A bstract We introduce and initiate the study of a general class of 2 d $$ \mathcal{N} $$ 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 BFT 2 ’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 master and moduli spaces. Invariance of the moduli space is indeed a powerful criterion for identifying theories in the same triality class. We also investigate the reducibility of these theories.
more »
« less
Calabi-Yau products: graded quivers for general toric Calabi-Yaus
A bstract 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 − 2 m )-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 CY m +2 and CY n +2 produces the quiver theory for a related CY m + n +3 . This method significantly supersedes existing ones, enabling the simple determination of quiver theories for geometries that were previously out of practical reach.
more »
« less
- NSF-PAR ID:
- 10232609
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2021
- Issue:
- 2
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
We revisit the correspondence between Calabi-Yau (CY) threefoldisolated singularities \mathbf{X} 𝐗 and five-dimensional superconformal field theories (SCFTs), which ariseat low energy in M-theory on the space-time transverse to \mathbf{X} 𝐗 .Focussing on the case of toric CY singularities, we analyze the“gauge-theory phases” of the SCFT by exploiting fiberwise M-theory/typeIIA duality. In this setup, the low-energy gauge group simply arises onstacks of coincident D6-branes wrapping 2-cycles in some ALE space oftype A_{M-1} A M − 1 fibered over a real line, and the map between the Kähler parameters of \mathbf{X} 𝐗 and the Coulomb branch parameters of the field theory (masses and VEVs)can be read off systematically. Different type IIA “reductions” giverise to different gauge theory phases, whose existence depends on theparticular (partial) resolutions of the isolated singularity \mathbf{X} 𝐗 .We also comment on the case of non-isolated toric singularities.Incidentally, we propose a slightly modified expression for theCoulomb-branch prepotential of 5d \mathcal{N}=1 𝒩 = 1 gauge theories.more » « less
-
A bstract Reflexive polytopes in n dimensions have attracted much attention both in mathematics and theoretical physics due to their connection to Fano n -folds and mirror symmetry. This work focuses on the 18 regular reflexive polytopes corresponding to smooth Fano 3-folds. For the first time, we show that all 18 regular reflexive polytopes have corresponding 2 d (0 , 2) gauge theories realized by brane brick models. These 2 d gauge theories can be considered as the worldvolume theories of D1-branes probing the toric Calabi-Yau 4-singularities whose toric diagrams are given by the associated regular reflexive polytopes. The generators of the mesonic moduli space of the brane brick models are shown to form a lattice of generators due to the charges under the rank 3 mesonic flavor symmetry. It is shown that the lattice of generators is the exact polar dual reflexive polytope to the corresponding toric diagram of the brane brick model. This duality not only highlights the close relationship between the geometry and 2 d gauge theory, but also opens up pathways towards new discoveries in relation to reflexive polytopes and brane brick models.more » « less
-
more » « less
Abstract Catalysis of
O ‐atom transfer (OAT) reactions is a characteristic of both natural (enzymatic) and synthetic molybdenum‐oxo and ‐peroxo complexes. These reactions can employ a variety of terminal oxidants, e. g. DMSO,N ‐oxides, and peroxides, etc., but rarely molecular oxygen. Here we demonstrate the ability of a set of Schiff‐base‐MoO2complexes (cy‐salen)MoO2(cy‐salen=N,N’ ‐cyclohexyl‐1,2‐bis‐salicylimine) to catalyze the aerobic oxidation of PPh3. We also report the results of a DFT computational investigation of the catalytic pathway, including the identification of energetically accessible intermediates and transition states, for the aerobic oxidation of PMe3. Starting from the dioxo species, (cy‐salen)Mo(VI)O2(1 ), key reaction steps include: 1) associative addition of PMe3to an oxo‐O to give LMo(IV)(O)(OPMe3) (2 ); 2) OPMe3dissociation from2 to produce mono‐oxo complex (cy‐salen)Mo(IV)O (3 ); 3) stepwise O2association with3 via superoxo species (cy‐salen)Mo(V)(O)(η1‐O2) (4 ) to form the oxo‐peroxo intermediate (cy‐salen)Mo(VI)(O)(η2‐O2) (5 ); 4) theO ‐transfer reaction of PMe3with oxo‐peroxo species5 at the oxo‐group, rather than the peroxo unit leading, after OPMe3dissociation, to a monoperoxo species, (cy‐salen)Mo(IV)(η2‐O2) (7 ); and 5) regeneration of the dioxo complex (cy‐salen)Mo(VI)O2(1 ) from the monoperoxo triplet3 7 or singlet1 7 by a concerted, asynchronous electronic isomerization. An alternative pathway for recycling of the oxo‐peroxo species5 to the dioxo‐Mo1 via a bimetallic peroxo complex LMo(O)‐O−O‐Mo(O)L8 is determined to be energetically viable, but is unlikely to be competitive with the primary pathway for aerobic phosphine oxidation catalyzed by1 . -
more » « less
Abstract We continue earlier efforts in computing the dimensions of tangent space cohomologies of Calabi–Yau manifolds using deep learning. In this paper, we consider the dataset of all Calabi–Yau four-folds constructed as complete intersections in products of projective spaces. Employing neural networks inspired by state-of-the-art computer vision architectures, we improve earlier benchmarks and demonstrate that all four non-trivial Hodge numbers can be learned at the same time using a multi-task architecture. With 30% (80%) training ratio, we reach an accuracy of 100% for
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/JHEP02(2021)174
