Instantons on Gravitons

Yang-Mills instantons on ALE gravitational instantons were constructed by Kronheimer and Nakajima in terms of matrices satisfying algebraic equations. These were conveniently organized into a quiver. We construct generic Yang-Mills instantons on ALF gravitational instantons. Our data are formulated in terms of matrix-valued functions of a single variable, that are in turn organized into a bow. We introduce the general notion of a bow, its representation, its associated data and moduli space of solutions. For a judiciously chosen bow the Nahm transform maps any bow solution to an instanton on an ALF space. We demonstrate that this map respects all complex structures on the moduli spaces, so it is likely to be an isometry, and use this fact to study the asymptotics of the moduli spaces of instantons on ALF spaces.     

Maximal symmetry and mass generation of Dirac fermions and gravitational gauge field theory in six-dimensional spacetime

The relativistic Dirac equation in four-dimensional spacetime reveals a coherent relation between the dimensions of spacetime and the degrees of freedom of fermionic spinors. A massless Dirac fermion generates new symmetries corresponding to chirality spin and charge spin as well as conformal scaling transformations. With the introduction of intrinsic W-parity, a massless Dirac fermion can be treated as a Majorana-type or Weyl-type spinor in a six-dimensional spacetime that reflects the intrinsic quantum numbers of chirality spin. A generalized Dirac equation is obtained in the six-dimensional spacetime with a maximal symmetry. Based on the framework of gravitational quantum field theory proposed in Ref. [1] with the postulate of gauge invariance and coordinate independence, we arrive at a maximally symmetric gravitational gauge field theory for the massless Dirac fermion in six-dimensional spacetime. Such a theory is governed by the local spin gauge symmetry SP(1,5) and the global Poincar′e symmetry P(1,5)= SO(1,5) P~(1,5) as well as the charge spin gauge symmetry SU(2). The theory leads to the prediction of doubly electrically charged bosons. A scalar field and conformal scaling gauge field are introduced to maintain both global and local conformal scaling symmetries. A generalized gravitational Dirac equation for the massless Dirac fermion is derived in the six-dimensional spacetime. The equations of motion for gauge fields are obtained with conserved currents in the presence of gravitational effects. The dynamics of the gauge-type gravifield as a Goldstone-like boson is shown to be governed by a conserved energy-momentum tensor, and its symmetric part provides a generalized Einstein equation of gravity. An alternative geometrical symmetry breaking mechanism for the mass generation of Dirac fermions is demonstrated.     

Gravitational energy-momentum density in teleparallel gravity

In the context of a gauge theory for the translation group, a conserved energy-momentum gauge current for the gravitational field is obtained. It is a true spacetime and gauge tensor, and transforms covariantly under global Lorentz transformations. By rewriting the gauge gravitational field equation in a purely spacetime form, it becomes the teleparallel equivalent of Einstein's equation, and the gauge current reduces to the Moller's canonical energy-momentum density of the gravitational field.     

Infrared regularization of superstring theory and the one-loop calculation of coupling constants

Infrared regularized versions of 4-D N = 1 superstring ground states are constructed by curving the spacetime. A similar regularization can be performed in field theory. For the IR regularized string ground states we derive the exact one-loop effective action for non-zero U(1) or chromomagnetic fields as well as gravitational and axionic-dilatonic fields. This effective action is IR and UV finite. Thus, the one-loop corrections to all couplings (gravitational, gauge and Yukawas) are unambiguously computed. These corrections are necessary for quantitative string superunification predictions at low energies. The one-loop corrections to the couplings are also found to satisfy Infrared Flow Equations.     

Reissner--Nordström-de--Sitter-type Solution by a Gauge Theory of Gravity

We use the theory based on a gravitational gauge group （Wu＇s model） to obtain a spherical symmetric solution of the field equations for the gravitational potential on a Minkowski spacetime. The gauge group, the gauge covariant derivative, the strength tensor of the gauge feld, the gauge invariant Lagrangean with the cosmological constant, the field equations of the gauge potentiaIs with a gravitational energy-momentum tensor as well as with a tensor of the field of a point like source are determined. Finally, a Reissner-Nordstrom-de Sitter-type metric on the gauge group space is obtained.     

Gauge Model Based on Group G×SU（2）

We present a model of gauge theory based on the symmetry group G×SU（2） where G is the gravitational gauge group and SU（2） is the internal group of symmetry. We employ the spacetime of four-dimensional Minkowski, endowed with spherical coordinates, and describe the gauge fields by gauge potentials. The corresponding strength field tensors are calculated and the field equations are written. A solution of these equations is obtained for the case that the gauge potentials have a particular form potentials induces a metric of Schwarzschild type on with spherical symmetry. The solution for the gravitational the gravitational gauge group space.     

