Scattering and Sequestering of Blow-Up Moduli in Local String Models

TL;DR

This work investigates sequestering of blow-up moduli in local string constructions by computing disk CFT correlators between blow-up (twist) fields and matter Yukawa couplings. The authors derive the full quantum and classical Yukawa correlator for a single twist, and, for multiple distant twists, show sequestering at disk level to all orders in $\alpha'$ by exploiting picture-changing and factorisation properties; no contact term $\tau_s\ldots\tau_s\psi\psi\phi$ arises at zero momentum unless the twist sits at the same singularity as the visible sector. The results imply that soft terms can be parametrically suppressed relative to the gravitino mass and enable a controlled passage to the smooth Swiss-cheese Calabi–Yau limit relevant to LVS. This provides a CFT-based bridge from orbifold models to LVS geometries, offering insight into how ultraviolet moduli affect low-energy flavor and SUSY-breaking structure. The work also outlines intriguing loop-level extensions and clarifies the role of twist-field correlators in estimating soft-term suppression in realistic string compactifications.

Abstract

We study the scattering and sequestering of blow-up fields - either local to or distant from a visible matter sector - through a CFT computation of the dependence of physical Yukawa couplings on the blow-up moduli. For a visible sector of D3-branes on orbifold singularities we compute the disk correlator < τ_s^{(1)} τ_s^{(2)} ... τ_s^{(n)} ψψφ> between orbifold blow-up moduli and matter Yukawa couplings. For n = 1 we determine the full quantum and classical correlator. This result has the correct factorisation onto lower 3-point functions and also passes numerous other consistency checks. For n > 1 we show that the structure of picture-changing applied to the twist operators establishes the sequestering of distant blow-up moduli at disk level to all orders in α'. We explain how these results are relevant to suppressing soft terms to scales parametrically below the gravitino mass. By giving vevs to the blow-up fields we can move into the smooth limit and thereby derive CFT results for the smooth Swiss-cheese Calabi-Yaus that appear in the Large Volume Scenario.

Figures (7)

• Figure 1: Resolving toroidal orbifold singularities gives the type of smooth geometry that appears in the Large Volume Scenario, with a large bulk attached to several small blow-ups.
• Figure 2: The six possible (and distinct) orderings of three vertex operator in relation to the location of the branch point on the boundary of the disk. The branch point is fixed to be at $\infty$.
• Figure 3: The three possible (and distinct) orderings of the vertex operator in relation to the location of the branch point on the boundary of the disk.
• Figure 4: The procedure of fixing the $SL(2, \mathbb{R})$ degeneracy while keeping the branch point at $\infty$.
• Figure 5: The origin of the $1/s$ pole as factorisation of the 4-point diagram onto a 3-pt Yukawa and an FI term.