4D Minkowski Spacetime Research Articles

Erratum: NS-branes in five-dimensional brane world models [Phys. Rev. D82, 046001 (2010)

We study codimension-1 brane solutions of the 5d brane world models compactified on $S_1 / \mathbb{Z}_2$. In string theoretical setup they suggest that the background branes located at orbifold fixed points should be NS-branes (in the five dimensional sense), rather than D-branes. Indeed, the existence of the background NS-branes is indispensable to obtain flat geometry $M_4 \times S_1 / \mathbb{Z}_2$ where $M_4$ represents the 4d Minkowski spacetime, and without these branes the 5d metric becomes singular everywhere. This result is very reminiscent of the $(p+3)$d effective string theory \cite{1} where the NS-NS type $p$-brane is indispensable to obtain a flat geometry $R_2$ or $R_2 /\mathbb{Z}_n$ on the transverse dimensions. Without this NS-NS type $p$-brane the 2d transverse space becomes a pin-shaped singular space. The correspondence between these two theories leads us to a conjecture that the whole flat backgrounds of the string theory inherently invovle the NS-branes implicitly in their ansatz, and hence the true background $p$-branes immanent in our spacetime may be NS-branes, instead of D-branes. We argue that this result can have a significant consequence in the context of the cosmological constant problem.

An invitation to higher gauge theory

In this easy introduction to higher gauge theory, we describe parallel transport for particles and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a gauge group, this generalization involves a gauge '2-group'. We focus on 6 examples. First, every abelian Lie group gives a Lie 2-group; the case of U(1) yields the theory of U(1) gerbes, which play an important role in string theory and multisymplectic geometry. Second, every group representation gives a Lie 2-group; the representation of the Lorentz group on 4d Minkowski spacetime gives the Poincar\'e 2-group, which leads to a spin foam model for Minkowski spacetime. Third, taking the adjoint representation of any Lie group on its own Lie algebra gives a 'tangent 2-group', which serves as a gauge 2-group in 4d BF theory, which has topological gravity as a special case. Fourth, every Lie group has an 'inner automorphism 2-group', which serves as the gauge group in 4d BF theory with cosmological constant term. Fifth, every Lie group has an 'automorphism 2-group', which plays an important role in the theory of nonabelian gerbes. And sixth, every compact simple Lie group gives a 'string 2-group'. We also touch upon higher structures such as the 'gravity 3-group' and the Lie 3-superalgebra that governs 11-dimensional supergravity.

N=1, 4D supermembrane from 11D

The action of the 11D supermembrane with nontrivial central charges compactified on a 7D toroidal manifold is obtained. It describes a supermembrane evolving in a 4d Minkowski space-time. The action is invariant under additional symmetries in comparison to the supermembrane on a Minkowski target space. The hamiltonian in the LCG is invariant under conformal transformations on the Riemann surface base manifold. The spectrum of the regularized hamiltonian is discrete with finite multiplicity. Its resolvent is compact. Susy is spontaneously broken, due to the topological central charge condition, to four supersymmetries in 4D, the vacuum belongs to an N=1 supermultiplet. When assuming the target-space to be an isotropic 7-tori, the potential does not contain any flat direction, it is stable on the moduli space of parameters.

RIGOROUS STEPS TOWARDS HOLOGRAPHY IN ASYMPTOTICALLY FLAT SPACETIMES

Scalar QFT on the boundary ℑ+at future null infinity of a general asymptotically flat 4D spacetime is constructed using the algebraic approach based on Weyl algebra associated to a BMS-invariant symplectic form. The constructed theory turns out to be invariant under a suitable strongly-continuous unitary representation of the BMS group with manifest meaning when the fields are interpreted as suitable extensions to ℑ+of massless minimally coupled fields propagating in the bulk. The group theoretical analysis of the found unitary BMS representation proves that such a field on ℑ+coincides with the natural wave function constructed out of the unitary BMS irreducible representation induced from the little group Δ, the semidirect product between SO(2) and the two-dimensional translations group. This wave function is massless with respect to the notion of mass for BMS representation theory. The presented result proposes a natural criterion to solve the long-standing problem of the topology of BMS group. Indeed the found natural correspondence of quantum field theories holds only if the BMS group is equipped with the nuclear topology rejecting instead the Hilbert one. Eventually, some theorems towards a holographic description on ℑ+of QFT in the bulk are established at level of C*-algebras of fields for asymptotically flat at null infinity spacetimes. It is proved that preservation of a certain symplectic form implies the existence of an injective *-homomorphism from the Weyl algebra of fields of the bulk into that associated with the boundary ℑ+. Those results are, in particular, applied to 4D Minkowski spacetime where a nice interplay between Poincaré invariance in the bulk and BMS invariance on the boundary at null infinity is established at the level of QFT. It arises that, in this case, the *-homomorphism admits unitary implementation and Minkowski vacuum is mapped into the BMS invariant vacuum on ℑ+.

