What keeps strings in their proper "shape" despite their enormous inherent tension?

Question

Here is an extract from a great answer by Luboš Motl to this question: Tension in Strings

Because the string tension is not far from the Planck tension - one Planck energy per one Planck length 10$^{52}$ Newtons or so - it is enough to shrink the string almost immediately to the shortest possible distance whenever it is possible. Unlike the piano strings, strings in string theory have a variable proper length.

Now to balance the level of knowledge, I would like to ask a few extremely naive questions, (and please bear with me as I am trying to transition from pop sci books to Physics for Grown Ups.)

I am not sure what shape means on this scale, and with the extra dimensions included, I am even less sure. It could be that we are working in a completely abstract space.

However, IF the shape is important and if the string is under the huge tension described above, how is the shape maintained?

Somewhere or other, I read it is by the action of quantum fluctuations. I realise the phrase quantum fluctuations is often a byword for misunderstandings, so I read Matt Strassler's Blog first.

From Wikipedia String Theory

Compactification can be used to construct models in which spacetime is effectively four-dimensional. However, not every way of compactifying the extra dimensions produces a model with the right properties to describe nature. In a viable model of particle physics, the compact extra dimensions must be shaped like a Calabi–Yau manifold. A Calabi–Yau manifold is a special space which is typically taken to be six-dimensional in applications to string theory.

Answer 1

If you take a classical string with a constant tension (NB unlike a rubber band the tension doesn't depend on how far the string it stretched) and let it relax then it will shrink to a point.

However once you quantise the string you have the Heisenberg uncertainty principle to contend with. That means if you were to shrink the string to a point its uncertainty in position would be zero so its uncertainty in momentum would be infinite (which also means its energy would be infinite). This means the ground state has a finite size not a zero size.

This is broadly the same as the reason a hydrogen atom stays in shape. The hydrogen atom ground state is a compromise between reducing the size, which reduces the energy, and increasing the uncertainty in the momentum, which increases the energy. So like the string the hydrogen atom ground state has a finite size.

At the risk of annoying the string theorists we could push this analogy a bit farther. If you add energy to a hydrogen atom to raise it to an excited state than it gets bigger (the average distance of the electron from the nucleus increases) and likewise the excited states of the string are larger than the ground state. This is why Luboš says the strings have a variable length.