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I encountered the notion of "string universality" in the TASI lectures on Supergravity (April 2011). What does this actually mean? Does it mean that every consistent (in particular cancellation of anomalies) supergravity theory has as UV-completion a string theory? After a bit of googling on it, it rather seems to be considered as a bit problematic because every kind of consistent supergravity would have UV-string completion according to the concept, even a 4D-supergravity theory.

As I am a novice in string theory (I have some basic knowledge of supergravity though) So I would appreciate an explanation without too much jargon. Thank you.

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  • $\begingroup$ What's "problematic" about the (conjectured) universality for 4 dimensions? $\endgroup$ Mar 14, 2021 at 16:02

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The five consistent superstring theories are UV-complete and consistent quantum theories of gravity; that's demonstrably true. Adding M-theory (the eleven-dimensional supergravity) to that set of maximally uncompactified theories, you can obtain a huge landscape of effective field theories obtained as compactifications of those string/M-theories.

Question: Is the set of all EFTs obtained from string theory a complete list of all the possible EFTs that can be consistently coupled to gravity?

The phrase "string universality" is the statement that the answer to the aforementioned question is affirmative.

String universality examples:

  1. 32 supercharges in d=11 and d=10. The only consistent (anomaly-free) supergravities are the eleven-dimensional supergravity, one non-chiral theory (the IIA one) and another chiral (2,0) one. All of them arise as low energy limits of string/M-theories.

  2. 16 supercharges in d=10. Anomaly cancellation does only allow four possibilities: $E_{8} \times E_{8}$, $SO(32)$ , $E_{8} \times U(1)^{248}$ and $U(1)^{496}$. Heterotic strings realize the first two ones and amazingly, an anomaly-inflow argument can be invoked to show that the other two options are inconsistent. Again, string theory exactly covers the space of all posibilities.

  3. See String Universality in Six Dimensions and the talk The Swampland in d larger than 6 for amazing dicussions for (2,0) theories in 6d.

I recommend the talk Supersymmetric Quantum Field Theories and the Swampland for more examples that exhibit the amazing match between string theory and all the consistent theories that can be coupled to gravity (specially in six dimensions).

Nowadays the common jargon for "string universality" is the "string lampost principle": The space of all possible EFTs that can be consistently coupled to quantum gravity are realizable as EFTs derived from string theory.

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  • $\begingroup$ Thank you for the answer. Actually I don't understand the $\bf{Question}$. it seems, a verb is missing. And I have the same impression with the following sentence ... I don't understand it neither well. $\endgroup$ Mar 14, 2021 at 17:42
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String universality is the conjecture that every consistent supergravity QFT arises as the low-energy effective QFT of a suitable compactification (essentially a choice of "small" compact dimensions that are to small to detect as dimensions in the effective theory) of (10-dimensional) string theory. The origin of this idea is in "String Universality in Six Dimensions" by Kumar and Taylor, where they show this for a large class of 6d SUGRAs.

The dimensionality of the effective QFT is "adjustable" by choosing a suitable compactification - e.g. for 6d SUGRAs the compactification manifold is four-dimensional, and for 4d SUGRAs the compactification manifold is six-dimensional.

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  • $\begingroup$ Thank you for the answer! So due to the large number of possible compactifications (there is no unique compactification) one gets the numerous string vacua (Or am I completely wrong)? $\endgroup$ Mar 14, 2021 at 17:38

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