Kaluza-Klein unification in the poincaré gauge theory of gravitation

We show that we can unify the gravitational and internal gauge interactions in a high dimensional Riemann-Cartan spacetime in the spirit of Kaluza-Klein, if we identify some of the connection coefficients as Yang-Mills potentials and if the dynamics of the spacetime is governed by the Poincaré gauge theory of gravitation whose lagrangian contains curvature and torsion squared.     

Unification of Electromagnetic Interactions and Gravitational Interactions

Unified theory of gravitational interactions and electromagnetic interactions is discussed in this paper.Based on gauge principle, electromagnetic interactions and gravitational interactions are formulated in the same mannerand are unified in a semi-direct product group of U(1) Abelian gauge group and gravitational gauge group.     

The dynamical structure of the Einstein-Cartan-Sciama-Kibble theory of gravity

It is shown that in the SO(3)-covariant Hamiltonian formulation the system of the ECSK equations can be reduced to 7 gravitational constraints, 18 gravitational dynamical equations, and a system of matter field equations. The geometric meaning of the canonical (symplectic) and gauge variables is also explained. Moreover, a general method of how to analyse degenerate matter field lagrangians in the framework of the ECSK theory is discussed. The exposition is given in the language of SO(3)-covariant differential operators on 3-dimensional slices of spacetime.     

On Yang–Mills Instantons over Multi-Centered Gravitational Instantons

 In this paper we explicitly calculate the analogue of the 't Hooft SU(2) Yang–Mills instantons on Gibbons–Hawking multi-centered gravitational instantons, which come in two parallel families: the multi-Eguchi–Hanson, or A _k ALE gravitational instantons and the multi-Taub–NUT spaces, or A _k ALF gravitational instantons. We calculate their energy and find the reducible ones. Following Kronheimer we also exploit the U(1) invariance of our solutions and study the corresponding explicit singular SU(2) magnetic monopole solutions of the Bogomolny equations on flat ℝ³. Received: 16 September 2002 / Accepted: 22 October 2002 Published online: 21 February 2003 Communicated by A. Connes     

THE PROBLEM OF THE COSMOLOGICAL CONSTANT

The cosmological term is necessaritly vanishing in a conformal gravitational theory, and the sum of the induced cosmological constants of all the brocken gauge symmetries cancels the curvature of the background spacetime. Thus the sum of all the cosmological constants is vanishing when the background spacetime is Minkowskian. Furthermore, the spontaneous breaking of a gauge symmetry through the Higgs mechanism is always accompanied by a phase transition of the background spacetime.     

Energy crisis or a new soliton in the noncommutative CP(1) model?

The non-commutative (NC) CP(1) model is studied from field theory perspective. Our formalism and definition of the NC CP(1) model differs crucially from the existing one [Phys. Lett. B 498 (2001) 277, hep-th/0203125, hep-th/0303090].

Due to the U(1) gauge invariance, the Seiberg–Witten map is used to convert the NC action to an action in terms of ordinary spacetime degrees of freedom and the subsequent theory is studied. The NC effects appear as (NC parameter) θ-dependent interaction terms. The expressions for static energy, obtained from both the symmetric and canonical forms of the energy momentum tensor, are identical, when only spatial noncommutativity is present. Bogomolny analysis reveals a lower bound in the energy in an unambiguous way, suggesting the presence of a new soliton. However, the BPS equations saturating the bound are not compatible to the full variational equation of motion. This indicates that the definitions of the energy momentum tensor for this particular NC theory (the NC theory is otherwise consistent and well defined), are inadequate, thus leading to the “energy crisis”.

A collective coordinate analysis corroborates the above observations. It also shows that the above mentioned mismatch between the BPS equations and the variational equation of motion is small.     

Unified Theory of Fundamental Interactions

Based on local gauge invariance, four different kinds of fundamental interactions in nature are unified in a theory which has SU(3)C( )SU SU(2)L( )U(1)( )s Gravitational Gauge Group gauge symmetry. In this approach,gravitational field, like electromagnetic field, intermediate gauge field, and gluon field, is represented by gauge potential.Four kinds of fundamental interactions are formulated in the similar manner, and therefore can be unified in a direct or semi-direct product group. The model discussed in this paper is a renormalizable quantum model and can be regarded as an extension of the standard model to gravitational interactions, so it can be used to study quantum effects of gravitational interactions.     

Kaluza-Klein electric monopole in a six-dimensional poincaré gauge theory of gravitation

We found a solution to the six-dimensional Poincaré gauge theory that can be interpreted as the gravitational field and the electric field of an electric monopole in four-dimensional spacetime. The extra dimensions are curled up into a compact space of a size characterized by the Planck length.     

