# Fundamental string theory questions

Can anyone answer some basic string theory questions for me?

The Veneziano Amplitude is celebrated for predicting the scattering amplitude of mesons and for practically giving birth to string theory. That makes me curious. Does the Veneziano Amplitude happen to calculate scattering amplitudes for both bosons and fermions?

Okay, calculations once showed that bosons exist in a Universe of 26 dimensions and then superstring theory said fermions live in ten. Are bosons now believed to be occupying these ten as well, and 26 is just a pre-compactication subtotal? Of course maybe they share M-Theory's 11 dimensions, I should instead ask? I know the question seems basic but string theory gets so weird part of me fears the answer is going to be that they live in separate 26-dimensional and 10-dimensional Universes. Brrr.

• Good question. The bosonic string theory is just a toy model. The fermionic 10d-one is 'supersymmetric' so it has fermions and bosons (and susyoperators to go fron one to the other). The low energy limit of 10d superstringtheory is 10d sugra. There is also 11d sugra, so it is surmised that this is the lowenergy limit of an unknown (M-)theory. I am notmaking this an answer sind i dont actually know how to show the terms of the bosons in the theory Nov 8, 2017 at 6:51
• "bosonic string theory is just a toy model." So we know now, but it's interesting to watch Leonard Susskind's String Theory lectures on Youtube Nov 8, 2017 at 9:05
• I mean, back when the whole approach was fresh and you could still see the trees for the forest. The simplicity and purity about the thought processes of string theory pioneers like Lenny is refreshing. They just followed the math. Nov 8, 2017 at 9:33

## 1 Answer

1. The Veneziano amplitude is the amplitude for the scattering of the tachyonic ground states of 4 open bosonic strings. The significance of the Veneziano amplitude was that mesonic resonances are well-described by an amplitude of this specific functional form and string theory gives rises to such an amplitude, which is why string theory initially was conceived of not as a theory of quantum gravity, but as a model of strong interactions. QCD turned out as the preferred model of strong interaction with better predictive power, meaning that from a modern viewpoint, the Veneziano amplitude of string theory is not really all that interesting anymore except as a historical curiosity.

2. String theory does not say that "bosons" live in 26 dimensions or that "fermions" live in 10. It says that bosonic string theory is only consistently quantizable in 26 dimensions, and that superstring theory, which gives rise to both bosonic and fermionic states, is only consistently quantizable in 10 dimensions. For why this is so, see this question and its answers.

3. Compactification does not enter into this - the restriction on the number of dimensions holds irrespective of the "shape" of the dimensions, large or not, compact or not.

4. M-theory is a conjectured 11-dimensional theory which is hoped to subsume the five different "flavours" of superstring theory in 10 dimensions as different limits of itself, but we don't really know much about genuine "M-theory" that is not gained either from one of the superstring theories or from its low-energy 11d SUGRA limit.