The Stable Compactification of Ten-Dimensional Supergravity Model

The effective potentials of 10-D supergravity model with one-loop Casimir corrections are derived in this paper.We show that compactification are unstable for Kalb-Ramond model,but in the case of ten-dimensional supergravity model it is possible to achieve a stable compactification by including the contribution of fermionic condensation.The relation of this kind of model with inflation cosmology is discussed.     

Constraint Algebra for Regge-Teitelboim Formulation of Gravity

We consider the formulation of the gravity theory first suggested by Regge and Teitelboim where the space-time is a four-dimensional surface in a flat ten-dimensional space. We investigate a canonical formalism for this theory following the approach suggested by Regge and Teitelboim. Under constructing the canonical formalism we impose additional constraints agreed with the equations of motion. We obtain the exact form of the first-class constraint algebra. We show that this algebra contains four constraints which form a subalgebra (the ideal), and if these constraints are fulfilled, the algebra becomes the constraint algebra of the Arnowitt-Deser-Misner formalism of Einstein’s gravity. The reasons for the existence of additional first-class constraints in the canonical formalism are discussed.     

String-induced space compactification

Motivated by the possibility of a finite theory of gravity provided by superstrings in ten space-time dimensions, we analyze the problem of space compactification in the context of string dynamics. Such an analysis is hampered by conceptual and technical problems, stemming from the existence of the quantum string's own graviton mode on the one hand, and from Witten's observation of anomalies in a not specially chosen curves space-time on the other hand. Still, in the context of a classical local field presentation of string theory à la Nambu and Hosotani, supplemented by gravitational and Kalb-Ramond interactions, we are able to find solutions with space compactification. It is the antisymmetric tensor zero modes that dictate this compactification towards three space-time dimensions for ordinary strings or towards four or five space-time dimensions for superstrings.     

Axionic black holes and wormholes

Theories in which gravity is coupled to a Kalb-Ramond field are known to have black hole solutions characterized by the value of the conserved axion charge. The Kalb-Ramond field configuration for these black holes has vanishing field strength. The axion charge may be measured by an analog of the Aharanov-Bohm interference effect. The axion-charge to mass ratio may be arbitrarily large, as contrasted to the case of the Reissner-Nordstrom black hole where the electric-charge to mass ratio has an upper bound of one. The generic endpoint of semiclassical evaporation of an axionic black hole would therefore be an object of very large axion charge with mass of order the Planck mass. Axion charge also couples to Giddings-Strominger type instantons (wormholes) present in these theories. Instead of evaporating completely, therefore, it is likely that an axionic black hole will be swallowed by a wormhole, avoiding the appearance of a naked singularity. The loss of quantum coherence is a more subtle issue.This essay received the third award from the Gravity Research Foundation for the year 1989-Ed.On leave from the Physics Department, Syracuse University, Syracuse NY 13244-1130, USA.     

Inverse scattering method and soliton double solution family for string effective action

A so-called modified Hauser-Ernst-type extended double-complex linear system is established and used to develop a new inverse scattering method for solving the equations of motion of the string effective action describing the coupled gravity, dilaton and Kalb-Ramond fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the application of the inverse scattering method fine and effective. As an application, a concrete family of soliton double solutions for the considered theory is obtained.      

Inverse Scattering Method and Soliton Solution Family for String Effective Action

A modified Hauser-Ernst-type linear system is established and used to develop an inverse scattering method for solving the motion equations of the string effective action describing the coupled gravity, dilaton and KalbRamond fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the proposed inverse scattering method applied fine and effective. As an application, a concrete family of soliton solutions for the considered theory is obtained.     

Does a randall-sundrum scenario create the illusion of a torsion-free universe?

We consider spacetime with torsion in a Randall-Sundrum scenario where torsion, identified with the rank-2 Kalb-Ramond field, exists in the bulk together with gravity. While the interactions of both graviton and torsion in the bulk are controlled by the Planck mass, an additional exponential suppression comes for the torsion zero-mode on the visible brane. This may serve as a natural explanation of why the effect of torsion is so much weaker than that of curvature on the brane. The massive torsion modes, on the other hand, are correlated with the corresponding gravitonic modes and may be detectable in TeV-scale experiments.     

