Abstract
Abstract We study the quantization of the M-theory G-flux on elliptically fibered Calabi-Yau fourfolds with singularities giving rise to unitary and symplectic gauge groups. We seek and find its relation to the Freed-Witten quantization of worldvolume fluxes on 7-branes in type IIB orientifold compactifications on Calabi-Yau threefolds. By explicitly constructing the appropriate four-cycles on which to calculate the periods of the second Chern class of the fourfolds, we find that there is a half-integral shift in the quantization of G-flux whenever the corresponding dual 7-brane is wrapped on a non-spin submanifold. This correspondence of quantizations holds for all unitary and symplectic gauge groups, except for SU(3), which behaves mysteriously. We also perform our analysis in the case where, in addition to the aforementioned gauge groups, there is also a ‘flavor’ U(1)-gauge group.
Highlights
We perform our analysis in the case where, in addition to the aforementioned gauge groups, there is a ‘flavor’ U(1)-gauge group
We study the quantization of the M-theory G-flux on elliptically fibered CalabiYau fourfolds with singularities giving rise to unitary and symplectic gauge groups
By explicitly constructing the appropriate four-cycles on which to calculate the periods of the second Chern class of the fourfolds, we find that there is a half-integral shift in the quantization of G-flux whenever the corresponding dual 7-brane is wrapped on a non-spin submanifold
Summary
Let us collect here the main results of this paper for the convenience of the reader. Given a holomorphic curve C ⊂ D, we explicitly construct a holomorphic surface C(4) in the resolved F-theory CY fourfold Z4, such that c2(Z4) = [7 c1(B3) − (2N − 1) D] This 4-cycle has the geometry of a P1 fibered over the curve C ⊂ D and it lifts a loop of type IIA open strings stretching between one D-brane of the stack and the Whitney umbrella D-brane. For the Sp-series we conjecture that odd-rank Sp groups lead to even second Chern classes and viceversa This is because in the odd-rank cases the two branches of the ‘flavour brane’ are separately non-spin and the induced flux on them is half-integral. In the even-rank cases, the branches of the ‘flavour brane’ are spin and the induced gauge flux is integrally quantized For this reason we still find, by explicit computation, an odd second Chern class for the U(1)-restricted SU(4)-model
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