A brane in five - dimensional Minkowski space ∗

Abstract

We discuss the propagation of gravity in five-dimensional Minkowski space in the presence of a four-dimensional brane. We show that there exists a solution to the wave equation that leads to a propagator exhibiting four-dimensional behavior at low energies (long distances) with five-dimensional effects showing up as corrections at high energies (short distances). We compare our results with propagators derived in previous analyses exhibiting five-dimensional behavior at low energies. We show that different solutions correspond to different physical systems. ∗Research supported in part by the DoE under grant DE-FG05-91ER40627. Extra dimensions have been shown to lead to phenomenologically viable results explaining the weakness of gravity compared to the other forces of Nature. This has been achieved with both compact extra dimensions [1, 2, 3] and uncompactified warped ones [4, 5]. Typically, one obtains a tower of Kaluza-Klein modes which contribute at high energies (short distances), whereas at low energies (long distances) one recovers ordinary four-dimensional gravity. These features are not apparent when the extra dimensions are flat [6, 7, 8]. It has been shown that four-dimensional gravity is not necessarily recovered at low energies. This is due to the existence of light Kaluza-Klein modes which may dominate even at low energies. It was shown in ref. [6] that for one extra flat dimension one obtains fivedimensional gravity at low energies, whereas in ref. [7] it was argued that for two or more extra flat dimensions, low energy physics is dominated by four-dimensional gravity. A more careful treatment of the singular limits considered in ref. [8] revealed that the light Kaluza-Klein modes dominate at low energies independently of the number of extra flat dimensions. In the analysis of ref. [6] the propagation of gravity in the extra dimension was modeled by considering incoming waves on both sides of the brane. If the extra dimension is given a finite size R, then this approach corresponds to imposing Neumann boundary conditions on both ends of the extra dimension [8]. Thus, one considers two distinct branes located at the ends of the extra dimension. The infinite R case is then recovered by letting the position of one brane go to infinity. We shall instead identify the two ends, thus considering a single brane in a toroidally compactified extra flat dimension. In this case, the Green function can be expressed in terms of standing waves. We find that at low energies the propagator on the brane behaves as 1/p, where p is the four-dimensional momentum, i.e., as a four-dimensional propagator. This is our main result. We should point out that it is not surprising that different boundary conditions lead to distinct physical systems. This is because, unlike in AdS space (see, e.g., [9]), there is no holomorphic principle in Minkowski space. Following refs. [6, 7, 8] we discuss the propagation of a single scalar field φ instead of a graviton. This simplifies the discussion because the complications due to the tensor structure of the graviton are avoided. The field φ is a function of five coordinates x = (x, y) where x (μ = 0, 1, 2, 3) span our four-dimensional world and y is the coordinate of the extra dimension. We will first consider a finite extra dimension of size R (so that 0 ≤ y ≤ R) and then study the large R limit. The brane is located at the four-dimensional slice y = 0. The action is S = M ∫

Cite this paper

@inproceedings{Avery2001ABI, title={A brane in five - dimensional Minkowski space ∗}, author={John Avery and Rob Mahurin and George Siopsis}, year={2001} }