Parity violation in four and higher dimensional spacetime with torsion

The possibility of parity violation in a gravitational theory with torsion is extensively explored in four and higher dimensions. In the former case, we have listed our conclusions on when and whether parity ceases to be conserved, with both two- and three-index antisymmetry of the torsion field. In the latter, the bulk spacetime is assumed to have torsion, and the survival of parity violating terms in the four dimensional effective action is studied, using the compactification schemes proposed by Arkani-Hamed-Dimopoulos-Dvali and Randall-Sundrum. An interesting conclusion is that the torsion-axion duality arising in a stringy scenario via the second rank antisymmetric Kalb-Ramond field leads to conservation of parity in the gravity sector in any dimension. However, parity violating interactions do appear for spin-1/2 fermions in such theories, which can have crucial phenomenological implications.Received: 17 July 2003, Revised: 12 February 2004, Published online: 23 April 2004     

Global Monopole in Kalb–Ramond Background

In recent, S. SenGupta and S. Sur [Phys. Lett. B 502 (2001) 350] have obtained static vacuum solutions of the gravitational field equations in back ground space time with torsion. The torsion is identified with the field strength of a second-rank anti-symmetric tensor field, namely Kalb-Ramond field. In this work, we present the solutions for the metric outside a monopole resulting from the breaking of a global 0(3) symmetry in Kalb-Ramond background. A comparison is made with the corresponding results predicted by general relativity.     

Off-shell representations with central charges for ten-dimensional super Yang-Mills theory

Using Bianchi identities and commutation relations we investigate the off-shell field content of the ten-dimensional super Yang-Mills theory when central charges are introduced. Possible constraints are found, but it is not clear whether they allow the construction of an invariant action.     

Heterotic and Type I string dynamics from eleven dimensions

We propose that the ten-dimensional E₈ × E₈ heterotic string is related to an eleven-dimensional theory on the orbifold in the same way that the Type IIA string in ten dimensions is related to . This in particular determines the strong coupling behavior of the ten-dimensional E₈ × E₈ theory. It also leads to a plausible scenario whereby duality between SO(32) heterotic and Type I superstrings follows from the classical symmetries of the eleven-dimensional world, just as the duality of the ten-dimensional Type IIB theory follows from eleven-dimensional diffeomorphism invariance.     

Gravitational Gauge Interactions of Scalar Field

Quantum gauge theory of gravity is formulated based on gauge principle. Because the Lagrangian has strict local gravitational gauge symmetry, gravitational gauge theory is a perturbatively renormalizable quantum theory. Gravitational gauge interactions of scalar field are studied in this paper. In quantum gauge theory of gravity, scalar field minimal couples to gravitational field through gravitational gauge covariant derivative. Comparing the Lagrangian for scalar field in quantum gauge theory of gravity with the corresponding Lagrangian in quantum fields in curved space-time, the definition for metric in curved space-time in geometry picture of gravity can be obtained, which is expressed by gravitational gauge field. In classical level, the Lagrangian and Hamiltonian approaches are also discussed.     

On closure of the light-cone gauge closed superstring algebra

We construct four-field generators to achieve closure of the ten-dimensional SUSY algebra for the heterotic and type II superstring light-cone gauge field theory. Closure for the heterotic case is achieved in a regularization independent manner, whilst that for type II needs the use of constant time and phase integration regularizations. The resulting four-field hamiltonians are briefly related to terms arising in the amplitudes for the two theories constructed from the cubic terms alone.     

Oscillating solutions in higher-dimensional cosmology

Behaviour characteristics of the mixmaster model of the early universe can be reproduced in ten dimensions by the low-energy superstring theory. The three-index tensor field H can produce, in the variation of the sizes of three-dimensional spaces, the characteristic jumping between Kasner solutions near a singularity. Behaviour which would otherwise by chaotic is moderated by the dilaton field of the ten-dimensional theory.     

