arXiv subjects

Marco Maria Baccianti

Publications and source records attributed to Marco Maria Baccianti.

3 recordsLinked to original sources

arXiv2026

Precision asymptotics of string amplitudes

Recent work revealed a tension between the Gross-Mende analysis of the high-energy fixed-angle behavior of string amplitudes and the explicit numerical data. Motivated by this puzzle, we revisit the problem of classifying saddle-point geometries for the one-loop amplitude. We find an infinite family of complex saddles that dominate the high-energy regime. Using general constraints and matching to numerical data, we formulate a bootstrap problem that determines their multiplicities. This procedure yields a precise asymptotic expansion of the one-loop amplitude at high energies. The resulting oscillatory contributions lead to a much richer high-energy behavior than that predicted by the original Gross-Mende analysis.

hep-th↗

arXiv2025

One-loop four-graviton string amplitude at finite $α'$

We evaluate the one-loop four-graviton scattering amplitude in type-II superstring theory exactly in $α'$. This result is achieved by combining physical insights into the $i\varepsilon$ prescription in string theory with a new technical application of the Rademacher expansion of modular integrals. We provide an implementation of our formula in $\texttt{C++}$ and use it to study the behavior of the amplitude at finite $α'$ and in different kinematic regimes. Our analysis reveals a tension between explicit computations and the saddle point analysis of Gross and Mende in the high-energy limit and suggests the presence of additional saddle points.

hep-th↗

arXiv2025

Rademacher expansion of modular integrals

We develop a method to evaluate integrals of non-holomorphic modular functions over the fundamental domain of the torus with modular parameter $τ$ analytically. It proceeds in two steps: first the integral is transformed to a Lorentzian contour by the same strategy that leads to the Lorentzian inversion formula in CFT, and then we apply a two-dimensional version of the Rademacher expansion. This computes the integral in terms of an expansion sensitive to the singular behaviour of the integrand near all the Lorentzian cusps $τ\to i \infty$, $\barτ \to x \in \mathbb{Q}$. We apply this technique to a variety of examples such as the evaluation of string one-loop partition functions, where it leads to the first analytic formula for the cosmological constants of the bosonic string and the $\mathrm{SO}(16) \times \mathrm{SO}(16)$ string.

hep-th↗