The general warped solution with conical branes in six-dimensional supergravity

We present the general regular warped solution with 4D Minkowski spacetime in six-dimensional gauged supergravity. In this framework, we can easily embed multiple conical branes into the warped geometry by choosing an undetermined holomorphic function. As an example, for the holomorphic function with many zeroes, we find warped solutions with multi-branes and discuss the generalized flux quantization in this case.

Hyperbolic phase transformation group and its applicaton to four-dimensional relativistic spacetime

The hyperbolic complex space RH defined by the Clifford algebra and the hyperbolic phase transformation group U4(H) acting on RH are endowed with definite physical meaning in this paper. The hyperbolic complex space RH is isomorphic to the 4-dimensional(4D) Minkowski spacetime, and the hyperbolic phase transformation group U4(H) in RH is just Lorentz transformation group on 4D relativistic spacetime. Furthermore, the general expressions of Lorentz transformation and the velocity transformation on 4D Minkowski spacetime are naturally derived using the composite transformations of the group U4(H). Hence, the well-known special Lorentz transformation in the special relativity(SR) is contained as a special case in our discussions.

Classification of Subsystems for Graded-Local Nets with Trivial Superselection Structure

We classify Haag-dual Poincaré covariant subsystems of a graded-local net on 4D Minkowski spacetime which satisfies standard assumptions and has trivial superselection structure. The result applies to the canonical field net of a net of local observables satisfying natural assumptions. As a consequence, provided that it has no nontrivial internal symmetries, such an observable net is generated by (the abstract versions of) the local energy-momentum tensor density and the observable local gauge currents which appear in the algebraic formulation of the quantum Noether theorem. Moreover, for a net of local observables as above, we also classify the Poincaré covariant local extensions which preserve the dynamics.

A Note on Deformations of 2D Fluid Motions Using 3D Born-Infeld Equations

Classical fluid motions can be described either by time dependent diffeomorphisms (Lagrangian description) or by the corresponding generating vector fields (Eulerian description). We are interested in interpolating two such fluid motions. For both analytic and numerical purposes, we would like the corresponding interpolating vector fields to evolve according to some hyperbolic evolution PDEs. In the 2D case, it turns out that a convenient set of such PDEs can be deduced from the BornInfeld (BI) theory of Electromagnetism. The 3D BI equations were originally designed as a nonlinear correction to the linear Maxwell equations allowing finite electric fields for point charges. They depend on a parameter λ. As λ goes to infinity, the classical Maxwell equations are recovered. It turns out that in the opposite case, as λ goes to zero, the BI equations provide a solution to our problem. These equations, as λ = 0, also describe classical strings (extremal surfaces) evolving in the 4D Minkowski space-time. In their static version, they can be interpreted in the framework of optimal transportation theory.

Twistor variational principle for null strings

I present a twistor action functional for null 2-surfaces (null strings) in 4D Minkowski spacetime. The proposed formulation is reparametrization invariant and free of algebraic and differential constraints. Proposed approach results in derivation of evolution equations for the null strings. It is shown that non-geodesic null strings are contained in the presented formalism. A discussion of the problem of minimality for 2-surfaces with degenerate induced metric is given. I also speculate on the possible description of strings (time-like 2-surfaces) and conventional (space-like) 2-surfaces.

Quantum interest for scalar fields in Minkowski spacetime

The quantum interest conjecture of Ford and Roman states that any negative energy flux in a free quantum field must be preceded or followed by a positive flux of greater magnitude, and the surplus of positive energy grows the further the positive and negative fluxes are apart. In addition, the maximum possible separation between the positive and negative energy decreases the larger the amount of negative energy. We prove that the quantum interest conjecture holds for arbitrary fluxes of non-interacting scalar fields in 4D Minkowski spacetime, and discuss the consequences in attempting to violate the second law of thermodynamics using negative energy. We speculate that quantum interest may also hold for the Electromagnetic and Dirac fields, and might be applied to certain curved spacetimes.