Integrated Correlators in N=4 Supersymmetric Yang-Mills Theory beyond Localization.

We study integrated correlators of four superconformal primaries O_{p} with arbitrary charges p in N=4 super Yang-Mills theory. The ⟨O_{2}O_{2}O_{p}O_{p}⟩ integrated correlators can be computed by supersymmetric localization, whereas correlators with more general charges are currently not accessible from this method and, in general, contain complicated multiple zeta values. Nevertheless, we observe that, if one sums over the contributions from all different channels in a given correlator, then all the multiple zeta values (and products of ζ's) cancel, leaving only ζ(2ℓ+1) at ℓ loops. We then propose an exact expression of such integrated correlators in the planar limit, valid for arbitrary 't Hooft coupling. The expression matches with the known exact localization-based results for specific charges, as well as with all existing perturbative and strong-coupling results in the literature for more general charges. As an application, our result is used to determine certain seven-loop Feynman integral periods and fix previously unknown coefficients in the correlators at strong coupling.

Kinematic Hopf Algebra for Bern-Carrasco-Johansson Numerators in Heavy-Mass Effective Field Theory and Yang-Mills Theory.

We present a closed formula for all Bern-Carrasco-Johansson (BCJ) numerators describing D-dimensional tree-level scattering amplitudes in a heavy-mass effective field theory with two massive particles and an arbitrary number of gluons. The corresponding gravitational amplitudes obtained via the double copy directly enter the computation of black-hole scattering and gravitational-wave emission. Our construction is based on finding a kinematic algebra for the numerators, which we relate to a quasishuffle Hopf algebra. The BCJ numerators thus obtained have a compact form and intriguing features: gauge invariance is manifest, locality is respected for massless exchange, and they contain poles corresponding to massive exchange. Counting the number of terms in a BCJ numerator for n-2 gluons gives the Fubini numbers F_{n-3}, reflecting the underlying quasishuffle Hopf algebra structure. Finally, by considering an appropriate factorization limit, the massive particles decouple, and we thus obtain a kinematic algebra and all tree-level BCJ numerators for D-dimensional pure Yang-Mills theory.

Novel Representation of an Integrated Correlator in N=4 Supersymmetric Yang-Mills Theory.

An integrated correlator of four superconformal stress-tensor primaries of N=4 supersymmetric SU(N) Yang-Mills theory (SYM), originally obtained by localization, is reexpressed as a two-dimensional lattice sum that is manifestly invariant under SL(2,Z) S duality. This expression is shown to satisfy a novel Laplace equation in the complex coupling constant τ that relates the SU(N) integrated correlator to those of the SU(N+1) and SU(N-1) theories. The lattice sum is shown to precisely reproduce known perturbative and nonperturbative properties of N=4 SYM for any finite N, as well as extending previously conjectured properties of the large-N expansion.

All Tree Amplitudes of 6D (2,0) Supergravity: Interacting Tensor Multiplets and the K3 Moduli Space.

We present a twistorlike formula for the complete tree-level S matrix of six-dimensional (6D) (2,0) supergravity coupled to 21 Abelian tensor multiplets. This is the low-energy effective theory that corresponds to type IIB superstring theory compactified on a K3 surface. The formula is expressed as an integral over the moduli space of certain rational maps of the punctured Riemann sphere. By studying soft limits of the formula, we are able to explore the local moduli space of this theory, {[SO(5,21)]/[SO(5)×SO(21)]}. Finally, by dimensional reduction, we also obtain a new formula for the tree-level S matrix of 4D N=4 Einstein-Maxwell theory.

Dualities for Ising Networks.

In this Letter, we study the equivalence between planar Ising networks and cells in the positive orthogonal Grassmannian. We present a microscopic construction based on amalgamation, which establishes the correspondence for any planar Ising network. The equivalence allows us to introduce two recursive methods for computing correlators of Ising networks. The first is based on duality moves, which generate networks belonging to the same cell in the Grassmannian. This leads to fractal lattices where the recursion formulas become the exact renormalization group equations of the effective couplings. The second, we use an amalgamation in which each iteration doubles the size of the seed lattice. This leads to an efficient way of computing the correlator where the complexity scales logarithmically with respect to the number of spin sites.

Vector Effective Field Theories from Soft Limits.

We present a bottom-up construction of vector effective field theories using the infrared structure of scattering amplitudes. Our results employ two distinct probes of soft kinematics: multiple soft limits and single soft limits after dimensional reduction applicable in four and general dimensions, respectively. Both approaches uniquely specify the Born-Infeld (BI) model as the only theory of vectors completely fixed by certain infrared conditions which generalize the Adler zero for pions. These soft properties imply new recursion relations for on-shell scattering amplitudes in BI theory and suggest the existence of a wider class of vector effective field theories.

Generalized Wilson-Fisher Critical Points from the Conformal Operator Product Expansion.

We study possible smooth deformations of the generalized free conformal field theory in arbitrary dimensions by exploiting the singularity structure of the conformal blocks dictated by the null states. We derive in this way, at the first nontrivial order in the ε expansion, the anomalous dimensions of an infinite class of scalar local operators, without using the equations of motion. In the cases where other computational methods apply, the results agree.

New Fermionic Soft Theorems for Supergravity Amplitudes.

Soft limits of a massless S matrix are known to reflect the symmetries of the theory. In particular, for theories with Goldstone bosons, the double-soft limit of scalars reveals the coset structure of the vacuum manifold. In this Letter, we propose that such universal double-soft behavior is not only true for scalars, but also for spin-1/2 particles in four dimensions and fermions in three dimensions. We first consider the Akulov-Volkov theory and demonstrate that the double-soft limit of Goldstinos yields the supersymmetry algebra. More surprisingly, we also find that amplitudes in 4≤N≤8 supergravity theories in four dimensions as well as N=16 supergravity in three dimensions behave universally in the double-soft-fermion limit, analogous to the scalar ones. The validity of the new soft theorems at loop level is also studied. The results for supergravity are beyond what is implied by supersymmetry Ward identities and may impose nontrivial constraints on the possible counterterms for supergravity theories.