A database of Calabi-Yau orientifolds and the size of D3-tadpoles

Abstract

The classification of 4D reflexive polytopes by Kreuzer and Skarke allows for a systematic construction of Calabi-Yau hypersurfaces as fine, regular, star triangulations (FRSTs). Until now, the vastness of this geometric landscape remains largely unexplored. In this paper, we construct Calabi-Yau orientifolds from holomorphic reflection involutions of such hypersurfaces with Hodge numbers h1,1≤ 12. In particular, we compute orientifold configurations for all favourable FRSTs for h1,1≤ 7, while randomly sampling triangulations for each pair of Hodge numbers up to h1,1 = 12. We find explicit string compactifications on these orientifolded Calabi-Yaus for which the D3-charge contribution coming from Op-planes grows linearly with the number of complex structure and Kähler moduli. We further consider non-local D7-tadpole cancellation through Whitney branes. We argue that this leads to a significant enhancement of the total D3-tadpole as compared to conventional SO(8) stacks with (4 + 4) D7-branes on top of O7-planes. In particular, before turning-on worldvolume fluxes, we find that the largest D3-tadpole in this class occurs for Calabi-Yau threefolds with $$ \left({h}_{+}^{1,1},{h}_{-}^{1,2}\right) $$ h + 1 , 1 h − 1 , 2 = (11, 491) with D3-brane charges |QD3| = 504 for the local D7 case and |QD3| = 6, 664 for the non-local Whitney branes case, which appears to be large enough to cancel tadpoles and allow fluxes to stabilise all complex structure moduli. Our data is publicly available under the following link https://github.com/AndreasSchachner/CY_Orientifold_database.

Topological constraints in the LARGE-volume scenario

“…The largest tadpole found in [39] is Q 3 = 3332 in a non-local model with h 1,1 + = 11. 16 If one restricts to h 1,1 + = 2 (as in the minimal version of the LVS considered in this paper), the maximal tadpole found in [39] is considering larger and larger κsss, | χ| beyond the ranges displayed in our plots. Indeed, one eventually reaches the r ≈ 0 regime where the expansion used to compute the λ(i4) terms in section 3 is not reliable anymore.…”

“…See [37][38][39] for explicit constructions of a large number of CY orientifolds including their tadpole data. An idea emphasized, e.g., in [8,37] and studied systematically in [39] is that models with non-local D7 tadpole cancellation (i.e., models where the D7 branes do not lie on top of the O7 planes but recombine into Whitney branes [40][41][42]) allow significantly larger D3 tadpoles than models where the D7 tadpole is cancelled locally (see also, e.g., [7,43,44] for constructions exploiting this fact). The largest tadpole found in [39] is Q 3 = 3332 in a non-local model with h 1,1 + = 11.…”

“…An idea emphasized, e.g., in [8,37] and studied systematically in [39] is that models with non-local D7 tadpole cancellation (i.e., models where the D7 branes do not lie on top of the O7 planes but recombine into Whitney branes [40][41][42]) allow significantly larger D3 tadpoles than models where the D7 tadpole is cancelled locally (see also, e.g., [7,43,44] for constructions exploiting this fact). The largest tadpole found in [39] is Q 3 = 3332 in a non-local model with h 1,1 + = 11. 16 If one restricts to h 1,1 + = 2 (as in the minimal version of the LVS considered in this paper), the maximal tadpole found in [39] is considering larger and larger κsss, | χ| beyond the ranges displayed in our plots.…”

“…15 Some contributions to C KK s can in principle be computed classically exploiting open/closed-string duality [29]. 16 The tadpoles in [39] are stated in the double cover of the orientifold so that we need to multiply them by a factor 1/2. If weakly coupled Swiss-cheese models with tadpoles of this order exist, one might hope that the control problems of the LVS described in this paper would be relaxed significantly.…”

“…therefore only exponentially large when χ s is small enough. On the other hand, it was emphasized in [8,39] that large Q 3 requires the branes to wrap divisors with large Euler numbers (or an appropriately generalized notion thereof [40][41][42]). In a viable LVS model, this contribution has to almost exclusively come from the large divisor.…”