Abstract
The aim of this article is to describe the minimum that any physicist might want to know about string theory, focusing on a few basic questions. How does string theory generalize standard quantum field theory? Why does string theory force us to unify General Relativity with the other forces of nature, while standard quantum field theory makes it so difficult to incorporate General Relativity? Why are there no ultraviolet divergences in string theory? And what happens to Einstein’s conception of spacetime?
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Notes
- 1.
To be published in Foundations of Mathematics and Physics, one century after Hilbert, ed. Joseph Kouneiher, Mathematical physics Studies, Springer 2017. Adapted with permission from an article that appeared in the November, 2015 issue of Physics Today.
- 2.
While maintaining conformal invariance, we can add to the action the usual Einstein-Hilbert term, the integral of the scalar curvature R. This plays no role in one dimension because a one-manifold has no intrinsic curvature. In two dimensions, there is a curvature scalar but its integral \(\frac{1}{4\pi }\int _\Sigma \text {d}^2x\sqrt{g} R\) is a topological invariant, the Euler characteristic of \(\Sigma \). We can and should include this term in the action. It turns out that the coefficient with which it appears determines the “string coupling constant,” the strength with which strings interact.
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Witten, E. (2018). What Every Physicist Should Know About String Theory. In: Kouneiher, J. (eds) Foundations of Mathematics and Physics One Century After Hilbert. Springer, Cham. https://doi.org/10.1007/978-3-319-64813-2_8
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DOI: https://doi.org/10.1007/978-3-319-64813-2_8
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