Quantum Fields and Strings

The study of string scattering in general curved spacetimes presents a stark contrast to the relatively well-understood framework in flat space, where perturbative techniques and worldsheet methods can be used. However, the AdS/CFT correspondence offers a powerful indirect method to compute string amplitudes in AdS. In this talk, I will present recent developments in the AdS Virasoro-Shapiro program. The tree-level amplitude of four gravitons in AdS^5 x S^5 is mapped to a four-point correlator in N=4 SYM at large central charge, and studied by CFT methods combined with single-valuedness, which echoes its importance in flat space. The amplitude itself is defined and constructed as an expansion around flat space. While the goal is to compute it to all orders, attention can be placed on more tractable limits. I will present our results for the High Energy limit, with dual insights from the spacetime and worldsheet perspectives, and the richer case of the Regge limit, which encodes full information on the intermediate operators in the leading Regge trajectory.

We construct the phase space of a spherically symmetric causal diamond in (d+2)-dimensional Minkowski spacetime. Utilizing the covariant phase space formalism, we identify the relevant degrees of freedom that localize to the d-dimensional bifurcate horizon and, upon canonical quantization, determine their commutators. On this phase space, we find two Iyer-Wald charges. The first of these charges, proportional to the area of the causal diamond, is responsible for shifting the null time along the horizon and has been well-documented in the literature. The second charge is much less understood, being integrable for d ≥ 2 only if we allow for field-dependent diffeomorphisms and is responsible for changing the size of the causal diamond. 

"Null Polygons" in N=4 SYM theory describe the multi-point correlators of 1/2-BPS local operators with large R-charge, when they approach the vertices of a light-like polygon. The leading UV divergences of null polygons is conjectured to satisfy a hierarchy of coupled Toda field theory equations [E.O., Vieira ’22]. I will present some progress towards the prediction of Null Polygons beyond leading logarithms via the hexagons technique, appropriately truncated in the light-cone regime. The method, still conjectural, relies on a series of weak-coupling derivations performed in the Fishnet limit of the theory, where the hexagon representation is derived in the basis of eigenfunctions of a conformal Heisenberg magnet in the principal series. I will present a number of worked-out examples for multi-point multi-loop Fishnet Feynman integrals and Null Polygons.

---

Zoom link