Hamiltonian Map to Conformal Modification of Spacetime Metric: Kaluza-Klein and TeVeS

It has been shown that the orbits of motion for a wide class of non-relativistic Hamiltonian systems can be described as geodesic flows on a manifold and an associated dual by means of a conformal map. This method can be applied to a four dimensional manifold of orbits in spacetime associated with a relativistic system. We show that a relativistic Hamiltonian which generates Einstein geodesics, with the addition of a world scalar field, can be put into correspondence in this way with another Hamiltonian with conformally modified metric. Such a construction could account for part of the requirements of Bekenstein for achieving the MOND theory of Milgrom in the post-Newtonian limit. The constraints on the MOND theory imposed by the galactic rotation curves, through this correspondence, would then imply constraints on the structure of the world scalar field. We then use the fact that a Hamiltonian with vector gauge fields results, through such a conformal map, in a Kaluza-Klein type theory, and indicate how the TeVeS structure of Bekenstein and Saunders can be put into this framework. We exhibit a class of infinitesimal gauge transformations on the gauge fields U_m(x){\mathcal{U}}_{\mu}(x) which preserve the Bekenstein-Sanders condition U_mU^m=-1{\mathcal{U}}_{\mu}{\mathcal{U}}^{\mu}=-1. The underlying quantum structure giving rise to these gauge fields is a Hilbert bundle, and the gauge transformations induce a non-commutative behavior to the fields, i.e. they become of Yang-Mills type. Working in the infinitesimal gauge neighborhood of the initial Abelian theory we show that in the Abelian limit the Yang-Mills field equations provide residual nonlinear terms which may avoid the caustic singularity found by Contaldi et al.     

Gravity and Spin Forces in Gravitational Quantum Field Theory

In the new framework of gravitational quantum field theory(GQFT) with spin and scaling gauge invariance developed in Phys. Rev. D 93(2016) 024012-1, we make a perturbative expansion for the full action in a background field which accounts for the early inflationary universe. We decompose the bicovariant vector fields of gravifield and spin gauge field with Lorentz and spin symmetries SO(1,3) and SP(1,3) in biframe spacetime into SO(3) representations for deriving the propagators of the basic quantum fields and extract their interaction terms. The leading order Feynman rules are presented. A tree-level 2 to 2 scattering amplitude of the Dirac fermions, through a gravifield and a spin gauge field, is calculated and compared to the Born approximation of the potential. It is shown that the Newton's gravitational law in the early universe is modified due to the background field. The spin dependence of the gravitational potential is demonstrated.     

Gravity and Spin Forces in Gravitational Quantum Field Theory

In the new framework of gravitational quantum field theory (GQFT) with spin and scaling gauge invariance developed in Phys. Rev. D 93 (2016) 024012-1, we make a perturbative expansion for the full action in a background field which accounts for the early inflationary universe. We decompose the bicovariant vector fields of gravifield and spin gauge field with Lorentz and spin symmetries SO(1,3) and SP(1,3) in biframe spacetime into SO(3) representations for deriving the propagators of the basic quantum fields and extract their interaction terms. The leading order Feynman rules are presented. A tree-level 2 to 2 scattering amplitude of the Dirac fermions, through a gravifield and a spin gauge field, is calculated and compared to the Born approximation of the potential. It is shown that the Newton's gravitational law in the early universe is modified due to the background field. The spin dependence of the gravitational potential is demonstrated.     

Accelerating Universe with spacetime torsion but without dark matter and dark energy

It is shown that cosmological equations for homogeneous isotropic models deduced in the framework of the Poincaré gauge theory of gravity by certain restrictions on indefinite parameters of gravitational Lagrangian take at asymptotics the same form as cosmological equations of general relativity theory for ΛCDM-model. Terms related to dark matter and dark energy in cosmological equations of standard theory for ΛCDM-model are connected in considered theory with the change of gravitational interaction provoked by spacetime torsion.     

Supersymmetric Yang-Mills,octonionic instantons and triholomorphic curves

In four-dimensional gauge theory there exists a well-known correspondence between instantons and holomorphic curves, and a similar correspondence exists between certain octonionic instantons and triholomorphic curves. We prove that this latter correspondence stems from the dynamics of various dimensional reductions of ten-dimensional supersymmetric Yang-Mills theory. More precisely we show that the dimensional reduction of the (5+1)-dimensional supersymmetric sigma model with hyper-Kähler (but otherwise arbitrary) target X to a four-dimensional hyper-Kähler manifold M is a topological sigma model localising on the space of triholomorphic maps M -+ X (or hyperinstantons). When X is the moduli space M_k of instantons on a four-dimensional hyper-Kdhler manifold K, this theory has an interpretation in terms of supersymmetric gauge theory. In this case, the topological sigma model can be understood as an adiabatic limit of the dimensional reduction of ten-dimensional supersymmetric Yang-Mills on the eight-dimensional manifold M × K of holonomy Sp(1) × Sp(1) ⊂ Spin(7), which is a cohomological theory localising on the moduli space of octonionic instantons.