Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spacetime with zero point length is two-dimensional at the Planck scale   It is generally believed that any quantum theory of gravity should have a
generic feature --- a quantum of length. We provide a physical ansatz to obtain
an effective non-local metric tensor starting from the standard metric tensor
such that the spacetime acquires a zero-point-length $\ell _{0}$ of the order
of the Planck length $L_{P}$. This prescription leads to several remarkable
consequences. In particular, the Euclidean volume $V_D(\ell,\ell_{0})$ in a
$D$-dimensional spacetime of a region of size $\ell $ scales as $V_D(\ell, \ell
_{0}) \propto \ell_{0}^{D-2} \ell^2$ when $\ell \sim \ell_{0}$, while it
reduces to the standard result $V_D(\ell,\ell_{0}) \propto \ell^D$ at large
scales ($\ell \gg \ell_{0}$). The appropriately defined effective dimension,
$D_{\rm eff} $, decreases continuously from $D_{\rm eff}=D$ (at $\ell \gg
\ell_{0}$) to $D_{\rm eff}=2$ (at $\ell \sim \ell_{0}$). This suggests that the
physical spacetime becomes essentially 2-dimensional near Planck scale.

29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga