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Generalized Toric Polygons, T-branes, and 5d SCFTs
by Antoine Bourget, Andrés Collinucci, Sakura Schafer-Nameki
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Submission summary
| Authors (as registered SciPost users): | Antoine Bourget · Sakura Schäfer-Nameki |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2301.05239v2 (pdf) |
| Date accepted: | 2025-02-18 |
| Date submitted: | 2025-01-28 13:13 |
| Submitted by: | Bourget, Antoine |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
5d Superconformal Field Theories (SCFTs) are intrinsically strongly-coupled UV fixed points, whose realization hinges on string theoretic methods: they can be constructed by compactifying M-theory on local Calabi-Yau threefold singularities or alternatively from the world-volume of 5-brane-webs in type IIB string theory. There is a correspondence between 5-brane-webs and toric Calabi-Yau threefolds, however this breaks down when multiple 5-branes are allowed to end on a single 7-brane. In this paper, we extend this connection and provide a geometric realization of brane configurations including 7-branes. A web with 7-branes defines a so-called generalized toric polygon (GTP), which corresponds to combinatorial data that is obtained by removing vertices along external edges of a toric polygon. We identify the geometries associated to GTPs as non-toric deformations of toric Calabi-Yau threefolds and provide a precise, algebraic description of the geometry, when 7-branes are introduced along a single edge. The key ingredients in our analysis are T-branes in a type IIA frame, which includes D6-branes. We show that performing Hanany-Witten moves for the 7-branes on the type IIB side corresponds to switching on semisimple vacuum expectation values on the worldvolume of D6-branes, which in turn uplifts to complex structure deformations of the Calabi-Yau geometries. We test the proposal by computing the crepant resolutions of the deformed geometries, thereby checking consistency with the expected properties of the SCFTs.
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- 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
List of changes
We have addressed the various points raised by the three referees as detailed below.
Referee 1 :
\begin{itemize}
\item We have added a more detailed explanation of the brane recombination process in section 1, around equations (1.3) to (1.9). We have also included a reference to this after equation (3.45).
\item Regarding question (a.), we have added a paragraph at the beginning of section 5.2 to clarify the origin of the matter states which are used to analyze the global symmetries.
\item Regarding question (b.) about equation (5.14), we have added an explanation about the $su(2)$ factor, whose representations can not be extracted directly from the CFD, hence the focus on the $su(4)^2$ representations only.
\item We have corrected the power of $Z$ in equation (4.9).
\end{itemize}
Referee 2 :
\begin{itemize}
\item We have added sentences below (2.7) to clarify the physical interest of the SNF.
\item The partition notation has been explicitly introduced in a paragraph on page 9. The same notation is then used in equations (2.10) and (2.27).
\item To address the requests on the Smith Normal Forms, we have slightly expanded the discussion in the Example on page 9, and we have added a clarifying sentence \textit{``This gives an algorithmic way to decide whether two tachyon maps encode equivalent physical systems. Several examples are given below. "}. We have also corrected a sign error in equation (2.11).
\end{itemize}
Referee 3 :
\begin{itemize}
\item The minor revision is addressed by adding to the introduction a sentence clarifying why the language of GTPs is used: \textit{The results of this paper could in principle be phrased purely in the language of stacks of D5 branes ending on D7 branes, dualized to a D6 setup. However, the GTP formalism is adopted as it paves the way towards the necessary generalizations to encompass arbitrary 5d SCFTs. }
\end{itemize}
Published as SciPost Phys. 18, 079 (2025)
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