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A proof of string theory



For a few decades, competent researchers of fundamental physicists have "almost known" that any consistent theory of quantum gravity has to be string theory.

For a long time, the evidence supporting this statement has been somewhat incomplete, somewhat circumstantial, somewhat built on fuzzy aesthetic criteria, and on the elimination of some imaginable, increasingly large classes of conceivable alternatives (which were never quite "all possible alternatives"). In recent years, however, a more systematic or more axiomatic analysis of the concepts and patterns has made many things clearer to get closer to establishing the equivalence

CONSISTENT QUANTUM GRAVITY = STRING-M/THEORY
which is basically the same thing that Cumrun Vafa calls the "String Lamppost Principle". Jared Kaplan and Sandipan Kundu (John Hopkins) posted a fun hep-th preprint
Closed Strings and Weak Gravity from Higher-Spin Causality
where they prove the existence of the closed string spectrum (a Hagedorn tower) from the assumption that higher-spin particles exist; and causality works.



First, there are lots of higher-spin composite particles in the Universe (like the atoms and molecules) but there have to be elementary ones, too. Rotating (small) black hole microstates are "nearly elementary" particles of an arbitrary allowed spin. These two Gentlemen first prove that even if you start with metastable higher-spin non-gravitational particles, there have to be higher-spin particles in the gravitational sector as well, for the amplitudes to be consistent at high energies. Causality is required; in fact, they show that a form of the weak gravity conjecture does follow from causality.



The harder and somewhat pre-existing ingredient in their proof is CKSŽ. In 2016, by an analysis of the meromorphic functions in scattering amplitudes, Caron-Huot, Komagordski, Sever, and Žibojedov have shown the unavoidability of the Veneziano amplitude under some assumptions: with these assumptions, the Regge trajectory has to exist in a consistent theory. Kaplan and Kundu applied the CKSŽ argument at a moment where they already established some assumptions from others. It follows that at some window of energies, \(s,t\gg 1\) (but smaller than some energy scale that goes to infinity for a weak coupling), the gravitational amplitude agrees with the scattering amplitude for 4 closed strings in string theory. To say the least, it means that in some energy window, string theory's formulae become vastly more precise than field-theoretical formulae; string theory is better than quantum field theory. They also show that all metastable higher-spin states obtained in this way are examples establishing the weak gravity conjecture.

Of course, for that statement to be nontrivial, some coupling has to be weak. After all, string theory with \(g\sim 1\) becomes indistinguishable from "generic quantum gravity" with all states' being black hole microstates. But indeed, the implicit assumption is that \(g\sim 1\) is a "limited landlocked region" in between some extreme limits that can be approached perturbatively because they have a weak coupling. You could hypothesize that such a strongly coupled theory exists independently of any string theory – where string theory is assumed to allow the weak string coupling. With this assumption, it would still be true that any theory with higher-spin particles that can be approached using some weak-coupling expansions has to start with string theory.

M-theory in 11 dimensions has no coupling of the type \(g_{\rm string}\) although its black hole microstates may still carry any spin. I think a discussion of this unique string theory vacuum and hypothetical similar "unavoidably strong coupling" vacua is naturally missing in the discussion. It should be clarified how constrained such extra possibilities are and whether it's unavoidable that string theory with the Veneziano behavior arises if we compactify a dimension of this strongly coupled theory in some way.

At any rate, while some loopholes remain (but they are shrinking), folks who think hard about these matters have damn good reasons to be almost certain that strings and the related mathematics can never go away in the research of consistent quantum theories including gravity, social justice warriors' misinformation in the would-be mainstream media notwithstanding.

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