The F-theory geometry with most flux vacua
The F-theory geometry with most flux vacua
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具有最大通量真空的F理论几何
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Yi
中科院分区：
文献类型：
--
作者：
W. Taylor;Yi
A bstractApplying the Ashok-Denef-Douglas estimation method to elliptic Calabi-Yau fourfolds suggests that a single elliptic fourfold ℳmax$$ {\mathrm{\mathcal{M}}}_{\max } $$ gives rise to O10272,000$$ \mathcal{O}\left({10}^{272,000}\right) $$ F-theory flux vacua, and that the sum total of the numbers of flux vacua from all other F-theory geometries is suppressed by a relative factor of O10−3000$$ \mathcal{O}\left({10}^{-3000}\right) $$. The fourfold ℳmax$$ {\mathrm{\mathcal{M}}}_{\max } $$ arises from a generic elliptic fibration over a specific toric threefold base Bmax, and gives a geometrically non-Higgsable gauge group of E89 × F48 × (G2 × SU(2))16, of which we expect some factors to be broken by G-flux to smaller groups. It is not possible to tune an SU(5) GUT group on any further divisors in ℳmax$$ {\mathrm{\mathcal{M}}}_{\max } $$, or even an SU(2) or SU(3), so the standard model gauge group appears to arise in this context only from a broken E8 factor. The results of this paper can either be interpreted as providing a framework for predicting how the standard model arises most naturally in F-theory and the types of dark matter to be found in a typical F-theory compactification, or as a challenge to string theorists to explain why other choices of vacua are not exponentially unlikely compared to F-theory compactifications on ℳmax$$ {\mathrm{\mathcal{M}}}_{\max } $$.
A bstractApplying the Ashok-Denef-Douglas estimation method to elliptic Calabi-Yau fourfolds suggests that a single elliptic fourfold ℳmax$$ {\mathrm{\mathcal{M}}}_{\max } $$ gives rise to O10272,000$$ \mathcal{O}\left({10}^{272,000}\right) $$ F-theory flux vacua, and that the sum total of the numbers of flux vacua from all other F-theory geometries is suppressed by a relative factor of O10−3000$$ \mathcal{O}\left({10}^{-3000}\right) $$. The fourfold ℳmax$$ {\mathrm{\mathcal{M}}}_{\max } $$ arises from a generic elliptic fibration over a specific toric threefold base Bmax, and gives a geometrically non-Higgsable gauge group of E89 × F48 × (G2 × SU(2))16, of which we expect some factors to be broken by G-flux to smaller groups. It is not possible to tune an SU(5) GUT group on any further divisors in ℳmax$$ {\mathrm{\mathcal{M}}}_{\max } $$, or even an SU(2) or SU(3), so the standard model gauge group appears to arise in this context only from a broken E8 factor. The results of this paper can either be interpreted as providing a framework for predicting how the standard model arises most naturally in F-theory and the types of dark matter to be found in a typical F-theory compactification, or as a challenge to string theorists to explain why other choices of vacua are not exponentially unlikely compared to F-theory compactifications on ℳmax$$ {\mathrm{\mathcal{M}}}_{\max } $$.