Abstract
The lightest mass eigenvalue of a six-dimensional theory compactified on a torus is numerically evaluated in the presence of the brane-localized mass term. The dependence on the cutoff scale $\Lambda$ is non-negligible even when $\Lambda$ is two orders of magnitude above the compactification scale, which indicates that the mass eigenvalue is sensitive to the size of the brane, in contrast to five-dimensional theories. We obtain an approximate expression of the lightest mass in the thin brane limit, which well fits the numerical calculations, and clarifies its dependence on the torus moduli parameter $\tau$. We find that the lightest mass is typically much lighter than the compactification scale by an order of magnitude even in the limit of a large brane mass.
Highlights
Many extra-dimensional models have four-dimensional (4D) brane-like defects on the compact space, such as orbifold fixed points or solitonic objects [1]-[4]
In five-dimensional (5D) theories, the effects of such brane masses can be translated into the change of the boundary conditions for the bulk fields
This is because the branes in 5D can be regarded as the boundaries of the extra dimension
Summary
Many extra-dimensional models have four-dimensional (4D) brane-like defects on the compact space, such as orbifold fixed points or solitonic objects [1]-[4]. In five-dimensional (5D) theories, the effects of such brane masses can be translated into the change of the boundary conditions for the bulk fields This is because the branes in 5D can be regarded as the boundaries of the extra dimension. In this case, large brane masses can make zero-modes of the bulk fields heavy enough up to half of the compactification scale. [11] discussed a closely related issue in the case of the T 2/Z2 compactification whose torus moduli parameter is τ = i, and obtained the result that the inverse of the lightest mass eigenvalue has a logarithmic dependence on the cutoff scale. M 2aδab c2 4π2R2Im τ is the mass matrix of our theory
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