TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.18.3.079
TI  - Generalized toric polygons, T-branes, and 5d SCFTs
PY  - 2025/03/04
UR  - https://www.scipost.org/SciPostPhys.18.3.079
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 18
IS  - 3
SP  - 079
A1  - Bourget, Antoine
AU  - Collinucci, Andrés
AU  - Schäfer-Nameki, Sakura
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.18.3.079,
	title={{Generalized toric polygons, T-branes, and 5d SCFTs}},
	author={Antoine Bourget and Andrés Collinucci and Sakura Schäfer-Nameki},
	journal={SciPost Phys.},
	volume={18},
	pages={079},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.18.3.079},
	url={https://scipost.org/10.21468/SciPostPhys.18.3.079},
}