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Quantum obstructions for $N=1$ infinite distance limits -- Part II: Kähler obstructions

Lukas Kaufmann, Jeroen Monnee, Timo Weigand, Max Wiesner

Abstract

We continue our analysis of quantum corrections in the complex structure moduli space of four-dimensional Type IIB/F-theory compactifications with N=1 supersymmetry. We find that limits in the complex structure moduli space of F-theory generically induce a strong backreaction on other sectors of the theory, reflecting the non-factorisation of the field space in genuine $N=1$ theories at the quantum level. Our focus is on quantum corrections to the Kähler moduli in F-theory on Calabi-Yau fourfolds and proceeds in two independent ways: A detailed analysis of the worldsheet theory of candidate EFT strings for pure complex structure infinite distance limits reveals a mismatch with expectations based on the classical effective action and points to a quantum obstruction of the limit. Complementary to this, we confirm, in large classes of theories, the existence of significant complex structure dependent quantum corrections to the action of BPS instantons which at tree-level are governed by the Kähler moduli. As the quantum corrections become uncontrolled at large complex structure, they require a co-scaling of the Kähler moduli to maintain perturbative control. As a result, the naive, classical effective action does not provide an accurate description of pure large complex structure regimes. We comment on possible implications for string phenomenology, specifically with regard to model building and moduli stabilisation.

Quantum obstructions for $N=1$ infinite distance limits -- Part II: Kähler obstructions

Abstract

We continue our analysis of quantum corrections in the complex structure moduli space of four-dimensional Type IIB/F-theory compactifications with N=1 supersymmetry. We find that limits in the complex structure moduli space of F-theory generically induce a strong backreaction on other sectors of the theory, reflecting the non-factorisation of the field space in genuine theories at the quantum level. Our focus is on quantum corrections to the Kähler moduli in F-theory on Calabi-Yau fourfolds and proceeds in two independent ways: A detailed analysis of the worldsheet theory of candidate EFT strings for pure complex structure infinite distance limits reveals a mismatch with expectations based on the classical effective action and points to a quantum obstruction of the limit. Complementary to this, we confirm, in large classes of theories, the existence of significant complex structure dependent quantum corrections to the action of BPS instantons which at tree-level are governed by the Kähler moduli. As the quantum corrections become uncontrolled at large complex structure, they require a co-scaling of the Kähler moduli to maintain perturbative control. As a result, the naive, classical effective action does not provide an accurate description of pure large complex structure regimes. We comment on possible implications for string phenomenology, specifically with regard to model building and moduli stabilisation.
Paper Structure (41 sections, 147 equations, 3 figures)

This paper contains 41 sections, 147 equations, 3 figures.

Table of Contents

  1. Introduction
  2. General overview and a simple example
  3. Complex structure and Kähler sector mixing
  4. A simple example: Kähler obstructions in O-Type B orientifolds
  5. F-theory complex structure limits and EFT strings
  6. Complex structure degenerations of Calabi--Yau fourfolds
  7. Worldsheet spectrum of EFT strings
  8. Universal geometric mode.
  9. Internal geometric modes.
  10. Modes from $p$-forms.
  11. Regular-fiber limits
  12. Example: Type II Limit in trivial fibration.
  13. In-type limits
  14. Example: Standard Sen-limit.
  15. Kähler obstructions for In-type limits
  16. ...and 26 more sections

Figures (3)

  • Figure 1: The two classes of semi-stable degeneration limits $W\to W_0$ for the elliptically fibered Calabi--Yau fourfold $W$. In (a) the double threefold is itself elliptically fibered with generic smooth fiber $\mathcal{E}$ corresponding to a regular-fiber limit, whereas in (b) the generic fiber over one base component degenerates to $\mathcal{E}_0$, corresponding to an I$_n$-type limit.
  • Figure 2: The left-hand side depicts an elliptic Calabi--Yau fourfold $W$ that in addition allows for a compatible Calabi--Yau threefold fibration. The right-hand side illustrates a regular-fiber type III limit of $W$ that is induced by a degeneration of the generic $X_3$-fiber over $\mathbb{P}^1$, such that the elliptic fiber $\mathcal{E}$ remains smooth in the limit. Here we have depicted the minimal case in which $X_{3,0}$ splits into three components $X_1,X_2,X_3$.
  • Figure 3: Dualities used in excluding regular-fiber type III limits in Calabi--Yau three-fibered Calabi--Yau fourfolds. After taking the adiabatic limit of large base $\mathbb{P}^1$, the theory is best described as F-theory on the generic fiber Calabi--Yau threefold. Our interest lies in the (geometric) hypermultiplet moduli space of this 6d theory, which is the same as the (geometric) hypermultiplet moduli space as probed by Type IIA on the generic fiber Calabi--Yau threefold. Finally, the $c$-map relates this to the vector multiplet moduli space of Type IIB compactified on the same threefold.

Theorems & Definitions (4)

  • Definition 1
  • Definition 2
  • Claim 1
  • Claim 2