Vanishing of cosmological constant and fully localized gravity in a brane world with extra time(s)

Abstract

We construct an intersecting brane configuration in six-dimensional space with one extra spacelike and one extra time-like dimensions. With a certain additional symmetry imposed on the extra space-time we have found that effective four-dimensional cosmological constant vanishes automatically, providing the static solution with gravity fully localized at the intersection region as there are no propagating massive modes of graviton. In this way, the same symmetry allows us to eliminate tachyonic states of graviton from the spectrum of the effective four-dimensional theory, thus avoiding phenomenological difficulties comming from the matter instability usually induced in theories with extra time-like dimensions.

Reconsidering extra time-like dimensions

“…A glance at ArXiv shows that there are hundreds of papers on extra dimensions in the last five years and almost all of them being wholly or mainly on spatial extra dimensions. From the theoretical point of view the scarcity of studies involving extra time-like dimensions [1,2,3,4,5,6,7] is mainly due to the existence of tachyonic modes in such models, which are problematic because of the violation of causality and unitarity and lack of an adequate field theoretic description of tachyonic fields [2] while from the phenomenological point of view the most serious problems are the extremely small empirical lower bound in literature on the size(s) of extra time-like dimensions [8], the spontaneous decay of stable particles induced by negative energy tachyons [2,9], the imaginary self energy for charged fermions induced by tachyonic photon modes, which in turn, seems to cause disappearance of the fermion into nothing in a very short time [2]. In this study we will focus on the phenomenological difficulties and try to seek if one may moderate the phenomenological problems mentioned above with the hope that a thorough consistent formulation of the field theory of tachyons and their interactions with the usual particles may be formulated in future (if tachyons exist at all).…”

“…The first phenomenological problem that will be considered here is the extremely small lower bound derived from the lower bound on the lifetime of proton [8]. In the light of this extremely small lower bound on the size of extra time-like dimension(s), in the order of a tenth of the Planck scale, either one should dare to employ such ( unnaturally) small dimension(s)or should use brane models where our physical world is a brane with an infinitesimal width in the extra time-like direction [2] or a scheme where tachyonic modes are not allowed to be produced [5,6]. A possible relaxation of the bound on the size of extra time dimension(s) would give more freedom to the model constructions with extra time-like dimension(s).…”

Hexad Preons and Emergent Gravity in 3-dimensional Complex Spacetime

“…Gravitation, electrodynamics and electroweak interaction were reconsidered in the sixdimensional spacetime with three times [26][27][28]. Other developments include time-like extra dimensions in the brane world scenarios [29][30][31][32][33][34][35][36], F-theory with one timelike extra dimension[37], supergravity and string theory involving a holographic principle and extra time dimensions [38][39][40], as well as quantum theory in spacetime with one time-like extra dimension [41,42]. In addition, the so called "two-time physics (2T-physics)" where the phase space is gauged, has established the unitarity and causality in 4+2 dimensions with one extra space and one extra time dimensions and have obtained many interesting results [43].…”

New asymptotic Anti-de Sitter solution with a timelike extra dimension in 5D relativity

“…The hierarchy problem can also be reconciled with a correct cosmological expansion of the visible universe by extra timelike dimension in Randall-Sundrum brane [21]. The effective 4D cosmological constant vanishes and avoids phenomenological difficulties from the matter instability by constructing one brane configuration in 6D space, in which one extra dimension is spacelike and the other is timelike [22]. The generic closed system of equations on a brane that describes its inner evolution is also obtained by considering the bulk spaces with spacelike/timelike extra dimension, and with/without Z 2 symmetry of reflection relative to the brane [23].…”