Ref HAL: hal-05340685_v1
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BPS indices encoding the entropy of supersymmetric black holes in compactifications of Type II string theory on Calabi-Yau threefolds, known in mathematics as generalized Donaldson-Thomas invariants, possess remarkable (mock) modular properties. I'll explain the physical origin of mock modularity and show, for a set of one-parameter threefolds, how it can be used, together with wall-crossing and direct integration of topological string, to compute the BPS indices and other topological invariants. As a result, one obtains explicit (mock) modular functions encoding infinite sets of D4-D2-D0 BPS indices as well as new boundary conditions for the holomorphic anomaly equation of the topological string partition function allowing to overcome the limitations of the direct integration method. In the end, I'll present preliminary results on the asymptotic growth of DT invariants hinting for the existence of some phase transitions.

Ref HAL: hal-05240961_v1
DOI: 10.48550/arXiv.2509.03293
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Instanton contributions in 2d string theory are known to include subtle numerical factors $ζ_n$ closely related to a contour prescription in multi-instanton string amplitudes. Both ingredients appear to be ambiguous due to a degeneracy between $(1,n)$-ZZ instantons and $n$ (1,1)-ZZ instantons in the linear dilaton background. We resolve this ambiguity using insights from the dual matrix quantum mechanics where the multipliers $ζ_n$ can be derived from an integral representation of the scattering phase and follow from the median resummation prescribed by resurgence theory. We evaluate multi-instanton string amplitudes in the theory compactified on a circle of finite radius for arbitrary number of instantons and show that they reproduce the matrix model predictions provided the Lorentzian contour prescription is used for their evaluation. We also show that the non-perturbative free energy matches the structure of the D-instanton induced string field theory effective action, which suggests the vanishing of contributions from worldsheet topologies of negative Euler number.

Ref HAL: hal-05184942_v1
Ref Arxiv: 2507.16908
Ref INSPIRE: 2953431
DOI: 10.48550/arXiv.2507.16908
Ref. & Cit.: NASA ADS
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Refined BPS indices give rise to a quantum Riemann-Hilbert problem that is inherently related to a non-commutative deformation of moduli spaces arising in gauge and string theory compactifications. We reformulate this problem in terms of a non-commutative deformation of a TBA-like equation and obtain its formal solution as an expansion in refined indices. As an application of this construction, we derive a generating function of solutions of the TBA equation in the unrefined case.

Ref HAL: hal-05136598_v1
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The normalization of multi-instanton effects in two-dimensional string theory involves numerical factors that are hard to determine. I'll show how they can be found using a chiral representation of the dual matrix quantum mechanics.The result is confirmed by a string field theory calculation of annuli amplitudes and nicely agrees with a median resummation of the Gamma function.

Ref HAL: hal-05060199_v1
Ref Arxiv: 2505.02572
DOI: 10.3390/e27070719
Ref. & Cit.: NASA ADS
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Mock modular forms, first invented by Ramanujan, provide a beautiful generalization of the usual modular forms. In recent years, it was found that they capture generating functions of the number of microstates of BPS black holes appearing in compactifications of string theory with 8 and 16 supercharges. This review describes these results and their applications which range from the actual computation of these generating functions for both compact and non-compact compactification manifolds (encoding, respectively, Donaldson-Thomas and Vafa-Witten topological invariants) to the construction of new non-commutative structures on moduli spaces of Calabi-Yau threefolds.

Ref HAL: hal-04809892_v1
Ref Arxiv: 2411.17699
Ref. & Cit.: NASA ADS
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Generating functions hr(τ ) of D4-D2-D0 BPS indices, appearing in Calabi-Yau compactifications of type IIA string theory and identical to rank 0 Donaldson-Thomas invariants, are known to be higher depth mock modular forms satisfying a specific modular anomaly equation, with depth determined by the D4-brane charge r. We develop a method to solve the anomaly equation for arbitrary charges, in terms of indefinite theta series. This allows us to find the generating functions up to modular forms that can be fixed by computing just a finite number of Fourier coefficients of hr.

Ref HAL: hal-04821368_v1
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Twistor space provides an efficient description of quaternion-Kahler (QK) manifolds. In physics, the latter appear as supergravity moduli spaces and often carry an isometric action of the S-duality group SL(2,Z). I’ll show that a lift of S-duality to the twistor space gives rise to a rich and interesting structure, and describe its consequences for a class of QK manifolds arising in Calabi-Yau string compactifications. In particular, this includes mock modularity of generating functions of DT invariants and the weak/strong coupling duality of topological string partition function.