3d printing of 2d $$ \mathcal{N}=\left(0,2\right) $$ gauge theories

Guo

et al. 2019

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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 = 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 = (0, 2) and 0d 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. arXiv:1811.07016v1 [hep-th]

Section: The Graded Quiversmentioning

confidence: 99%

Section: The Graded Quiversmentioning

confidence: 99%

Section: The Graded Quiversmentioning

confidence: 99%

Section: The Geometriesmentioning

confidence: 99%

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Graded quivers and B-branes at Calabi-Yau singularities

Closset

Guo

et al. 2019

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“…, v m+1 . Let us now review the quiver theories for these geometries, which were first derived in [20] by a combination of the 3d printing algorithm of [40] with partial resolution and, independently, using the topological B-model. The quiver has m + 1 nodes which we will label by 0, · · · , m. The arrows are:…”

Section: Chiral Cycles For Small Mmentioning

confidence: 99%

Graded quivers, generalized dimer models and toric geometry

Hasan

2019

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The open string sector of the topological B-model model on CY (m + 2)-folds is described by m-graded quivers with superpotentials. This correspondence extends to general m the well known connection between CY (m + 2)-folds and gauge theories on the worldvolume of D(5 − 2m)-branes for m = 0, . . . , 3. We introduce mdimers, which fully encode the m-graded quivers and their superpotentials, in the case in which the CY (m+2)-folds are toric. Generalizing the well known m = 1, 2 cases, mdimers significantly simplify the connection between geometry and m-graded quivers.A key result of this paper is the generalization of the concept of perfect matching, which plays a central role in this map, to arbitrary m. We also introduce a simplified algorithm for the computation of perfect matchings, which generalizes the Kasteleyn matrix approach to any m. We illustrate these new tools with a few infinite families of CY singularities. arXiv:1904.07954v1 [hep-th] 16 Apr 2019 9 Chiral cycles and perfect matchings for Y 1,0 (P m ) 35 9.1 Chiral cycles and the moduli space 37 -i -10 Orbifolds of C m+2 39 10.1 Orbifolds of C m+2 with SU (m + 2) global symmetry 43 11 Conclusions 44 A Perfect matchings for F (m) 0 46 B Perfect matchings for general orbifolds of C m+2 483 The framework of m-graded quivers can be extended to theories with gauge groups that are not unitary and with fields that do not transform in the bifundamental or adjoint representations, i.e. theories that are not of quiver type. We will not consider these possibilities in this paper. 4 The range of degrees in (2.3) is just a conventional choice. The n c "fundamental" degrees can be picked differently. Moreover, as we will later illustrate in examples, sometimes it is convenient to deal with all possible values of the degrees. For every arrow, either Φ (c) ij or Φ (m−c) jican be regarded as the fundamental object, while the other one is its conjugate.

Spin(7) orientifolds and 2d $$ \mathcal{N} $$ = (0, 1) triality

Mininno

Uranga

et al. 2022

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We present a new, geometric perspective on the recently proposed triality of 2d $$ \mathcal{N} $$ N = (0, 1) gauge theories, based on its engineering in terms of D1-branes probing Spin(7) orientifolds. In this context, triality translates into the fact that multiple gauge theories correspond to the same underlying orientifold. We show how Spin(7) orientifolds based on a particular involution, which we call the universal involution, give rise to precisely the original version of $$ \mathcal{N} $$ N = (0, 1) triality. Interestingly, our work also shows that the space of possibilities is significantly richer. Indeed, general Spin(7) orientifolds extend triality to theories that can be regarded as consisting of coupled $$ \mathcal{N} $$ N = (0, 2) and (0, 1) sectors. The geometric construction of 2d gauge theories in terms of D1-branes at singularities therefore leads to extensions of triality that interpolate between the pure $$ \mathcal{N} $$ N = (0, 2) and (0, 1) cases.