Gravitational Gauge Interactions of Scalar Field

Quantum gauge theory of gravity is formulated based on gauge principle. Because the Lagrangian hasstrict local gravitational gauge symmetry, gravitational gauge theory is a perturbatively renormalizable quantum theory.Gravitational gauge interactions of scalar field are studied in this paper. In quantum gauge theory of gravity, scalar fieldminimal couples to gravitational field through gravitational gauge covariant derivative. Comparing the Lagrangian forscalar field in quantum gauge theory of gravity with the corresponding Lagrangian in quantum fields in curved space-time, the definition for metric in curved space-time in geometry picture of gravity can be obtained, which is expressedby gravitational gauge field. In classical level, the Lagrangian and Hamiltonian approaches are also discussed.     

Static vacuum solution of direct Poincaré gauge theory in ten dimensions with four external

A torsion-free solution of the free gauge field equations of direct Poincaré gauge theory on a ten-dimensional Minkowski space is constructed. This solution exhibits nontrivial curvature two-forms, but shaves the metric structure down to that of a four-dimensional Minkowski space. Universality of this solution with respect to the choice of the free field Lagrangian is established.     

Letter: Antisymmetric Tensor Contribution to the Muon g − 2

We investigate the Kalb-Ramond antisymmetric tensor field as a solution to the muon g – 2 problem. In particular we calculate the lowest-order Kalb-Ramond contribution to the muon anomalous magnetic moment and find that we can fit the new experimental value for the anomaly by adjusting the coupling without affecting the electron anomalous magnetic moment results.     

Renormalizable Quantum Gauge Theory of Gravity

The quantum gravity is formulated based on the principle of local gauge invariance. The model discussed in this paper has local gravitational gauge symmetry, and gravitational field is represented by gauge field. In the leading-order approximation, it gives out classical Newton's theory of gravity. In the first-order approximation and for vacuum, it gives out Einstein's general theory of relativity. This quantum gauge theory of gravity is a renormalizable quantum theory.     

Superstring theory

Dual string theories, initially developed as phenomenological models of hadrons, now appear more promising as candidates for a unified theory of fundamental interactions. Type I superstring theory (SST I), is a ten-dimensional theory of interacting open and closed strings, with one supersymmetry, that is free from ghosts and tachyons. It requires that an SO(n) or Sp(2n) gauge group be used. A light-cone-gauge string action with space-time supersymmetry automatically incorporates the superstring restrictions and leads to the discovery of type II superstring theory (SST II). SST II is an interacting theory of closed strings only, with two D = 10 supersymmetries, that is also free from ghosts and tachyons. By taking six of the spatial dimensions to form a compact space, it becomes possible to reconcile the models with our four-dimensional perception of spacetime and to define low-energy limits in which SST I reduces to N = 4, D = 4 super Yang-Mills theory and SST II reduces to N = 8, D = 4 supergravity theory. The superstring theories can be described by a light-cone-gauge action principle based on fields that are functionals of string coordinates. With this formalism any physical quantity should be calculable. There is some evidence that, unlike any conventional field theory, the superstring theories provide perturbatively renormalizable (SST I) or finite (SST II) unifications of gravity with other interactions.     

Gravitational Shielding Effect in Gauge Theory of Gravity

In 1992, E.E. Podkletnov and R. Nieminen found that under certain conditions, ceramic superconductor with composite structure reveals weak shielding properties against gravitational force. In classical Newton's theory of gravity and even in Einstein's general theory of gravity, there are no grounds of gravitational shielding effects. But in quantum gauge theory of gravity, the gravitational shielding effects can be explained in a simple and natural way. In quantum gauge theory of gravity, gravitational gauge interactions of complex scalar field can be formulated based on gauge principle. After spontaneous symmetry breaking, if the vacuum of the complex scalar field is not stable and uniform, there will be a mass term of gravitational gauge field. When gravitational gauge field propagates in this unstable vacuum of the complex scalar field, it will decays exponentially, which is the nature of gravitational shielding effects. The mechanism of gravitational shielding effects is studied in this paper, and some main properties of gravitational shielding effects are discussed.