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Home > Journal of High Energy Physics (Springer/SISSA) > Graded quivers and B-branes at Calabi-Yau singularities |

Closset, Cyril (0000 0004 1936 8948, Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG, U.K.) ; Franco, Sebastián (0000 0001 2264 7145, Physics Department, The City College of the CUNY, 160 Convent Avenue, New York, NY, 10031, U.S.A.) (0000000122985718, The Graduate School and University Center, The City University of New York, 365 Fifth Avenue, New York, NY, 10016, U.S.A.) ; Guo, Jirui (0000 0001 0125 2443, Department of Physics and Center for Field Theory and Particle Physics, Fudan University, 220 Handan Road, 200433, Shanghai, China) ; Hasan, Azeem (0000 0001 2264 7145, Physics Department, The City College of the CUNY, 160 Convent Avenue, New York, NY, 10031, U.S.A.) (0000000122985718, The Graduate School and University Center, The City University of New York, 365 Fifth Avenue, New York, NY, 10016, U.S.A.)

14 March 2019

**Abstract: **A graded quiver with superpotential is a quiver whose arrows are assigned degrees c ∈ {0 , 1 , ⋯ , m }, for some integer m ≥ 0, with relations generated by a superpotential of degree m − 1. Ordinary quivers ( m = 1) often describe the open string sector of D-brane systems; in particular, they capture the physics of D3-branes at local Calabi-Yau (CY) 3-fold singularities in type IIB string theory, in the guise of 4d N $$ \mathcal{N} $$ = 1 supersymmetric quiver gauge theories. It was pointed out recently that graded quivers with m = 2 and m =3 similarly describe systems of D-branes at CY 4-fold and 5-fold singularities, as 2d N $$ \mathcal{N} $$ = (0 , 2) and 0d N $$ \mathcal{N} $$ = 1 gauge theories, respectively. In this work, we further explore the correspondence between m -graded quivers with superpotential, Q ( m ) , and CY ( m + 2)-fold singularities, X m +2 . For any m , the open string sector of the topological B-model on X m +2 can be described in terms of a graded quiver. We illustrate this correspondence explicitly with a few infinite families of toric singularities indexed by m ∈ ℕ, for which we derive “toric” graded quivers associated to the geometry, using several complementary perspectives. Many interesting aspects of supersymmetric quiver gauge theories can be formally extended to any m ; for instance, for one family of singularities, dubbed C ( Y 1,0 (ℙ m )), that generalizes the conifold singularity to m > 1, we point out the existence of a formal “duality cascade” for the corresponding graded quivers.

**Published in: ****JHEP 1903 (2019) 053**
**Published by: **Springer/SISSA

**DOI: **10.1007/JHEP03(2019)053

**arXiv: **1811.07016

**License: **CC-BY-4.0