Superstring Theory - Beyond Superstring Theory

Beyond Superstring Theory

It is conceivable that the five superstring theories are approximated to a theory in higher dimensions possibly involving membranes. Unfortunately because the action for this involves quartic terms and higher so is not Gaussian the functional integrals are very difficult to solve and so this has confounded the top theoretical physicists. Edward Witten has popularised the concept of a theory in 11 dimensions M-theory involving membranes interpolating from the known symmetries of superstring theory. It may turn out that there exist membrane models or other non-membrane models in higher dimensions which may become acceptable when new unknown symmetries of nature are found, such as noncommutative geometry for example. It is thought, however, that 16 is probably the maximum since O(16) is a maximal subgroup of E8 the largest exceptional lie group and also is more than large enough to contain the Standard Model. Quartic integrals of the non-functional kind are easier to solve so there is hope for the future. This is the series solution which is always convergent when a is non-zero and negative:

$\int_{-\infty}^\infty \exp({a x^4+b x^3+c x^2+d x+f}) \, dx = e^f \sum_{n,m,p=0}^\infty \frac{ b^{4n}}{(4n)!} \frac{c^{2m}}{(2m)!} \frac{d^{4p}}{(4p)!} \frac{ \Gamma(3n+m+p+\frac14) }{a^{3n+m+p+\frac14} }$

In the case of membranes the series would correspond to sums of various membrane interactions that are not seen in string theory.

Read more about this topic: Superstring Theory

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