Moduli webs and superpotentials for five-branes

Abstract

We investigate the one-parameter Calabi-Yau models and identify families of D5-branes which are associated to lines embedded in these manifolds. The moduli spaces are given by sets of Riemann curves, which form a web whose intersection points are described by permutation branes. We arrive at a geometric interpretation for bulk-boundary correlators as holomorphic differentials on the moduli space and use this to compute effective open-closed superpotentials to all orders in the open string couplings. The fixed points of D5-brane moduli under bulk deformations are determined.

On D-brane moduli stabilisation

“…For instance, one may wonder which other D-branes (or NS5-branes) may develop a superpotential of the form (1.1). In particular one may compare our results with the open-closed superpotentials involving D5-branes [43,[48][49][50][51][52][53][54]. Also, it would be interesting to see how the D7-brane Wilson line stabilisation of section 5 is generalised to (p, q)-7-branes in F-theory compactifications.…”

Open string multi-branched and Kähler potentials

“…In addition, we will absorb the D7-brane index a into the Wilson line index i. We start by noting 14 Note that the condition (7.29) is necessary to have Sa Ω ∧ γ i = 0 thus ensuring that the differential forms γ i are of Hodge type (1,0) even when Ω| S4 is non-trivial. that in this limit the relations (5.18), (5.19) continue to hold if we assume that f a ij is a linear function on the complex structure moduli, which we shall assume henceforth.…”

“…There the techniques to achieve full moduli stabilisation are not so well developed, but on the other hand moduli in the gravity and gauge sector are treated on equal footing. In these setups one can see that, in general, the presence of D-branes/vector bundle sectors modifies the moduli stabilisation potential [12][13][14][15][16]. Of course, all these different constructions are related to each other by dualities like mirror symmetry, which has been used to match superpotentials involving open and closed string modes in type IIA compactifications with D6-branes.…”

D-brane moduli spaces and superpotentials in a two-parameter model

“…Similarly as in [26], we can represent the data from table 2 in a graph, by assigning a vertex to each family and an edge to an intersection. Since this graph is unoriented and contains self-intersections, we construct its universal cover, which we display in figure 2 (see [26] for a related discussion).…”