# Quantized Superstrings

B. E. Baaquie and
Marakani Srikant, Department of Physics, National University
of Singapore
Quantum string have tensions of order 10^{39} tons!
Also unlike the classical case, the quantum superstring can
exist only in a **10-dimensional spacetime**.

How do we interpret 10 (1 time + 9 space) dimensions? There
are two ways of interpreting the apparently invisible extra
dimensions of space : compactification and confinement
(i.e. we are confined to a 3-dimensional subspace of the
9-dimensional space) (not to be confused with quark
confinement).

## Compactification

Consider a water hose. From afar, it looks like a line,
but from up close we see that it is in fact a
two-dimensional object.

At every point of ordinary 3-dimensional, there are 6 more
orthogonal directions and a tiny 6-dimensional bubble of
radius 10^{-35} m exists at every point of
3-space.

What is the geometry & topology of this 6-dimensional
bubble? The answer is not yet known but esoteric
mathematical spaces such as Ricci flat complex Kähler
manifolds are favorites.

## Why are only 3 space dimensions large?

Of the 9 space dimensions, why are 6 dimensions
infinitesimal and the remaining 3 large? This is because
the closed loops of strings girdled 6 of the 9 dimensions
10^{-43} seconds after the big bang due to their
enormous tensions. These dimensions cannot stretch the
string and hence cannot expand.

### Confinement

We can consider ourselves to be confined to a
3-dimensional submanifold of 9-dimensional space. This
will become clearer when we discuss the concept of
D-branes.

## Creation and Destruction of Spacetime

On quantizing gravity, spacetime itself becomes only an
approximate semi-classical concept-----quantum
randomness implies the continuous creation and
destruction of space and time.

Consider a 2-dimensional projection of space evolving
in time.

At the scale of the string, spacetime is full of
"gaps" of nothingness. At the cosmic scale,
the same phenomenon is going on.

Last updated: 03 March, 2000