Infinitely many M2-instanton corrections to M-theory on G2-manifolds

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M-theory on compact eight-manifolds with Spin(7)-holonomy is a framework for geometric engineering of 3d N = 1 gauge theories coupled to gravity. We propose a new construction of such Spin(7)-manifolds, based on a generalized connected sum, where the building blocks are a Calabi-Yau four-fold and a G 2 -holonomy manifold times a circle, respectively, which both asymptote to a Calabi-Yau three-fold times a cylinder. The generalized connected sum construction is first exemplified for Joyce orbifolds, and is then used to construct examples of new compact manifolds with Spin(7)-holonomy. In instances when there is a K3-fibration of the Spin(7)-manifold, we test the spectra using duality to heterotic on a T 3 -fibered G 2 -holonomy manifold, which are shown to be precisely the recently discovered twisted-connected sum constructions.

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confidence: 99%

“…This observation may be used to study non-perturbative corrections, e.g. M2-brane instantons [16], which has been initiated for TCS-manifolds in [7,8,14].…”

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confidence: 99%

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

Braun¹,

Schäfer‐Nameki²

2018

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“…In particular we do not consider deformations, where the topology changes or the associative ceases to exists, or splits. The type of wall-crossing considered by Joyce in [41] is more closely connected to the M2-instanton partition function, as recently discussed in [56].…”

Section: Jhep07(2018)052mentioning

confidence: 87%

“…In fact one of the most common associative cycles in compact G 2 -manifolds that are known are three-spheres or simple modifications thereof -see e.g. the twisted connected sum constructions in [26][27][28], where associatives are either S 3 or diffeomorphic to S 2 × S 1 , or more recently the conjecture for an infinite family of associative three-cycles with topology S 3 in these geometries [56].…”

Section: Specializingmentioning

confidence: 99%

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

Eckhard

Schäfer‐Nameki

Wong

2018

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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 .

“…To illustrate this further, let us look, for example, at a Calabi-Yau one-fold, that is a two-torus, with trivial bundle (no A and B fields) and a geometric description either as a cubic curve in È 2 or as a degree 6 curve inside the weighted projective space È 1,2,3 . In either case, there is only a single ambient space factor (and, hence, one U(1)), a single constraint field P , and three coordinate fields Z I with charges È 2 [3] : Q I = (1, 1, 1) , − q 1 = 3 , È 1,2,3 [6] : Q I = (1, 2, 3) , − q 1 = 6 .…”

Section: Review Of Gauged Linear Sigma Modelsmentioning

confidence: 99%

Heterotic instantons for monad and extension bundles

Buchbinder

Lukas

Ovrut

et al. 2020

We consider non-perturbative superpotentials from world-sheet instantons wrapped on holomorphic genus zero curves in heterotic string theory. These superpotential contributions feature prominently in moduli stabilization and large field axion inflation, which makes their presence or absence, as well as their functional dependence on moduli, an important issue. We develop geometric methods to compute the instanton superpotentials for heterotic string theory with monad and extension bundles. Using our methods, we find a variety of examples with a non-vanishing superpotential. In view of standard vanishing theorems, we speculate that these results are likely to be attributed to the non-compactness of the instanton moduli space. We test this proposal, for the case of monad bundles, by considering gauged linear sigma models where compactness of the instanton moduli space can be explicitly checked. In all such cases, we find that the geometric results are consistent with the vanishing theorems. Surprisingly, linearly dependent Pfaffians even arise for cases with a noncompact instanton moduli space. This suggests some gauged linear sigma models with a non-compact instanton moduli space may still have a vanishing instanton superpotential. 1