Engineering quantum field theories in String Theory in terms of branes is a powerful approach for understanding their dynamics. We review recent progress in the realization of 2d \(\mathcal {N}=(0,2)\) gauge theories in terms of branes. We discuss Brane Brick Models, a new class of Type IIA brane configurations which are T-dual to D1-branes over singular toric Calabi-Yau 4-folds. They fully encode the infinite class of 2d \(\mathcal {N}=(0,2)\) quiver gauge theories on the worldvolume of the D1-branes and significantly streamline their connection to the probed geometries. As an application, we explain how these constructions provide a brane realization of triality. We also comment on the realization of 2d \(\mathcal {N}=(0,1)\) theories via Spin(7) orientifolds. This note is based on the author’s talk at the Nankai Symposium on Mathematical Dialogues celebrating the 110th anniversary of the birth of Prof. S.-S. Chern.

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2d Supersymmetric Gauge Theories, D-Branes and Trialities

  • Sebastián Franco

摘要

Engineering quantum field theories in String Theory in terms of branes is a powerful approach for understanding their dynamics. We review recent progress in the realization of 2d \(\mathcal {N}=(0,2)\) gauge theories in terms of branes. We discuss Brane Brick Models, a new class of Type IIA brane configurations which are T-dual to D1-branes over singular toric Calabi-Yau 4-folds. They fully encode the infinite class of 2d \(\mathcal {N}=(0,2)\) quiver gauge theories on the worldvolume of the D1-branes and significantly streamline their connection to the probed geometries. As an application, we explain how these constructions provide a brane realization of triality. We also comment on the realization of 2d \(\mathcal {N}=(0,1)\) theories via Spin(7) orientifolds. This note is based on the author’s talk at the Nankai Symposium on Mathematical Dialogues celebrating the 110th anniversary of the birth of Prof. S.-S. Chern.