Quantum obstructions for N=1 infinite distance limits -- Part I: $g_s$ obstructions

Abstract

We analyse quantum obstructions to classical infinite distance limits in four-dimensional string compactifications with N=1 supersymmetry. Such quantum effects signal a severe departure from the perturbative effective action and can be of considerable importance for string model building. Our focus is on the complex structure moduli space of Type IIB orientifolds with O7/O3-planes and its F-theory description. In this first part of our analysis, we investigate the behaviour of $g_s$ corrections in infinite distance complex structure limits. Our main finding is that, depending on the location of the O7-plane, non-perturbative corrections in $g_s$ can become unsuppressed, thus obstructing a perturbative Type IIB description in the corresponding asymptotic region of the field space. In particular, this applies to large complex structure limits. To show this, we study the F-theory description of the Type IIB orientifold, in which all pure $g_s$ corrections are encoded in the (classical) geometry of an elliptic Calabi-Yau fourfold. This $g_s$-corrected moduli space is found to differ significantly from the classical moduli space. In extreme cases the classical infinite distance degeneration can be completely removed at the $g_s$-corrected quantum level. The behaviour of $α'$ corrections, as well as implications for string model building, are discussed in a companion paper.

Figures (6)

• Figure 1: A semi-stable degeneration as in \ref{['eq:3foldV']} in which the central fiber $V_0$ splits into the union of two components $V_1$ and $V_2$ that intersect over $V_{12}$.
• Figure 2: An example of an O-type A/B orientifold in a two-component type II degeneration, in which the threefold splits into two components $V_1$ and $V_2$, intersecting over the double surface $V_{12}$. In the O-type A limit, the O7-plane (indicated in red) wraps the whole double surface $V_{12}$, whereas in the O-type B limit it intersects it in codimension 1.
• Figure 3: The dual graphs (a) $\Pi(V_0^{\phi_1})$ and (b) $\Pi(V_0^{\phi_2})$ corresponding to the type III limit $\phi_1\to\infty$ and the type II limit $\phi_2\to\infty$, respectively. The action of the two O-type A orientifolds and the resulting orientifolded dual graph are depicted in blue. In both cases the orientifold action reduces the dimension of the dual graph by one.
• Figure 4: (a) For O-type A limits, the divisors $\Delta_S$ and $\Delta_F$ intersect in a point of tangency from the Type IIB perspective. (b) In the F-theory moduli space, the point of tangency can be resolved via blow-up, introducing an exceptional divisor $\hat{\Delta}_{FS}$.
• Figure 5: An illustration of the quantum moduli space for the F-theory lift of the type II O-type A limit $\phi_2\to\infty$ in the mirror of $\mathbb{P}^4_{2,2,2,3,3}[12]$. (a) A generic point on $\hat{\Delta}_S$, where the fourfold $W$ undergoes the standard Sen-limit. (b) A generic point on $\hat{\Delta}_F$, where the base becomes $\mathcal{B}_{3,0}=\{(p^2-h)^2=0\}/G_{\mathrm{GP}}$, which is smooth. For generic $g$, $W$ is smooth, but can acquire Kodaira type III singularities in codimension-3 (indicated in grey) for non-generic $g$. (c) The non-minimal Kodaira fiber and its resolution at $\hat{\Delta}_F\cap \hat{\Delta}_{FS}$. (d) The non-minimal Kodaira fiber and its resolution at $\hat{\Delta}_S\cap \hat{\Delta}_{FS}$. In (c) and (d) blowing down the component $\{e_0 =0\}$ leads to a semi-stable model.

Theorems & Definitions (2)

• Definition 1
• Definition 2: O-type A/B