M-theory on Elliptic Calabi-Yau Threefolds and 6d Anomalies

Esole, Mboyo; Shao, Shu-Heng

doi:10.48550/arxiv.1504.01387

Cited by 20 publications

(40 citation statements)

References 80 publications

(180 reference statements)

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“…Reference [3] provided a description of XT for all T that are rank one 6d SCFTs. This was done by explicitly performing resolutions of X T using methods described in detail in [9][10][11][12][13][14][15]. In this paper, we extend the work of [3] and provide a description of XT for T that are 6d SCFTs of any arbitrary rank (see [16][17][18] for related analyses of F-theory models involving collisions of elliptic fibers in cases of semi-simple, as opposed to simple, gauge algebras.…”

Section: Introductionmentioning

confidence: 99%

Classifying 5d SCFTs via 6d SCFTs: arbitrary rank

Bhardwaj

Jefferson

2019

J. High Energ. Phys.

111

175

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According to a conjecture, all 5d SCFTs should be obtainable by rankpreserving RG flows of 6d SCFTs compactified on a circle possibly twisted by a background for the discrete global symmetries around the circle. For a 6d SCFT admitting an F-theory construction, its untwisted compactification admits a dual M-theory description in terms of a "parent" Calabi-Yau threefold which captures the Coulomb branch of the compactified 6d SCFT. The RG flows to 5d SCFTs can then be identified with a sequence of flop transitions and blowdowns of the parent Calabi-Yau leading to "descendant" Calabi-Yau threefolds which describe the Coulomb branches of the resulting 5d SCFTs. An explicit description of parent Calabi-Yaus is known for untwisted compactifications of rank one 6d SCFTs. In this paper, we provide a description of parent Calabi-Yaus for untwisted compactifications of arbitrary rank 6d SCFTs. Since 6d SCFTs of arbitrary rank can be viewed as being constructed out of rank one SCFTs, we accomplish the extension to arbitrary rank by identifying a prescription for gluing together Calabi-Yaus associated to rank one 6d SCFTs. 1 lbhardwaj@fas.harvard.edu 2 patrickjefferson@fas.harvard.edu 42 4.8 e 6 , e 7 , e 8 and f 4 48 4.9 su(3) on −3 50 -i -5 Gluing rules 50 5.1 Gluing of su(m), m ≥ 1 or m =6 and su(n), n ≥ 1 50 5.2 Gluing of sp(m), m ≥ 1 and su(n), n ≥ 1 52 5.3 Gluing of sp(m), m ≥ 1 and so(2r), r ≥ 4 52 5.4 Gluing of sp(m), m ≥ 1 and so(2r + 1), r ≥ 4 53 5.5 Gluing of sp(m), m ≥ 1 and so(7) 53 5.6 Gluing of sp(m), m ≥ 1 and g 2 54 5.7 Gluings of sp(0) = E-string 54 5.7.1 Simply laced 55 5.7.2 Non-simply laced 66 6 Future work 76 A User's guide for Mathematica notebook Pushforward.nb 77 • The set of compact holomorphic surfaces S i .

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Section: Introductionmentioning

confidence: 99%

Classifying 5d SCFTs via 6d SCFTs: arbitrary rank

Bhardwaj

Jefferson

2019

J. High Energ. Phys.

111

175

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“…A proof of this conjecture will likely rely heavily on ideas from Mori's program along the lines of [13]. The Intriligator-Morrision-Seiberg prepotential F (ϕ) can also be obtained geometrically [14,16,11].…”

Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

“…Given two points P and Q in E * n , such that P ≤ Q, consider the rectangle with vertical and horizontal edges whose NE-SW diagonal is the segment P Q. The lattice points of this rectangle are exactly the points of the interval 16 for examples of intervals in E * n . The discrete quarter-plane N 2 is equipped with a grading given by the level function.…”

Section: Preliminaries On the Poset E *mentioning

confidence: 99%

Incidence geometry in a Weyl chamber I: GL

Esole

Jackson

Jagadeesan

et al. 2020

Advances in Applied Mathematics

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We study the central hyperplane arrangement whose hyperplanes are the vanishing loci of the weights of the first and the second fundamental representations of gl n restricted to the dual fundamental Weyl chamber. We obtain generating functions that count flats and faces of a given dimension. This counting is interpreted in physics as the enumeration of the phases of the Coulomb and mixed Coulomb-Higgs branches of a five dimensional gauge theory with 8 supercharges in presence of hypermultiplets transforming in the fundamental and antisymmetric representation of a U (n) gauge group as described by the Intriligator-Morrison-Seiberg superpotential.2010 Mathematics Subject Classification. 05E10, 52C35, 05A15, 17B10, 17B81.

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“…The theory of hyperplane arrangements has connections to many different areas of pure and applied mathematics [1,2,3]. A new type of hyperplane arrangement [4] defined by a representation R of a reductive Lie algebra g has emerged from string geometry [5] and is relevant in the study of elliptic fibrations [6,7,8,9]. Its hyperplanes are the kernels of the weights of R. Moreover, the arrangement lives in a dual fundamental Weyl chamber of g instead of a full Cartan subalgebra.…”

Section: Introductionmentioning

confidence: 99%

“…When the Calabi-Yau variety is elliptically fibered, it has been conjectured that the gauge algebra g and the representation R can be determined from the singular fibers of the elliptic fibration over points of codimensions one and two in the base of the fibration, respectively [5,12,13,14,15,16,17]. Chambers are conjectured to correspond to crepant resolutions of the Weierstrass model of the elliptic fibration, and the resolutions corresponding to chambers that share a facet are conjectured to be related by an (extremal) flop [6,7,8,9,10,18,20].…”

Section: Introductionmentioning

confidence: 99%

Incidence geometry in a Weyl chamber II: SL

Esole

Jackson

Jagadeesan

et al. 2020

Advances in Applied Mathematics

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We study the polyhedral geometry of the hyperplanes orthogonal to the weights of the first and the second fundamental representations of sl n inside the dual fundamental Weyl chamber. We obtain generating functions that enumerate the flats and the faces of a fixed dimension. In addition, we describe the extreme rays of the incidence geometry and classify simplicial faces.From the perspective of supersymmetric gauge theories with 8 supercharges in five dimensional spacetime, the poset of flats is isomorphic to the network of mixed Coulomb-Higgs branches. On the other hand, the poset of faces is conjectured to be isomorphic to the network of crepant partial resolutions of an elliptic fibration with gauge algebra sl n and "matter representation" given by the sum of the first two fundamental representations.

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M-theory on Elliptic Calabi-Yau Threefolds and 6d Anomalies

Cited by 20 publications

References 80 publications

Classifying 5d SCFTs via 6d SCFTs: arbitrary rank

Classifying 5d SCFTs via 6d SCFTs: arbitrary rank

Incidence geometry in a Weyl chamber I: GL

Incidence geometry in a Weyl chamber II: SL

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