arXiv 0704.14762007-04hep-th

紧致复双曲三重体上Horava-Witten理论中的TeV-scale引力

TeV-scale gravity in Horava-Witten theory on a compact complex hyperbolic threefold

Chris Austin

备注：: LaTeX2e, 317 pages. v2: corrections to subsections 5.1 and 5.3. Subsection 2.3.3 revised and extended, bibliography revised, other minor improvements. v3: revisions to subsection 5.2, reference added

摘要：

本文研究了在光滑紧致自旋商CH ^3上紧化的Horava-Witten理论的场方程和边界条件，其中CH ^3表示CP ^3的双曲表亲，并引入Casimir能量密度项.如果某个边界附近的卡西米尔能量密度导致某个积分常数的值大于10^5（单位为d = 11的引力长度），那么就可以发现一种通过ADD机制实现TeV尺度引力的厚管几何形式，而该边界成为我们所居住的厚管的内表面。考虑了三种可供选择的方法，在这些方法中，粗管的外表面可能与有效d = 4宇宙学常数的观测值相一致地被稳定。在第一种选择中，外表面稳定在经典区域，积分常数固定在d = 11引力长度单位的10^{13}左右，以与观测到的宇宙学常数保持一致。在第二种情况下，观测到的四个维度在外表面的尺寸已经减小到d = 11的引力长度，并且在外表面附近存在卡西米尔效应。在第三种方案中，外表面被稳定在经典区域的额外通量的三形式的规范场，其四形式的场强包裹三个周期的紧凑的六流形倍的径向尺寸的厚管。讨论了强/电弱标准模型的拟合问题。

英文摘要：

The field equations and boundary conditions of Horava-Witten theory, compactified on a smooth compact spin quotient of CH^3, where CH^3 denotes the hyperbolic cousin of CP^3, are studied in the presence of Casimir energy density terms. If the Casimir energy densities near one boundary result in a certain constant of integration taking a value greater than around 10^5 in units of the d = 11 gravitational length, a form of thick pipe geometry is found that realizes TeV-scale gravity by the ADD mechanism, with that boundary becoming the inner surface of the thick pipe, where we live. Three alternative ways in which the outer surface of the thick pipe might be stabilized consistent with the observed value of the effective d = 4 cosmological constant are considered. In the first alternative, the outer surface is stabilized in the classical region and the constant of integration is fixed at around 10^{13} in units of the d = 11 gravitational length for consistency with the observed cosmological constant. In the second alternative, the four observed dimensions have reduced in size down to the d = 11 gravitational length at the outer surface, and there are Casimir effects near the outer surface. In the third alternative, the outer surface is stabilized in the classical region by extra fluxes of the three-form gauge field, whose four-form field strength wraps three-cycles of the compact six-manifold times the radial dimension of the thick pipe. Some problems related to fitting the strong/electroweak Standard Model are considered.

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摘要：

英文摘要：

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