Congkao Wen

We study the giant graviton integrated correlator in SU ( N ) N = 4 super-Yang-Mills at finite complexified coupling τ . Despite the formidable complexity arising from the heavy nature of the operators considered, the large- N expansion simplifies dramatically and exhibits manifest modular invariance. At each order in 1 / N , the expansion coefficients are linear combinations of nonholomorphic Eisenstein series, thus capturing the full spectrum of perturbative and nonperturbative effects in the Yang-Mills coupling. Furthermore, we find additional contributions, which are modular functions exponentially suppressed in N . In the ’t Hooft limit, this yields an all-orders result in the 1 / N expansion at arbitrary coupling λ , extending beyond prior results of leading orders. For the U ( N ) theory, we obtain a closed-form expression valid for all N and τ and show that the coupling-dependent sector of the large- N expansion is universal between SU ( N ) and U ( N ) to all orders. Crucially, we exploit the integrated correlator constraints and determine the giant graviton correlator itself to two-loop order at finite N , previously only accessible in the planar limit.

We develop bootstrap methods for mixed heavy-light four-point correlators ⟨ G G O O ⟩ in N = 4 super-Yang-Mills theory at large N , where O ≡ O 2 is the chiral primary operator in the stress-tensor multiplet and G are (dual) giant graviton operators with dimension of order N , including the maximal determinant case. The loop integrand is expanded in a basis of labeled f -graphs—necessarily including nonplanar topologies due to the dimension- N nature of the giant gravitons—and the coefficients are fixed by various bootstrap conditions, including double-triangle and triangle rules in the cusp and operator product expansion limits, integrated correlators from supersymmetric localization, and a ten-dimensional hidden symmetry, the latter also allowing extension to correlators involving generic chiral primaries O k . Together, these inputs uniquely determine the correlator through three loops, passing further nontrivial consistency checks. For the maximal determinant operator, we reproduce the known results through two loops and obtain the full three-loop correction.

We establish a precise formula relating the world sheet integral of the anti–de Sitter (AdS) Virasoro-Shapiro amplitude to the energy-energy correlator (EEC) in N = 4 super Yang-Mills theory at strong coupling. This mapping allows us to evaluate the coefficients of the AdS curvature expansion of the EEC in terms of the world sheet integral over a unit disk. To illustrate this idea, we explicitly compute the flat-space contribution and the first curvature correction to the EEC. Our results provide a rigorous description of the stringy energy flow, demonstrating how world sheet correlators imprint themselves on collider observables and offering a potential template for effective string descriptions of energy correlators in general gauge theories.

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 Letter 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 N = ( 2 , 0 ) and 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.