F-theory flux vacua at large complex structure

Abstract

We compute the flux-induced F-term potential in 4d F-theory compactifications at large complex structure. In this regime, each complex structure field splits as an axionic field plus its saxionic partner, and the classical F-term potential takes the form V = ZABρAρB up to exponentially-suppressed terms, with ρ depending on the fluxes and axions and Z on the saxions. We provide explicit, general expressions for Z and ρ, and from there analyse the set of flux vacua for an arbitrary number of fields. We identify two families of vacua with all complex structure fields fixed and a flux contribution to the tad- pole Nflux which is bounded. In the first and most generic one, the saxion vevs are bounded from above by a power of Nflux. In the second their vevs may be unbounded and Nflux is a product of two arbitrary integers, unlike what is claimed by the Tadpole Conjecture. We specialise to type IIB orientifolds, where both families of vacua are present, and link our analysis with previous results in the literature. We illustrate our findings with several examples.

D7 moduli stabilization: the tadpole menace

“…This result applies both to compactifications over any of the O(10 15 ) toric weak Fano bases [11] and also to more general compactifications whose weak Fano base is not necessarily toric, 14 and spectacularly confirms the Tadpole Conjecture [1], both by the linear growth of the tadpole sourced by the fluxes with the number of moduli they stabilize, 15 and also by the fact that the proportionality coefficient, α, is larger than 1/3. Since this is larger than 0.259, the ratio allowed by the tadpole cancelation condition (see (2.11)), D7 moduli cannot be stabilized by fluxes dual to a curve of genus zero, within the tadpole bound.…”

Small cosmological constants in string theory

“…We now construct classical flux vacua with exponentially small W 0 = |W flux | , following [5]. We make use of the form F = F poly + F inst of the prepotential near LCS, 9 which was explained below (2.3), and write…”

“…The divisors in question are D 3 , D 7 , D 8 , D 9 , D 43 , D 44 , D 45 , and D 46 , and correspond to points (3,7,8,9,43,44,45,46)…”

“…The points (3,7,8,9) are vertices of ∆ • , while (43,44,45,46) are interior to 1-faces: see figure 1.…”

“…Recent advances have made it possible to find quantized fluxes for which 1 W 0 := |W flux | 1 [5][6][7][8][9]. However, the problem of finding such fluxes is Diophantine in character, and the computation becomes extremely expensive for h 2, 1 1.…”