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This page collects links related to
Physical Mathematics and the Future
talk at Strings 2014
on the mathematical physics of string theory.
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The most spectacular successes and interactions with math have been in the areas of algebra, geometry, and topology. A hallmark of the subject is the astonishing converse of Wigner's title: The unreasonable effectiveness of physics in the mathematical sciences. The subject is dauntingly vast. I will limit my comments to just a few possible future paths.
We still have no fundamental formulation of “M-theory” - the hypothetical theory of which 11-dimensional supergravity and the five string theories are all special limiting cases. Work on formulating the fundamental principles underlying M-theory has noticeably waned.
A good start was given by the Matrix theory approach of Banks, Fischler, Shenker and Susskind. We have every reason to expect that this theory produces the correct scattering amplitudes of modes in the 11-dimensional supergravity multiplet in 11-dimensional Minkowski space - even at energies sufficiently large that black holes should be created. (This latter phenomenon has never been explicitly demonstrated). But Matrix theory is only a beginning and does not give us the whole picture of M-theory. The program ran into increasing technical difficulties when more complicated compactifications were investigated. (For example, compactification on a six-dimensional torus is not very well understood at all. $[...]$). Moreover, to my mind, as it has thus far been practiced it has an important flaw: It has not led to much significant new mathematics.
If history is a good guide, then we should expect that anything as profound and far-reaching as a fully satisfactory formulation of M-theory is surely going to lead to new and novel mathematics. Regrettably, it is a problem the community seems to have put aside - temporarily. But, ultimately, Physical Mathematics must return to this grand issue.
(Moore 14, section 12, p. 43-44)
Perhaps we need to understand the nature of time itself better. $[...]$ One natural way to approach that question would be to understand in what sense time itself is an emergent concept, and one natural way to make sense of such a notion is to understand how pseudo-Riemannian geometry can emerge from more fundamental and abstract notions such as categories of branes.
Last revised on May 16, 2020 at 04:49:28. See the history of this page for a list of all contributions to it.