Résumé:

Using dualities of string theory, I derive modular constraints onthe generating function of MSW invariants, which coincide withgeneralized Donaldson-Thomas invariants of a Calabi-Yau threefoldat the large volume attractor point in the moduli space. Thefunction is labeled by a divisor and when the divisor isirreducible, it is known to be modular. I show that in the case ofa reducible divisor, the modularity is lost, but can be restored in a non-holomorphic completion. I find a general form of thecompletion for arbitrary degree of reducibility and provide its explicit expression up to degree 5.

Ref HAL: hal-01875307_v1
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Résumé:

A class of BPS solutions in N=2 supergravity describes multi-centered black holes. Generically, they are stable only in a chamber of the moduli space so that the BPS index, counting these solutions, jumps across walls of marginal stability. I'll show how the attractor flow conjecture allows to express this index in terms of "attractor degeneracies" counting black holes at theattractor point. Besides, using duality constraints from string theory, I predict the behavior of the generating function of these degeneracies under modular transformations, which connects it to the theory of mock modular forms.

Ref HAL: hal-01852413_v2
Ref Arxiv: 1808.08479
DOI: 10.1007/s00220-019-03609-y
WoS: 000527910200005
Ref. & Cit.: NASA ADS
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Résumé:

By enforcing invariance under S-duality in type IIB string theory compactified on a Calabi-Yau threefold, we derive modular properties of the generating function of BPS degeneracies of D4-D2-D0 black holes in type IIA string theory compactified on the same space.Mathematically, these BPS degeneracies are the generalized Donaldson-Thomas invariants counting coherent sheaves with support on a divisor$\cal D$ , at the large volume attractor point. For $\cal D$ irreducible, this function is closely related to the elliptic genus of the superconformal field theory obtained by wrapping M5-brane on $\cal D$ and is therefore known to be modular. Instead, when $\cal D$ is the sum of $n$ irreducible divisors ${\cal D}_i$, we show that the generating function acquires a modular anomaly. We characterize this anomaly for arbitrary $n$ by providing an explicit expression for a non-holomorphic modular completion in terms of generalized error functions. As a result, the generating function turns out to be a (mixed) mock modular form of depth $n−1$.

Ref HAL: hal-01852407_v1
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Résumé:

A class of BPS solutions in N=2 supergravity describes multi-centered black holes. Generically, they are stable only in a chamber of the moduli space so that the BPS index, counting these solutions, jumps across walls of marginal stability. I'll show how the attractor flow conjecture allows to express this index in terms of "attractor degeneracies" counting black holes at theattractor point. Besides, using duality constraints from string theory, I predict the behavior of the generating function of these degeneracies under modular transformations, which connects it to the theory of mock modular forms.

Ref HAL: hal-01781942_v1
Ref Arxiv: 1804.06928
Ref INSPIRE: 1668938
DOI: 10.4310/ATMP.2019.v23.n3.a2
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
Résumé:

Inspired by the split attractor flow conjecture for multi-centered black hole solutions in $N = 2$ supergravity, we propose a formula expressing the BPS index $\Omega (\gamma , z)$ in terms of ‘attractor indices’ $\Omega_{\ast} (\gamma_i)$. The latter count BPS states in their respective attractor chamber. This formula expresses the index as a sum over stable flow trees weighted by products of attractor indices. We show how to compute the contribution of each tree directly in terms of asymptotic data, without having to integrate the attractor flow explicitly. Furthermore, we derive new representations for the index which make it manifest that discontinuities associated to distinct trees cancel in the sum, leaving only the discontinuities consistent with wall-crossing. We apply these results in the context of quiver quantum mechanics, providing a new way of computing the Betti numbers of quiver moduli spaces, and compare them with the Coulomb branch formula, clarifying the relation between attractor and single-centered indices.

Ref HAL: hal-03929817_v1
DOI: 10.1002/ADMI.201700984
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Résumé:

Chemical vapor deposition (CVD) processes had been around for nearly 100 years before they began to attract interest from materials scientists and electronics engineers in the 60s and 70s, as a result of the rapidly growing microelectronics industry. The successful development of this complicated technology required a deep physicochemical understanding of deposition processes and reaction mechanisms. This resulted in a large number of scientists from different disciplines studying the basics of CVD...

Résumé:

I'll discuss the modular properties of D3-brane instantons appearing in Calabi-Yau string compactifications. I'll show that the D3-instanton contribution to a certain geometric potential on the hypermultiplet moduli space can be related to the elliptic genus of (0,4) SCFT. The modular properties of the potential imply that the elliptic genus associated with non-primitive divisors of Calabi-Yau is only mock modular. I'll show how to construct its modular completion and to make manifest the modular invariance of the twistorial construction of D-instanton corrected hypermultiplet moduli space.