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Finiteness and the Emergence of Dualities
by Matilda Delgado, Damian van de Heisteeg, Sanjay Raman, Ethan Torres, Cumrun Vafa, Kai Xu
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Matilda Delgado |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2412.03640v3 (pdf) |
| Date submitted: | May 21, 2025, 2:49 p.m. |
| Submitted by: | Matilda Delgado |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We argue that the finiteness of quantum gravity amplitudes in fully compactified theories (at least in supersymmetric cases) leads to a bottom-up prediction for the existence of non-trivial dualities. In particular, finiteness requires the moduli space of massless fields to be compactifiable, meaning that its volume must be finite or at least grow no faster than that of Euclidean space. Moreover, we relate the compactifiability of moduli spaces to the condition that the lattice of charged objects transform in a semisimple representation under the action of the duality group. These ideas are supported by a wide variety of string theory examples.
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- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
List of changes
To address the minor revisions in referee report 1, we: - Added a sentence to the footnote 1 to explain that the additional elements in the $\GL^+$-lift of the 10D type IIB duality group do not act on moduli space and therefore do not affect the compactifiability criterion. - We clarified our point by replacing the following sentence on page 48: "Thus, they are in some sense the only states that we should count when studying the sigma model probing M in this limit.” with this one "In particular, higher energy states will be sensitive to the tower of light states present in the $\Lambda\rightarrow 0$ limit.”
To address the minor revisions in referee report 2, we: - Added a short footnote at the bottom of page 8 - Edited the paragraph below equation 2.1 to further explain why duality groups are discrete - Fixed the typo
Current status:
Reports on this Submission
Report
The first sentence after eq. (2.1) is now grammatically incoherent.
Additionally, I do not find that the newly added footnote on page 8 satisfactorily addresses my earlier remark. The misleading statement that eq. (2.5) is a definition of the duality group remains. I would recommend the authors to be more precise here. This also applies, for example, to the subsequent paragraph.
Recommendation
Ask for minor revision