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Full-Text Articles in Physical Sciences and Mathematics
Bft2: A General Class Of 2d N = (0, 2) Theories, 3-Manifolds And Toric Geometry, Sebastían Franco, Xingyang Yu
Bft2: A General Class Of 2d N = (0, 2) Theories, 3-Manifolds And Toric Geometry, Sebastían Franco, Xingyang Yu
Publications and Research
We introduce and initiate the study of a general class of 2d N = (0, 2) quiver gauge theories, defined in terms of certain 2-dimensional CW complexes on oriented 3- manifolds. We refer to this class of theories as BFT2’s. They are natural generalizations of Brane Brick Models, which capture the gauge theories on D1-branes probing toric Calabi-Yau 4-folds. The dynamics and triality of the gauge theories translate into simple transformations of the underlying CW complexes. We introduce various combinatorial tools for analyzing these theories and investigate their connections to toric Calabi-Yau manifolds, which arise as their …
The Octagon At Large M, Riccardo Argurio, Matteo Bertolini, Sebastían Franco, Eduardo García-Valdecasas, Shani Meynet, Antoine Pasternak, Valdo Tatitscheff
The Octagon At Large M, Riccardo Argurio, Matteo Bertolini, Sebastían Franco, Eduardo García-Valdecasas, Shani Meynet, Antoine Pasternak, Valdo Tatitscheff
Publications and Research
Recently, the first instance of a model of D-branes at Calabi-Yau singularities where supersymmetry is broken dynamically into stable vacua has been proposed. This construction was based on a system of N regular and M = 1 fractional branes placed at the tip of the so-called (orientifolded) Octagon singularity. In this paper we show that this model admits a large M generalization, having the same low energy effective dynamics. This opens up the possibility that the effect on geometry is smooth, and amenable to describing the gauge theory all along the RG flow, including the deep IR, in terms of …
Calabi-Yau Products: Graded Quivers For General Toric Calabi-Yaus, Sebastián Franco, Azeem Hasan
Calabi-Yau Products: Graded Quivers For General Toric Calabi-Yaus, Sebastián Franco, Azeem Hasan
Publications and Research
The open string sector of the topological B-model on CY (m + 2)-folds is described by m-graded quivers with superpotentials. This correspondence generalizes the connection between CY (m + 2)-folds and gauge theories on the worldvolume of D(5 − 2m)-branes for m = 0, . . . , 3 to arbitrary m. In this paper we introduce the Calabi-Yau product, a new algorithm that starting from the known quiver theories for a pair of toric CYm+2 and CYn+2 produces the quiver theory for a related CYm+n+3 …
Dimers, Orientifolds And Anomalies, Riccardo Argurio, Matteo Bertolini, Sebastían Franco, Eduardo Garcia-Valdecasas, Shani Meynet, Antoine Pasternak, Valdo Tatitscheff
Dimers, Orientifolds And Anomalies, Riccardo Argurio, Matteo Bertolini, Sebastían Franco, Eduardo Garcia-Valdecasas, Shani Meynet, Antoine Pasternak, Valdo Tatitscheff
Publications and Research
We study 4d N = 1 gauge theories engineered via D-branes at orientifolds of toric singularities, where gauge anomalies are cancelled without the introduction of non-compact flavor branes. Using dimer model techniques, we derive geometric criteria for establishing whether a given singularity can admit anomaly-free D-brane configurations purely based on its toric data and the type of orientifold projection. Our results therefore extend the dictionary between geometric properties of singularities and physical properties of the corresponding gauge theories.
On The Classification Of Duality Webs For Graded Quivers, Sebastían Franco, Azeem Hasan, Xingyang Yu
On The Classification Of Duality Webs For Graded Quivers, Sebastían Franco, Azeem Hasan, Xingyang Yu
Publications and Research
We study the m-graded quiver theories associated to CY (m+2)-folds and their order (m + 1) dualities. We investigate how monodromies give rise to mutation invariants, which in turn can be formulated as Diophantine equations characterizing the space of dual theories associated to a given geometry. We discuss these ideas in general and illustrate them in the case of orbifold theories. Interestingly, we observe that even in this simple context the corresponding Diophantine equations may admit an infinite number of seeds for m ≥ 2, which translates into an infinite number of disconnected duality webs. Finally, …
Graded Quivers, Generalized Dimer Models And Toric Geometry, Sebastián Franco, Azeem Hasan
Graded Quivers, Generalized Dimer Models And Toric Geometry, Sebastián Franco, Azeem Hasan
Publications and Research
The open string sector of the topological B-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 world-volume of D(5-2m)-branes for m = 0, ..., 3. We introduce m-dimers, 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, m-dimers significantly simplify the connection between geometry and m-graded quivers. A key …
3d Printing Of 2d N = (0, 2) Gauge Theories, Sebastían Franco, Azeem Hasan
3d Printing Of 2d N = (0, 2) Gauge Theories, Sebastían Franco, Azeem Hasan
Publications and Research
We introduce 3d printing, a new algorithm for generating 2d N = (0, 2) gauge theories on D1-branes probing singular toric Calabi-Yau 4-folds using 4d N = 1 gauge theories on D3-branes probing toric Calabi-Yau 3-folds as starting points. Equivalently, this method produces brane brick models starting from brane tilings. 3d printing represents a significant improvement with respect to previously available tools, allowing a straightforward determination of gauge theories for geometries that until now could only be tackled using partial resolution. We investigate the interplay between triality, an IR equivalence between different 2d N = …
Bipartite Field Theories And D-Brane Instantons, Sebastían Franco, Eduardo García-Valdecasas, Angel M. Uranga
Bipartite Field Theories And D-Brane Instantons, Sebastían Franco, Eduardo García-Valdecasas, Angel M. Uranga
Publications and Research
We study D-brane instantons in systems of D3-branes at toric CY 3-fold singularities. The instanton effect can be described as a backreaction modifying the geometry of the mirror configuration, in which the breaking of U(1) symmetries by the instanton translates into the recombination of gauge D-branes, which also directly generates the instanton-induced charged field theory operator. In this paper we describe the D-brane instanton backreaction in terms of a combinatorial operation in the bipartite dimer diagram of the original theory. Interestingly, the resulting theory is a general Bipartite Field Theory (BFT), defined by a bipartite graph tiling a general (possibly …