Special geometry and the swampland

Self Cite

Motivated by the swampland program, we show that the Weil-Petersson geometry of the moduli space of a Calabi-Yau manifold of complex dimension d ≤ 4 is a gravitational instanton (i.e. a finite-action solution of the Euclidean equations of motion of gravity with matter). More precisely, the moduli geometry of Calabi-Yau d-folds (d ≤ 4) describes instantons of (E)AdS Einstein gravity coupled to a standard chiral model.From the point of view of the low-energy physics of string/M-theory compactified on the Calabi-Yau X, the various fields propagating on its moduli space are the couplings appearing in the effective Lagrangian "Image missing".

“…E.g. the homogeneous N = 2 models constructed in [14], all of which fall in the swampland [15], do satisfy eqs. (1.9), (1.10) but have infinite action.…”

Section: Jhep12(2020)008mentioning

confidence: 99%

Section: An Informal Sketchmentioning

confidence: 99%

“…In the present set-up and notations, this Bochner-formula takes the form (see eqs. (4.1)-(4.8) of [15])…”

Section: Review Of Tt * Geometrymentioning

confidence: 99%

“…We return to tt * geometry. A short computation [15,28] shows that the compatibility condition of (2.13) with (2.14), [D,D]C = 0, implies…”

Section: Review Of Tt * Geometrymentioning

confidence: 99%

“…See, e.g. chapter 11 of[29] 15. Here it is crucial that in the SCFT case the real Lie group G is of "Mumford-Tate type" i.e.…”

mentioning

confidence: 99%

See 3 more Smart Citations

Moduli spaces of Calabi-Yau d-folds as gravitational-chiral instantons

Cecotti

2020

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Cobordism conjecture, anomalies, and the String Lamppost Principle

Montero

Vafa

2021

108

We consider consequences of triviality of cobordism classes and anomaly cancellation in supergravity theories in d > 6. We argue that this leads to the existence of certain defects which we call “I-folds” (a generalization of orientifolds). The requirement that compactifications to lower dimensions involving these defects be anomaly free leads to conditions on the higher dimensional theory. We show that in theories with 16 supercharges in d > 6 this leads to restrictions on the rank of the allowed gauge groups and thus provides an explanation for the observed restrictions in known string theory constructions. In particular, in eight and nine dimensions the only solutions to our constraints are precisely the ones realized in string theory compactifications. We also use these techniques to place constraints on the global structure of the gauge group in eight and nine dimensions.

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

Gendler

Valenzuela

2021

106

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.