Six-dimensional (1,0) effective action of F-theory via M-theory on Calabi-Yau threefolds

Abstract

The six-dimensional effective action of F-theory compactified on a singular elliptically fibred Calabi-Yau threefold is determined by using an M-theory lift. The low-energy data are derived by comparing a circle reduction of a general six-dimensional (1, 0) gauged supergravity theory with the effective action of M-theory on the resolved Calabi-Yau threefold. The derivation includes six-dimensional tensor multiplets for which the (anti-) self-duality constraints are imposed on the level of the five-dimensional action. The vector sector of the reduced theory is encoded by a non-standard potential due to the GreenSchwarz term in six dimensions. This Green-Schwarz term also contains higher curvature couplings which are considered to establish the full map between anomaly coefficients and geometry. F-/M-theory duality is exploited by moving to the five-dimensional Coulomb branch after circle reduction and integrating out massive vector multiplets and matter hypermultiplets. The associated fermions then generate additional Chern-Simons couplings at one-loop. Further couplings involving the graviphoton are induced by quantum corrections due to excited Kaluza-Klein modes. On the M-theory side integrating out massive fields corresponds to resolving the singularities of the Calabi-Yau threefold, and yields intriguing relations between six-dimensional anomalies and classical topology.

F-theory and AdS3/CFT2

“…To construct this solution one may either T-dualize the "pre near-horizon" solution obtained in (3.87) along the Hopf fiber and then uplift or use the brane smearing techniques employed previously to combine N M5-branes wrapping R 1,1 × C and M M5-branes wrapping R 1,1 × B, in the background R 1,1 × R 3 × Y 3 with M > 0. Both methods result in the same solution given JHEP08(2017)043 13) where…”

“…The total Chern class for the Calabi-Yau can be written as 13) where c(B) is the total Chern class of the base and the denominator corresponds to the class of the hypersurface equation (2.1). Expanding this to second order we obtain 11 14) which allows the computation of integrals over c 2 (Y 3 ) using the intersection numbers in (2.11).…”

“…These are supplemented by the Bianchi identities 13) and the self-duality constraint F = * F . (3.14)…”

“…Observe from the algebraic equations (C.14)-(C.17) we have the relation which is a warped form of the equations obeyed by the SU(2) invariant one-forms. 13 13 The Maurer-Cartan left-invariant one-forms in the coordinates we are using are σ1,L = − sin ψdθ + cos ψ sin θdϕ , σ2,L = cos ψdθ + sin ψ sin θdϕ , σ3,L = dψ + cos θdϕ .…”

Onα′corrections inN=1F-theory compactifications

“…In this case c 3 (Y 4 ) = 0 and the volume correction (13) vanishes identically. In contrast, both corrections are non-vanishing for 6d, N = 1 vacua arising from F-theory on elliptically fibered Calabi-Yau threefolds with classical action derived in [22,23]. The terms are generated by taking the F-theory limit of the 5d theory briefly discussed at the end of section II.…”