Spin(7)-manifolds as generalized connected sums and 3d $$ \mathcal{N}=1 $$ theories

Braun, Andreas P.; Schäfer‐Nameki, Sakura

doi:10.1007/jhep06(2018)103

Cited by 23 publications

(58 citation statements)

References 48 publications

(114 reference statements)

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“…This last assumptions is slightly weaker than the assumptions made for technical simplicity in[27]. By following the same analysis presented there, it is straightforward to see that (4.2) holds in the present case.…”

mentioning

confidence: 64%

“…This potentially constrains which antiholomorphic involutions and which resolution can be chosen to construct M ∨ and hence Z ∨ − . As shown in [27], the GCS construction of Spin (7) manifolds is closely related to the work of [35], in which Spin (7) manifolds are found by resolving anti-holomorphic quotients of Calabi-Yau fourfolds. This offers another possible perspective on mirror maps of Spin (7) manifolds in general, and the ones considered here in particular.…”

Section: A Mirror Map For Gcs Spin(7) Manifoldsmentioning

confidence: 96%

“…Second, compactifications of heterotic string theory on TCS G 2 manifolds should have a lift to M-Theory on a Spin (7) manifold which can also be decomposed into two pieces. By applying an appropriate fibrewise duality map to a TCS G 2 manifold, the authors of [27] argued that one finds a decomposition such as (4.1) on the M-Theory side and checked the equivalence of the spectra of light fields in a few examples. Finally, acyl G 2 manifolds Z − can be realized as (a resolution of) a quotient (X 3 × R) /Z 2 in which the Z 2 acts as an anti-holomorphic quotient on X 3 and as t → −t on R. In this case, Z can be globally described as a resolution of an anti-holomorphic quotient of a suitably chosen Calabi-Yau fourfold Y , recovering the construction of [35].…”

Section: Constructing Spin(7) Manifolds As Generalized Connected Sumsmentioning

confidence: 99%

“…For an acyl Calabi-Yau fourfold Z + and an acyl G 2 manifold Z − given as a resolution of (X 3 × R) /Z 2 , the Betti numbers of Z are found to be [27] b 1 (Z) = 0 b 2 (Z) = n 2…”

Section: Constructing Spin(7) Manifolds As Generalized Connected Sumsmentioning

confidence: 99%

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On mirror maps for manifolds of exceptional holonomy

Braun

Majumder

Otto

2019

J. High Energ. Phys.

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We study mirror symmetry of type II strings on manifolds with the exceptional holonomy groups G 2 and Spin(7). Our central result is a construction of mirrors of Spin(7) manifolds realized as generalized connected sums. In parallel to twisted connected sum G 2 manifolds, mirrors of such Spin(7) manifolds can be found by applying mirror symmetry to the pair of non-compact manifolds they are glued from. To provide non-trivial checks for such geometric mirror constructions, we give a CFT analysis of mirror maps for Joyce orbifolds in several new instances for both the Spin(7) and the G 2 case. For all of these models we find possible assignments of discrete torsion phases, work out the action of mirror symmetry, and confirm the consistency with the geometrical construction. A novel feature appearing in the examples we analyse is the possibility of frozen singularities.

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mentioning

confidence: 64%

Section: A Mirror Map For Gcs Spin(7) Manifoldsmentioning

confidence: 96%

Section: Constructing Spin(7) Manifolds As Generalized Connected Sumsmentioning

confidence: 99%

“…For an acyl Calabi-Yau fourfold Z + and an acyl G 2 manifold Z − given as a resolution of (X 3 × R) /Z 2 , the Betti numbers of Z are found to be [27] b 1 (Z) = 0 b 2 (Z) = n 2…”

Section: Constructing Spin(7) Manifolds As Generalized Connected Sumsmentioning

confidence: 99%

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On mirror maps for manifolds of exceptional holonomy

Braun

Majumder

Otto

2019

J. High Energ. Phys.

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“…from orbifolds of N = 2 theories. Thanks to some resurgence in interest in dualities in 3d theories without [78][79][80][81] and with minimal [82][83][84][85] supersymmetry, as well as new geometric constructions [86], further progress on 3d N = 1 theories may be on the horizon. Another interesting direction to pursue is the relation of the N = 1 3d-3d correspondence to an N = 1 AGT type correspondence, much along the lines of [4], where the 3d theories are defects in the 4d N = 1 theories.…”

Section: Jhep07(2018)052mentioning

confidence: 99%

An $$ \mathcal{N}=1 $$ 3d-3d correspondence

Eckhard

Schäfer‐Nameki

Wong

2018

J. High Energ. Phys.

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M5-branes on an associative three-cycle M 3 in a G 2 -holonomy manifold give rise to a 3d N = 1 supersymmetric gauge theory, T N =1 [M 3 ]. We propose an N = 1 3d-3d correspondence, based on two observables of these theories: the Witten index and the S 3 -partition function. The Witten index of a 3d N = 1 theory T N =1 [M 3 ] is shown to be computed in terms of the partition function of a topological field theory, a super-BFmodel coupled to a spinorial hypermultiplet (BFH), on M 3 . The BFH-model localizes on solutions to a generalized set of 3d Seiberg-Witten equations on M 3 . Evidence to support this correspondence is provided in the abelian case, as well as in terms of a direct derivation of the topological field theory by twisted dimensional reduction of the 6d (2, 0) theory. We also consider a correspondence for the S 3 -partition function of the T N =1 [M 3 ] theories, by determining the dimensional reduction of the M5-brane theory on S 3 . The resulting topological theory is Chern-Simons-Dirac theory, for a gauge field and a twisted harmonic spinor on M 3 , whose equations of motion are the generalized 3d Seiberg-Witten equations. For generic G 2 -manifolds the theory reduces to real Chern-Simons theory, in which case we conjecture that the S 3 -partition function of T N =1 [M 3 ] is given by the Witten-ReshetikhinTuraev invariant of M 3 .

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F‐theory and Dark Energy

Heckman

Lawrie

Lin

et al. 2019

Fortschritte der Physik

125

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Motivated by its potential use as a starting point for solving various cosmological constant problems, we study F-theory compactified on the warped product R time × S 3 × Y 8 where Y 8 is a Spi n(7) manifold, and the S 3 factor is the target space of an SU (2) Wess-Zumino-Witten (WZW) model at level N. Reduction to M-theory exploits the abelian duality of this WZW model to an S 3 /Z N orbifold. In the large N limit, the untwisted sector is captured by 11D supergravity. The local dynamics of intersecting 7-branes in the Spi n(7) geometry is controlled by a Donaldson-Witten twisted gauge theory coupled to defects. At late times, the system is governed by a 1D quantum mechanics system with a ground state annihilated by two real supercharges, which in four dimensions would appear as "N = 1/2 supersymmetry" on a curved background. This leads to a cancellation of zero point energies in the 4D field theory but a split mass spectrum for superpartners of order m 4D ∼ √ M IR M UV specified by the IR and UV cutoffs of the model. This is suggestively close to the TeV scale in some scenarios. The classical 4D geometry has an intrinsic instability which can produce either a collapsing or expanding Universe, the latter providing a promising starting point for a number of cosmological scenarios. The resulting 1D quantum mechanics in the time direction also provides an appealing starting point for a more detailed study of quantum cosmology.

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Spin(7)-manifolds as generalized connected sums and 3d $$ \mathcal{N}=1 $$ theories

Cited by 23 publications

References 48 publications

On mirror maps for manifolds of exceptional holonomy

On mirror maps for manifolds of exceptional holonomy

An $$ \mathcal{N}=1 $$ 3d-3d correspondence

F‐theory and Dark Energy

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