Jumping Through Loops: On Soft Terms from Large Volume Compactifications

TL;DR

This paper tests the robustness of the Large Volume Scenario (LVS) against string loop corrections in the four-dimensional effective action, focusing on how D-branes and O-planes affect stabilization and soft terms. It shows that, in Swiss-cheese Calabi–Yau compactifications, loop corrections to the Kähler potential are subleading relative to the leading $ ext{α}'$ effects, so the LVS minimum and gaugino-mass suppression $|M_a|\,ig| \,rac{m_{3/2}}{ ext{ln}(1/m_{3/2})} ig.$ persist, with loop-induced changes appearing only in subleading orders. The paper also analyzes a concrete two-modulus model, $ ext{P}_{[1,1,1,6,9]}^4$, where loop corrections influence $ au_s$ in a way that still preserves the large-volume minimum; it further discusses regimes (toroidal orientifolds and fibered Calabi–Yau manifolds) where loop corrections can become comparatively sizable and potentially threaten LVS. Overall, the findings support LVS as a viable string-phenomenology framework while highlighting geometries and corrections that require further study, including possible effects from fluxes and higher-order $ ext{α}'$ contributions.

Abstract

We subject the phenomenologically successful large volume scenario of hep-th/0502058 to a first consistency check in string theory. In particular, we consider whether the expansion of the string effective action is consistent in the presence of D-branes and O-planes. Due to the no-scale structure at tree-level, the scenario is surprisingly robust. We compute the modification of soft supersymmetry breaking terms, and find only subleading corrections. We also comment that for large-volume limits of toroidal orientifolds and fibered Calabi-Yau manifolds the corrections can be more important, and we discuss further checks that need to be performed.

Figures (5)

• Figure 1: The loop correction $\mathcal{E}^{(K)}$ comes from the exchange of closed strings, or equivalently an open-string one-loop diagram, between the D3-brane and D7-branes (or O7-planes) wrapped on either the small 4-cycle $\tau_{\rm s}$ (as in a) or the large 4-cycle $\tau_{\rm b}$ (as in b). The exchanged closed strings carry Kaluza-Klein momentum.
• Figure 2: The loop correction $\mathcal{E}^{(W)}$ comes from the exchange of winding strings on the intersection between the small 4-cycle $\tau_{\rm s}$ and the large 4-cycle $\tau_b$. If this intersection is empty, there are no terms with $\mathcal{E}^{(W)}$.
• Figure 3: A D7-brane is wrapped on a 4-cycle A, which intersects the 4-cycle B on a 2-cycle C. For Dirichlet strings, the relevant topological condition (the existence of nontrivial 1-cycles) is on the intersection locus C, not on cycle B or on the whole Calabi-Yau. In other words, without the D-brane, the string on cycle C could have been unwound by sliding it along cycle B (as shown in the figure). With the D-brane, the string on cycle C is stuck.
• Figure 4: The top surface is the $\alpha'$ correction, the second is the $g_{\rm s}$ correction, and the "red carpet" is $10/\Delta$ (we used the values $A=1, W_0=1, a=2 \pi/8$). We see that for most of the parameter range, the $\alpha'$ correction dominates, and only for large $\mathcal{E}^{(K)}_s$, with the string coupling $g_{\rm s}=1/S_1$ not too small, do the contributions become comparable.
• Figure 5: Similarly to figure \ref{['fig:compare']}, the top surface is the $\alpha'$ correction, the second is the $g_{\rm s}$ correction (with $F=1$ in the left graph and $F=3$ in the right), and the "red carpet" is $10/\Delta$, with $\Delta$ from \ref{['Delta2']}, using the same values as in fig. \ref{['fig:compare']}. The result is qualitatively the same as before. Note, however, that the range for $\mathcal{E}^{(K)}_s$ differs. For larger values of $F$ one does not need to fine-tune $\mathcal{E}^{(K)}_s$ as much in order for the two corrections to become of similar order.