Are there any experiments going on to verify the validity of string theory to study theoretical particle physics?
As far as I know, there is no way to test string theory. The scales are simply too small. So it remains as is – a theory.
There have been experiments, that did verify the validity of string theory as a description of low energy hadronic resonances. The problem was the absence of a massless hadronic state, with spin 2. How QCD, as the theory of quarks and gluons at high energies, can describe, quantitatively, the low energy hadronic resonances is, still, however, an open problem.
As matter of fact string theory isn't technically a physical theory as no experiment is able to approve or disprove it and many doubt it could ever be so. At present it's a beautiful and consistent mathematical construct.
The framework of string theory, as a description of all properties of hadrons, can and has been checked-and it was found that, while it does describe many properties of the scattering of hadrons at low energies, it isn't the correct description at high energies, where quarks can be resolved. The correct theory, in that régime, is a very special quantum field theory of particles, QCD. What isn't known is how QCD describes the low energy behavior of hadrons-lattice calculations are very challenging-how the string description emerges and how the massless spin 2 resonance is removed. The reason is that it's not known how to do a calculation under controlled approximations in that case and, therefore, to describe search strategies for experiments.
It's actually useful to know the technical issues-content does matter, metaphysical speculations don't.
A dimension is just a label, which means a field has an inifinite number of components, that's all. Eleven dimensions simply mean that the fields have seven continuous labels. And even there there are assumptions-it is known how to define string theories in four dimensions, so it's useful not to discuss technical issues from the popular press. Once more, one shouldn't confuse mathematics with physics.
Metaphysical speculation doesn't involve calculations, but making statements of belief-which are irrelevant for physics or mathematics. It's more useful to learn to calculate.
There are many ways in which string theory may turn out not to be a useful framework for describing natural phenomena, with the strong interactions at high energies being one of them-but personal prejudices about ways of expressing technical issues aren't among them.
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