arXiv subjects

Michele Santagata

Publications and source records attributed to Michele Santagata.

6 recordsLinked to original sources

arXiv2026

Quantum Gravity on AdS$_3\times$S$^3$ from CFT: Bootstrapping $n=21$

We consider the simplest four-point scattering amplitude of $SO(n)$ tensor multiplets in six-dimensional (2,0) supergravity on AdS$_3\times$S$^3$. Using crossing symmetry and the consistency of the operator product expansion in the dual CFT, we explicitly construct the one-loop contribution to the correlator at order $1/c^2$, both in position space and in Mellin space. We show that a strong form of the bootstrap equations imposes constraints on the value of $n$. Remarkably, we find that our bootstrap approach uniquely determines $n=21$, which corresponds to the spectrum of IIB string theory compactified on K3. This stands in sharp contrast to the tree-level correlator for which $n$ is unconstrained. We also analyse the spectrum of unprotected double-trace operators and solve the mixing problem in the first case that involves both tensor and graviton correlators. When $n=21$, the anomalous dimensions rationalise and one of them vanishes. Lastly, we study the flat-space limit of the correlator and find perfect agreement with the one-loop amplitude recently obtained in [arXiv:2510.24558].

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arXiv2026

Degenerations of flat connections on Riemann surfaces

The integration kernels for polylogarithm functions on a compact Riemann surface of arbitrary genus $h$ are shown to close as the surface undergoes a non-separating degeneration to one of genus $h{-}1$. Explicit formulas are obtained for the non-separating degeneration of the multivariable Enriquez connection for genus $h$ with an arbitrary number of variables to the Enriquez connection for genus $h{-}1$ with two additional punctures whose Lie algebra generators are related to the original ones by the characteristic Bernoulli generating functions known from the degeneration at $h=1$. Analogous degeneration formulas are obtained for the single-valued DHS kernels at the leading order in the real degeneration parameter that is adapted to relating modular tensors at genus $h$ and $h{-}1$.

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arXiv2026

Surprising one-loop finiteness of 6D half-maximal supergravities

In four dimensions, it has long been established that gravity coupled to matter exhibits ultraviolet divergences at one loop, irrespective of supersymmetry. Notably, the four-matter one-loop amplitudes of half-maximal supergravity coupled to Maxwell multiplets were shown in the 1970s to be divergent. Surprisingly, we demonstrate in this work that half-maximal theories can nevertheless become one-loop finite when uplifted to higher dimensions, contrary to naive expectations. Specifically, we study the ultraviolet properties of the four-matter and two-matter two-graviton amplitudes in six-dimensional $\mathcal{N}=(2,0)$ and $\mathcal{N}=(1,1)$ supergravities, coupled to $n_T$ tensor and $n_V$ vector multiplets, respectively. We find that the one-loop amplitudes are finite for $n_T=21$ and $n_V=20$. This finiteness is unexpected, as symmetry-preserving counterterms do exist. Interestingly, both values exactly correspond to low-energy limits of type II string theories compactified on K3, which hints at possible origins to the surprising cancellations.

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arXiv2024

Non-analytic terms of string amplitudes from partial waves

We describe a general formalism based on the partial-wave decomposition to compute the iterative $s$-channel discontinuity of four-point amplitudes at any loop order. As an application, we focus on the low-energy expansions of type I and II superstring amplitudes. Besides providing new results for their leading and sub-leading logarithmic contributions beyond genus one, our approach elucidates the general structure of non-analytic threshold terms. In the case of open strings, the use of orthogonal colour projectors allows us to efficiently compute all contributions from different worldsheet topologies at a given loop order.

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arXiv2024

Genus-one open string amplitudes on AdS$_5\times$S$^3$ from CFT

We bootstrap one-loop string corrections to the four-point function of half-BPS operators in a 4d $\mathcal{N}=2$ SCFT with flavour group $SO(8)$, dual to gluon scattering at genus one on AdS$_5\times$S$^3$. We identify an 8-dimensional organising principle which governs the spectrum of double-trace anomalous dimensions, valid to all orders in the string length. This has precise implications for the structure of one-loop Mellin amplitudes, which we explicitly compute for the first three orders beyond the field-theory limit. We also consider the corresponding position space representation, which is entirely determined by the square of a certain differential operator acting on a simpler "pre-correlator". Finally, we show that the flat-space limit of the Mellin amplitudes exactly matches the logarithmic terms of the genus-one amplitude in 8-dimensional flat space, which we compute via a partial-wave analysis.

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arXiv2022

Two-particle spectrum of tensor multiplets coupled to $AdS_3\times S^3$ gravity

We study the spectrum of certain two-particle operators in the supergravity regime of the D1-D5 system, focussing on the four-point correlators of tensor multiplets on $AdS_3\times S^3$ at tree level. In Mellin space, these are nicely determined by a single amplitude, which makes manifest the large $p$ limit, the connection with the flat space S-matrix, and the six dimensional conformal symmetry. We compute the $(1,1)\times \overline{(1,1)}$ superconformal blocks for the two-dimensional $\mathcal{N}=(4,4)$ conformal theory at the boundary, and then we obtain a formula for the anomalous dimensions of the operators exchanged in the symmetric and anti-symmetric flavor channels. These anomalous dimensions solve an unmixing problem which is analogous to the one in $AdS_5\times S^5$, with interesting modifications. Along the way we show how the $(1,1)\times \overline{(1,1)}$ superconformal blocks relate to those in $\mathcal{N}=4$ SYM in four dimensions, and we provide new intuition on the known data for $AdS_5\times S^5$.

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