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>Unification of gauge couplings in Kaluza-Klein theory with two internal manifolds
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Unification of gauge couplings in Kaluza-Klein theory with two internal manifolds
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机译:Kaluza-Klein理论中的规范耦合与两个内部歧管的统一
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摘要
We consider a Kaluza-Klein theory whose ground state is ${f R}^4 imes {f M } imes {f K}$ where ${f M}$ and ${f K}$ are compact, irreducible, homogenous internal mani folds. This is the simplest ground state compatible with the existence of the graviton, gauge fields, massless scalar fields and the absence of the cosmological constan t. The requirement for these conditions to be satisfied are the odd dimensionality of ${f M}$ and ${f K}$, and the choice of a dimensionally continued Euler form action whose dimension is the same as the dimension of ${f M} imes {f K}$. We show that in such a theory, which is not simple due to presence of two internal manifolds, the gauge couplings $g^2_M$ and $g^2_K$ are actually unified provided that the internal space sizes are constant. For ${f M} imes {f K} = S^{2m+ 1} imes S^{2k+1}$ this gauge coupling unification relation reads $g^2_M / g^2_K = m / k$.
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机译:我们考虑一个基态为$ { bf R} ^ 4 times { bf M} times { bf K} $的Kaluza-Klein理论,其中$ { bf M} $和$ { bf K} $是紧凑的,不可还原的,均匀的内部歧管。这是最简单的基态,与引力子,规范场,无质量标量场的存在以及宇宙常数的存在不相容。满足这些条件的要求是$ { bf M} $和$ { bf K} $的奇数维,以及选择维数连续的Euler形式动作,该维数与$ {的维数相同 bf M} time { bf K} $。我们表明,在这种理论(由于存在两个内部歧管而并不简单)中,如果内部空间尺寸恒定,则规范联接器$ g ^ 2_M $和$ g ^ 2_K $实际上是统一的。对于$ { bf M} times { bf K} = S ^ {2m + 1} times S ^ {2k + 1} $,该量具耦合统一关系为$ g ^ 2_M / g ^ 2_K = m / k $ 。
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