Résumé:

: String theory predicts that generating functions of rank 0 Donaldson-Thomas invariants, realized physically as D4-D2-D0 BPS indices in type IIA string theory on a CalabiYau threefold, are (higher depth) mock moduar forms with a specific modular completion. I'll show how the modular anomaly equations can be solved to get the generating functions up to modular ambiguities. The solution is found in terms of indefinite theta series.

Résumé:

I'll explain the modular properties of the generating functions of rank 0 Donaldson-Thomas invariants, equal to D4-D2-D0 BPS indices in Calabi-Yau compactifications of string theory, and their physical origin. These properties can be used to find generating functions up to a finite number of coefficients, the so-called polar terms, which in turn can be fixed using wall-crossing. I'll show how this program is realized for compact one-parameter Calabi-Yau threefolds and 2 units of D4-brane charge, leading to explicit mock modular forms encoding BPS indices. For higher charges, the polar terms remain so far inaccessibble, but I'll present a general solution of modular anomaly equations in terms of indefinite theta series.

Ref HAL: hal-04609830_v1
Ref Arxiv: 2406.02531
Ref INSPIRE: 2794447
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
Résumé:

We construct a hybrid-inflation model where the inflaton potential is generated radiatively, as gauge symmetries guarantee it to be accidentally flat at tree level. The model can be regarded as a small-field version of Natural Inflation, with inflation ending when the mass of a second scalar, the waterfall field, turns tachyonic. This provides a minimal, robust realisation of hybrid inflation, which predicts specific correlations among CMB observables. Tachyonic preheating leads to the production of gravitational waves which, for a low inflationary scale, might be detected by upcoming experiments. Simple variations of the model can give rise to topological defects, such as unstable domain walls. Their dynamics produces a stochastic gravitational-wave background, which can be compatible with the recent detection by pulsar timing arrays.

Résumé:

I'll review some open open problems in determination of the effective action for Calabi-Yau compactifications of type II string theory, and argue that their solution requires a combination of modularity and resurgence.

Ref HAL: hal-04572367_v1
Ref Arxiv: 2405.04584
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
Résumé:

We propose to use the winding number of the gradient of a scalar potential as a simple topological index that relates critical points in the interior of the scalar field space to the behavior of the potential at the (asymptotic) boundary of the field space. We demonstrate this technique for supersymmetric flux compactifications of M-theory on Calabi-Yau four-folds, and use the Fermat sextic as a simple, one-parameter example.

Commentaires: 43 pages, 3 figures

Résumé:

I'll review the construction of topological string theory which has a lot of applications in usual string theory and mathematics. I'll start by summarizing the geometry of Calabi-Yau manifolds, where topological strings will be defined, introduce topological twist, define A and B models, and discuss a relation to F-terms in the effective action of type II strings. In the end, I'll explain the wave function property related to the issue of background independence.

Résumé:

BPS indices encoding entropy of supersymmetric black holes in compactifications of Type II string theory on compact Calabi-Yau threefolds coincide with generalized Donaldson-Thomas invariants whose computation represents an outstanding problem. I'll show how this problem can be solved for a set of one-parameter threefolds by combining a direct integration of topological string, modular properties of rank 0 DT invariants counting D4-D2-D0 BPS states, and wall-crossing relations between rank 1 and rank 0 DT invariants. As a result, one obtains explicit (mock) modular functions encoding infinite sets of D4-D2-D0 BPS indices, which in turn can be used to generate new boundary conditions for the holomorphic anomaly equation of topological string allowing to overcome the limitations of the direct integration method.