is done for small values of the spacetime cross-ratio where global SL(2) and SU(2) descendants may be neglected in the intermediate channel. Ignoring also current algebra descendants, we find that in the non-extremal case the integrated worldsheet correlators factorize into spacetime three-point functions, which is non-trivial due to the integration over the moduli space. We then restrict to the extremal case and compare our result…
A geometric understanding of the origin of mass hierarchy among the standard model fermions have been addressed in a multiple warped spacetime. We show that the requirement of $10^{16}$ order warping between the Planck and the visible branes without creating any significant hierarchy among the moduli results into splitting of fermion masses in the standard model. Values of the various parameters of the extra dimensional model and the corresponding fermion masses are determined.
Defining a Chiral Fermion Theory on a lattice has presented an ongoing challenge both in Condensed Matter physics and in Lattice Gauge Theory. In this paper, we demonstrate that a chiral free-fermion theory can live on an ultra-local spacetime lattice if we allow the Lagrangian to be non-hermitian. Rather than a violation of unitarity, the non-hermitian structure of our Lagrangian arises because time is discrete, and we show that our model is obeys an elementary unitarity condition: namely, that the norm of the two-point functions conserves probability. Beyond unitarity, our model displays sev…
Perturbations of the Dirac field in the Schwarzschild spacetime are characterized by two wave equations (for two chiralities) with effective potentials which are iso-spectral and one of which is positive definite. Therefore, the stability of a Dirac field in the Schwarzschild background is straightforward. This is not so for the Schwarzschild-de Sitter case, because potentials for both chiralities have negative gaps and the fact that the stability is not automatically guaranteed in the asymptotically de Sitter case was apparently omitted in the literature. Performing the time-domain integratio…
We find the excitations and construct the conserved charges ( mass and angular momentum) of the recently found Minimal Massive Gravity (MMG) in 2+1 dimensions in asymptotically Anti-de Sitter (AdS) spacetimes. The field equation of the theory does not come from an action and hence lacks the required Bianchi Identity needed to define conserved charges. But the theory, which also provides a healthy extension of the Topologically Massive Gravity in the bulk and boundary of spacetime, does admit conserved charges for metric that are solutions. Our construction is based on background Killing vector…
In a spacetime with nonvanishing torsion there can occur topologically stable configurations associated with the frame bundle which are independent of the curvature. The relevant topological invariants are integrals of local scalar densities first discussed by Nieh and Yan (N-Y). In four dimensions, the N-Y form $N= (T^a \wedge T_a - R_{ab} \wedge e^a \wedge e^b)$ is the only closed 4-form invariant under local Lorentz rotations associated with the torsion of the manifold. The integral of $N$ over a compact D-dimensional (Euclidean) manifold is shown to be a topological invariant related to th…
Emergence of Dark Energy from topology and chiral spinors
Universidad de La Frontera（弗雷罗纳大学）；Universidad de La Serena（拉塞雷纳大学）；Lanzhou University（兰州大学）；Instituto de Astrofísica e Ciências do Espaço, Universidade de Lisboa（里斯本大学空间天体物理研究所）；Université de Paris-Cité（巴黎西岱大学）
An algebraic quantum field theory (AQFT) may be expressed as a functor from a category of spacetimes to a category of algebras of observables. However, a generic category $\mathsf{C}$ whose objects admit interpretation as spacetimes is not necessarily viable as the domain of an AQFT functor; often, additional constraints on the morphisms of $\mathsf{C}$ must be imposed. We introduce disjointness relations, a generalisation of the orthogonality relations of Benini, Schenkel and Woike (arXiv:1709.08657). In any category $\mathsf{C}$ equipped with a disjointness relation, we identify a subcategor…
In 3+1 dimensional spacetime, two vector gauge anomalies are known: The chiral anomaly and the mixed axial-gravitational anomaly. While the former is well documented and tied to the presence of a magnetic field, the latter instead requires a nonzero spacetime curvature, which has made it rather difficult to study. In this work, we show that a quantum anomaly arises in the second-order electrical response for zero magnetic field, which creates a dc-current that can be either longitudinal or transverse to electric field. Consequently, the continuity equation for the chiral current is not conserv…
We introduce a new class of duality symmetries amongst quantum field theories. The new class is based upon global spacetime symmetries, such as Poincare invariance and supersymmetry, in the same way as the existing duality transformations are based on global internal symmetries. We illustrate these new duality transformations by dualizing several scalar and spin-half theories in 1+1 spacetime dimensions, involving nonsupersymmetric as well as (1,1) and (2,2) supersymmetric models. For (2,2) models the new duality transformations can interchange chiral and twisted-chiral multiplets.
Recently, the asymptotic behaviour of three-dimensional anti-de Sitter gravity with a topological mass term was investigated. Boundary conditions were given that were asymptotically invariant under the two-dimensional conformal group and that included a fall-off of the metric sufficiently slow to consistently allow pp-wave type of solutions. Now, pp-waves can have two different chiralities. Above the chiral point and at the chiral point, however, only one chirality can be considered, namely the chirality that has the milder behaviour at infinity. The other chirality blows up faster than AdS an…
