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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
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Submission summary
| Authors (as registered SciPost users): | Matilda Delgado |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202502_00029v2 (pdf) |
| Date accepted: | July 28, 2025 |
| Date submitted: | July 18, 2025, 12:54 p.m. |
| Submitted by: | Matilda Delgado |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| 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.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
We thank the referee for their comments.
List of changes
We have made the following edits to address the referee's points:
-We fixed the typo in the sentence after eq.(2.1)
-Above eq (2.5), we replaced "...where Γ' is possibly a quotient of the full duality group." with "...where Γ' (which is possibly a quotient of Γ) acts non-trivially on \mathcal{M}." We also replaced "This means that the duality group can in some sense be \textit{identified} with the topology of $\C{M}$" with "This means that the part of the duality group that acts non-trivially on moduli space can in some sense be \textit{identified} with the topology of $\C{M}$"?
-We fixed the typo in the sentence after eq.(2.1)
-Above eq (2.5), we replaced "...where Γ' is possibly a quotient of the full duality group." with "...where Γ' (which is possibly a quotient of Γ) acts non-trivially on \mathcal{M}." We also replaced "This means that the duality group can in some sense be \textit{identified} with the topology of $\C{M}$" with "This means that the part of the duality group that acts non-trivially on moduli space can in some sense be \textit{identified} with the topology of $\C{M}$"?
Published as SciPost Phys. 19, 047 (2025)