Large extra dimension

In particle physics, the ADD model, also known as the model with large extra dimensions (LED), is a model framework that attempts to solve the hierarchy problem by explaining the weakness of gravity relative to the other forces. This hypothesis requires that the fields of the Standard Model be confined to a four-dimensional membrane, while gravity propagates in several additional spatial dimensions that are large compared to the Planck scale.

The model was proposed by Nima Arkani-Hamed, Savas Dimopoulos, and Gia Dvali in 1998.

Results from the Large Hadron Collider do not appear to support the model thus far. However the operation range of the LHC (13 TeV collision energy) covers only a small part of the predicted range in which evidence for LED would be recorded (a few TeV to 10¹⁶ TeV).

Traditionally in theoretical physics the Planck scale is the highest energy scale and all dimensionful parameters are measured in terms of the Planck scale. There is a great hierarchy between the weak scale and the Planck scale and explaining the ratio of strength of weak force and gravity ${\displaystyle G_{F}/G_{N}=10^{32}}$ is the focus of much of beyond-Standard-Model physics. In models of large extra dimensions the fundamental scale is much lower than the Planck. This occurs because the power law of gravity changes. For example, when there are two extra dimensions of size ${\displaystyle d}$, the power law of gravity is ${\displaystyle 1/r^{4}}$ for objects with ${\displaystyle \scriptstyle r\ll d}$ and ${\displaystyle 1/r^{2}}$ for objects with ${\displaystyle \scriptstyle r\gg d}$. If we want the Planck scale to be equal to the next accelerator energy (1 TeV), we should take ${\displaystyle d}$ to be approximately 1 mm. For larger numbers of dimensions, fixing the Planck scale at 1 TeV, the size of the extra-dimensions become smaller and as small as 1 femtometer for six extra dimensions.

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