Refined swampland distance conjecture and exotic hybrid Calabi-Yaus

121

We calculate the generating functions of BPS indices using their modular properties in Type II and M-theory compactifications on compact genus one fibered CY 3-folds with singular fibers and additional rational sections or just N-sections, in order to study string dualities in four and five dimensions as well as rigid limits in which gravity decouples. The generating functions are Jacobi-forms of Γ 1 (N) with the complexified fiber volume as modular parameter. The string coupling λ, or the ± parameters in the rigid limit, as well as the masses of charged hypermultiplets and non-Abelian gauge bosons are elliptic parameters. To understand this structure, we show that specific auto-equivalences act on the category of topological B-branes on these geometries and generate an action of Γ 1 (N) on the stringy Kähler moduli space. We argue that these actions can always be expressed in terms of the generic Seidel-Thomas twist with respect to the 6-brane together with shifts of the B-field and are thus monodromies. This implies the elliptic transformation law that is satisfied by the generating functions. We use Higgs transitions in F-theory to extend the ansatz for the modular bootstrap to genus one fibrations with N-sections and boundary conditions fix the all genus generating functions for small base degrees completely. This allows us to study in depth a wide range of new, non-perturbative theories, which are Type II theory duals to the CHL Z N orbifolds of the heterotic string on K3 × T 2. In particular, we compare the BPS degeneracies in the large base limit to the perturbative heterotic one-loop amplitude with R 2 + F 2g−2 + insertions for many new Type II geometries. In the rigid limit we can refine the ansatz and obtain the elliptic genus of superconformal theories in 5d.

Section: Jhep11(2019)170mentioning

confidence: 89%

Topological strings on genus one fibered Calabi-Yau 3-folds and string dualities

Cota¹,

Klemm

Schimannek

2019

121

“…Identifying a tower becoming massless is not enough: one further needs to show that the mass scale is suppressed exponentially in the distance, as given in (1.5), and finally estimate λ. In the following, we will focus on works that obtained such results for Kaluza-Klein states [53,60] or brane states [52,54,56,57,59,62]. This will provide us with estimates of λ for different states and various (infinite distance) directions in the moduli space or field space.…”

Section: Jhep07(2020)162mentioning

confidence: 98%

“…Such states were studied e.g. in [52][53][54][55][56][57][58][59][60][61][62]. Further works [63][64][65][66][67][68][69][70] studied the relation of…”

Section: Distance Conjecture and λ Valuesmentioning

confidence: 99%

The web of swampland conjectures and the TCC bound

Andriot

Cribiori

Erkinger

2020

Self Cite

121

We consider the swampland distance and de Sitter conjectures, of respective order one parameters λ and c. Inspired by the recent Trans-Planckian Censorship conjecture (TCC), we propose a generalization of the distance conjecture, which bounds λ to be a half of the TCC bound for c, i.e. $$ \lambda \ge \frac{1}{2}\sqrt{\frac{2}{3}} $$ λ ≥ 1 2 2 3 in 4d. In addition, we propose a correspondence between the two conjectures, relating the tower mass m on the one side to the scalar 1 potential V on the other side schematically as $$ m\sim {\left|V\right|}^{\frac{1}{2}} $$ m ∼ V 1 2 , in the large distance limit. These proposals suggest a generalization of the scalar weak gravity conjecture, and are supported by a variety of examples. The lower bound on λ is verified explicitly in many cases in the literature. The TCC bound on c is checked as well on ten different no-go theorems, which are worked-out in detail, and V is analysed in the asymptotic limit. In particular, new results on 4d scalar potentials from type II compactifications are obtained.

“…Hence, the SDC suggests a stronger version of the WGC for which there must be not only a single particle but a sublattice or a tower of particles satisfying the WGC bound. In the past years, a lot of effort has been dedicated to rigorously identifying the tower of particles that become light in the infinite field distance limits of Calabi-Yau string compactifications [14][15][16][18][19][20][21][22][23][24][25][26][27] (see also [13,[28][29][30][31][53][54][55][56][57][58]). It is the aim of this paper to study the relation between these conjectures in more detail, using the knowledge we have recently gained about these towers to define the Swampland conjectures in a precise way.…”

Section: Jhep01(2021)176mentioning

confidence: 99%

Merging the weak gravity and distance conjectures using BPS extremal black holes

Gendler

Valenzuela

2021

103

176

We analyze the charge-to-mass structure of BPS states in general infinite-distance limits of $$ \mathcal{N} $$ N = 2 compactifications of Type IIB string theory on Calabi-Yau three-folds, and use the results to sharpen the formulation of the Swampland Conjectures in the presence of multiple gauge and scalar fields. We show that the BPS bound coincides with the black hole extremality bound in these infinite distance limits, and that the charge-to-mass vectors of the BPS states lie on degenerate ellipsoids with only two non-degenerate directions, regardless of the number of moduli or gauge fields. We provide the numerical value of the principal radii of the ellipsoid in terms of the classification of the singularity that is being approached. We use these findings to inform the Swampland Distance Conjecture, which states that a tower of states becomes exponentially light along geodesic trajectories towards infinite field distance. We place general bounds on the mass decay rate λ of this tower in terms of the black hole extremality bound, which in our setup implies $$ \lambda \ge 1/\sqrt{6} $$ λ ≥ 1 / 6 . We expect this framework to persist beyond $$ \mathcal{N} $$ N = 2 as long as a gauge coupling becomes small in the infinite field distance limit.