On the Search for Low W₀

Abstract

The magnitude of the vacuum expectation value of the Gukov‐Vafa‐Witten superpotential |W0|$|W_0|$ 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 |W0|$|W_0|$. 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 |W0|$|W_0|$. Our preliminary analysis indicates that these perturbatively flat vacua are statistically sparse in the whole set of vacua at low |W0|$|W_0|$ 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 (two moduli) cases are good examples for existence proofs but they do not feature a large statistical tuning freedom for phenomenological applications.

Over-extremal brane shells from string theory?

“…Whether the size of our over-extremal balloon like objects can truly become large (beyond particle physics length scales or the de Broglie wavelength) seems to depend on how far flux numbers, warping effects and spacing between vacuum energies can be tuned. The possibility of this tuning is a crucial debate within the current Swampland paradigm [9][10][11] that has been discussed for instance in [12][13][14][15][16][17][18][19][20][21][22][23].…”

On the intermediate Jacobian of M5-branes

“…2 See also [9][10][11], which showcase the lightness of conifold moduli in generic KKLT-like constructions. 3 For recent studies of flux vacua with small flux superpotential, see [12][13][14][15][16][17][18][19]. 4 A sufficient condition for the generation of the superpotential is h • (D, O D ) = (1, 0, 0, 0) for a smooth D. An important open problem is to understand when a non-rigid divisor D can contribute to the superpotential by means of rigidification by spacetime filling D-branes or fluxes [21,22].…”

“…Whenever the distinction is clear from the context, we abuse notation and use the same symbol D to denote both a divisor and its representative in the appropriate Chow ring. In this case, we use Z to denote the class of the divisor Z ⊂ P Σ 14. Recall that the dual σ ∨ of a cone σ is defined in (2.7).…”

Asymptotic String Compactifications

“…A vanishing superpotential W = 0 at the minimum corresponds to supersymmetric vacuum (including the Kähler moduli sector), while the second possibility is important for the KKLT and Large Volume Scenarios [105,106]. In particular, for KKLT it is needed that the vacuum superpotential takes an exponentially small value (see [3,[107][108][109][110][111][112][113][114][115] for some recent constructions of such flux vacua), which we investigate further in chapter 8.…”

“…One of the most prominent moduli stabilization scenarios, the KKLT scenario [105], requires to find vacua in complex structure moduli space, such that the vacuum superpotential is taking a very small, non-zero value. 2 It was recently suggested in [107] and further explored in [108][109][110][111][112][113][114][115] that, in fact, exponentially small vacuum superpotentials can be found near large complex structure and conifold-large complex structure boundaries. 3 It was argued that the construction proceeds by introducing fluxes that preserve a continuous version of the monodromy symmetry at some leading order with a vanishing superpotential, while then including instanton corrections generates an exponentially small superpotential.…”