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. In particular, one obtains explicit (mock) modular functions encoding infinite sets of D4-D2-D0 BPS indices and new boundary conditions for the holomorphic anomaly equation allowing to overcome the limitations of the direct integration method.

Ref HAL: hal-04236880_v1
Ref Arxiv: 2309.14440
Ref INSPIRE: 2703100
DOI: 10.1007/JHEP01(2024)140
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
Résumé:

The metric on the hypermultiplet moduli space of Calabi-Yau compactifications of type II string theory is known to receive D-brane and NS5-brane instanton corrections. We compute explicit expressions for these corrections in the one-instanton approximation, but to all orders in the string coupling expansion around the instantons. As a consistency check, we prove that in the case of one (universal) hypermultiplet, the resulting metric fits the Przanowski description of self-dual Einstein spaces. We also show that in the small string coupling limit the metric acquires a certain square structure, consistently with expectations from the string amplitudes analysis. This result provides explicit predictions for yet mysterious string amplitudes in the presence of NS5-branes.

Résumé:

I'll review the recent results on modular properties of generating functions of BPS indices counting states of D4-D2-D0 black holes in Calabi-Yau compactifications of type IIA string theory. These generating functions can be shown to be (higher depth) mock modular forms with a specific non-holomorphic modular completion. This result turns out to have a wider range of applicability than the original framework and has numerous applications ranging from compactifications with higher SUSY to Vafa-Witten theory. In the end, I'll show how one can determine the generating functions explicitly for compact Calabi-Yau threefolds with one Kahler modulus, and how this allows to overcome the usual limitations for computation of GV, DT and PT topological invariants.

Résumé:

Sine-Liouville (SL) theory is a 2d string theory in a background with a tachyon condensate and has a dual description in terms of Matrix Quantum Mechanics. Using this description, almost 20 years ago instanton corrections to the partition function of SL theory have been found. However, this result left several puzzles and it was unclear how it can be reproduced using CFT technique. I reconsider this problem using recent insights about D-instantons in string theory, which allows both to resolve the puzzles and to match the instanton effects in the two formulations.

Ref HAL: hal-03948966_v1
Ref Arxiv: 2301.08066
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
Résumé:

By exploiting new mathematical relations between Pandharipande-Thomas (PT) invariants, closely related to Gopakumar-Vafa (GV) invariants, and rank 0 Donaldson-Thomas (DT) invariants counting D4-D2-D0 BPS bound states, we rigorously compute the first few terms in the generating series of Abelian D4-D2-D0 indices for compact one-parameter Calabi-Yau threefolds of hypergeometric type. In all cases where GV invariants can be computed to sufficiently high genus, we find striking confirmation that the generating series is modular, and predict infinite series of Abelian D4-D2-D0 indices. Conversely, we use these results to provide new constraints for the direct integration method, which allows to compute GV invariants (and therefore the topological string partition function) to higher genus than hitherto possible. The triangle of relations between GV/PT/DT invariants is powered by a new explicit formula relating PT and rank 0 DT invariants, which is proven in an Appendix by the second named author. As a corollary, we obtain rigorous Castelnuovo-type bounds for PT and GV invariants for CY threefolds with Picard rank one.

Résumé:

I'll explain the role of modular symmetry in the counting of black hole microstates.

Ref HAL: hal-03811118_v1
Exporter : BibTex | endNote
Résumé:

I'll give a review of the role that modular symmetry plays in description of BPS black holes and counting of their microstates.