On the Search for Low $W_0$

Abstract

The magnitude of the vacuum expectation value of the Gukov-Vafa-Witten superpotential |W 0 | plays a central role in the phenomenology of type IIB flux compactifications. Recent analytical constructions have shown that perturbatively flat vacua can be used to obtain very low values of |W 0 |. We present systematic algorithms to carry out exhaustive numerical searches for such vacua. We also analyse them in the statistical context, as part of the entire ensemble of type IIB flux vacua at low |W 0 |. Our preliminary analysis indicates that these perturbatively flat vacua are statistically sparse in the whole set of vacua at low |W 0 | as calculated by Denef and Douglas. Two-moduli examples are used to illustrate these more general findings in specific settings. We find that these simple cases are good examples for existence proofs but they do not feature a large statistical tuning freedom for phenomenological applications.

Analytic Periods via Twisted Symmetric Squares

“…In the large voume regime the N = 2 special geometry data is encapsulated in the prepotential 11226 [12] taken from [15]. The shown distances are the ones computed in said paper.…”

“…2.1 P 4 1,1,2,2,6 [12] The topological numbers corresponding to the P 4 1,1,2,2,6 [12] hypersurface and appearing in its prepotential are given by…”

“…The usual strategy when studying flux compactifications is to obtain locally valid expressions for these objects by expanding the periods of the CY around a point in moduli space and then requiring the fluxes to be chosen in a selfconsistent way such that the initially assumed approximation holds. As an example, the recently proposed constructions of exponentially small superpotentials [6][7][8][9][10][11][12][13] develop the periods around the large complex structure point (LCS) or the conifold and drop the higher order exponentially small corrections. Globally valid expressions for the periods remove this limitation and would allow easier scans over flux vacua.…”

“…This can be used to directly test the refined swampland distance conjecture in this setup. We perform this computation for two examples, the manifolds P 4 1,1,2,2,2 [8] and P 4 1,1,2,2,6 [12], finding agreement with [20]. This paper is organized as follows.…”

Remarks on the effects of quantum corrections on moduli stabilization and de Sitter vacua in type IIB string theory

“…For the recent debate on Swampland conjectures see for example [1][2][3] and related reviews [4][5][6]. Also, an incomplete list of 10d supergravity dS solutions and other related issues is [7][8][9][10][11][12] 4 For recent developments on related work see [15][16][17][18][19][20][21] the cosmological inflation have been studied. It was found that hybrid inflation is successfully implemented with the internal volume modulus acting as the inflaton [28], and the rôle of the waterfall field is played by open string excitations associated with the D7 brane stacks [29].…”