Algorithmically solving the Tadpole Problem

Abstract

The extensive computer-aided search applied in [1] to find the minimal charge sourced by the fluxes that stabilize all the (flux-stabilizable) moduli of a smooth K3×K3 compactification uses differential evolutionary algorithms supplemented by local searches. We present these algorithms in detail and show that they can also solve our minimization problem for other lattices. Our results support the Tadpole Conjecture: The minimal charge grows linearly with the dimension of the lattice and, for K3×K3, this charge is larger than allowed by tadpole cancelation.Even if we are faced with an NP-hard lattice-reduction problem at every step in the minimization process, we find that differential evolution is a good technique for identifying the regions of the landscape where the fluxes with the lowest tadpole can be found. We then design a "Spider Algorithm," which is very efficient at exploring these regions and producing large numbers of minimal-tadpole configurations.

A New de Sitter Solution with a Weakly Warped Deformed Conifold

“…be large enough 7 , this translates into a lower bound on M K which makes the D3-tadpole cancellation condition difficult to satisfy (see [7,[15][16][17]).…”

“…Together, large √ g s M and large 8πK gsM imply large M K and a large positive contribution to the D3-tadpole in the compact internal manifold, which may be difficult to cancel within perturbative type IIB string theory [7]. The bound on M K, and other flux numbers required to stabilise bulk moduli, was further refined in [14][15][16], with M K 500.…”

“…In (3.16), ζ 4/3 ∼ V −2/3 , which means that the brane potential suppression comes from the volume modulus itself, provided there is a solution. This might be especially useful for the tadpole problem discussed in [15,16], since we no longer require a large hierarchy ) gs M = 13.9…”

On the Search for Low $W_0$

“…• How does the subclass fit within the larger ensemble of the full set of vacua? More specifically, what can we say about the set from the point of view of the statistical approach to string phenomenology [30][31][32][33][34] (see [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49] for studies in various settings in this context)?…”

Applying machine learning to the Calabi-Yau orientifolds with string vacua

“…Machine learning has been a good implement in theoretical physics research and leads to fruitful results during the last couple of years. With the help of machine learning people are able to deal with problems with more computational efficiency, especially the problems involving big data, for example, study the landscape of string flux vacua [8][9][10][11][12][13][14][15][16][17] as well as F-theory compactifications [18][19][20]. This technique allows people to learn lots of quantities of Calabi-Yau manifolds, from its toric building blocks like the polytope structure [21,22] and triangulations [23,24], to the calculation of Hodge numbers [25][26][27][28], numerical metrics [29][30][31][32] and line bundle cohomologies [33,34].…”