Motivated by the recent discovery of hidden zeros in particle and string amplitudes, we characterize zeros of individual graph contributions to the cosmological wavefunction of a scalar field theory. We demonstrate that these contributions factorize near these zeros for all tree graphs and provide evidence that this extends to loop graphs as well. We explicitly construct polytopal realizations of the relevant graph associahedra and show that the cosmological zeros have natural geometric and physical interpretations. As a byproduct, we establish an equivalence between the wavefunction coefficients of chain graphs and flat-space Tr($\textit{ϕ}$ ) amplitudes, enabling us to leverage the cosmological zeros to uncover the recently discovered hidden zeros of colored amplitudes.

United States

Shounak De

Shruti Paranjape

Andrzej Pokraka

Marcus Spradlin

Anastasia Volovich

Hidden zeros of the cosmological wavefunction

We develop a spinor helicity formalism for five-dimensional scattering amplitudes of any mass and spin configuration. While five-dimensional spinor helicity variables have been previously studied in the context of $$ \mathcal{N} $$ = 2, 4 supersymmetric Yang-Mills scattering amplitudes with spin less than two [1], we propose an alternative viewpoint that stems from $\textit{d}$-dimensional spinor helicity variables avoiding the decomposition of a massive momentum into the sum of two massless momenta. By enumerating all possible independent little group tensors, we systematically build the full space of five-dimensional three-point tree-level scattering amplitudes for any configuration of spins and masses. Furthermore, we provide a prescription for computing the high energy limit of scattering amplitudes written in our spinor helicity variables. We also expect that our formalism will be applicable to effective field theories with higher spin, in particular, the scattering of highly spinning black holes in five dimensions.

Smita Rajan

Lecheng Ren

W. Zhao

Five-dimensional spinor helicity for all masses and spins

We use partial wave unitarity to constrain various bespoke four-point amplitudes. We start by constructing bespoke generalizations of the type-I superstring amplitude, which we show satisfy dual resonance and have suitable high-energy limits. By analyzing the behavior of partial wave coefficients for highly massive states, we strictly rule out all bespoke amplitudes with asymptotically nonlinear Regge trajectories and place constraints on the first few nontrivial parameters in asymptotically linear cases. Finally, we argue that while a large class of unitary bespoke amplitudes fails to satisfy Regge sum rules, there exists a smaller subclass with a vanishing mass gap that is superpolynomially bounded.

Rishabh Bhardwaj

He-Chen Weng

Unitarity of bespoke amplitudes

Arkani-Hamed and collaborators have recently shown that scattering amplitudes for colored theories can be expressed as integrals over combinatorial objects simply constructed from surfaces decorated by kinematic data. In this paper we extend the curve integral formalism to theories with colored fermionic matter and present a compact formula for the all-loop, all-genus, all-multiplicity amplitude integrand of a colored Yukawa theory. The curve integral formalism makes certain properties of the amplitudes manifest and repackages non-trivial numerators into a single combinatorial object. We also present an efficient formula for L-loop integrated amplitudes in terms of a sum over 2 L  combinatorial determinants.

Marcos Skowronek

Surfaceology for colored Yukawa theory

We compute the leading (first-type Landau) singularities of a certain four-loop 7-point graph that is related to the 7-point “ziggurat” graph by the graphical moves familiar from equivalent circuit theory. We find perfect agreement with a subset of the “heptagon symbol alphabet” that has appeared in the context of planar   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 super-Yang-Mills theory. The remaining heptagon symbol letters are found in its subleading Landau singularities, which we address in a companion paper.

Luke Lippstreu

Landau singularities of the 7-point ziggurat. Part I

Recently in arXiv:2012.05599 Rudenko presented a formula for the volume of hyperbolic orthoschemes in terms of alternating polylogarithms. We use this result to provide an explicit analytic result for the one-loop scalar -gon Feynman integral in dimensions, for even , with massless or massive internal and external edges. Furthermore, we evaluate the general six-dimensional hexagon integral in terms of classical polylogarithms.

Denmark

Cristian Vergu

One-loop integrals from volumes of orthoschemes

In this paper we study the simplifying effects of supersymmetry on celestial OPEs at both tree and loop level. We find at tree level that theories with unbroken supersymmetry around a stable vacuum have celestial soft current algebras satisfying the Jacobi identity, and we show at one loop that celestial OPEs in these theories have no double poles.

Canada

Adam Ball

United Kingdom

Akshay Srikant

Supersymmetry and the celestial Jacobi identity

We compute scattering amplitudes involving one massive scalar and two, three, or four gravitons. We show that when the conformal dimension of the massive scalar is set to zero, the resulting celestial correlators depend only on the coordinates of the gravitons. Such correlators of gravitons are well-defined and do not suffer from divergences associated with the Mellin transform of usual graviton amplitudes. Moreover, they are non-distributional and take the form of standard CFT correlators. We show that they are consistent with the usual OPEs but the statement of the soft theorem is modified.

Scalar-graviton amplitudes and celestial holography

We solve the Landau equations to find the singularities of nine three-loop 7-point graphs that arise as relaxations of the graph studied in [22]. Along the way we establish that Y − ∆ equivalence fails for certain branches of solutions to the Landau equations. We find two graphs with singularities outside the heptagon symbol alphabet; in particular they are not cluster variables of Gr(4, 7). We compare maximal residues of scalar graphs exhibiting these singularities to those in   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 super-Yang-Mills theory in order to probe their cancellation from its amplitudes.

Landau singularities of the 7-point ziggurat. Part II

We show that the Killing tensor of the Kerr spacetime has an analogue in the   <math> <msqrt> <mtext>Kerr</mtext> </msqrt> </math>  $$ \sqrt{\textrm{Kerr}} $$  gauge theory solution related to it by the classical double copy. This hidden symmetry of   <math> <msqrt> <mtext>Kerr</mtext> </msqrt> </math>  $$ \sqrt{\textrm{Kerr}} $$  leads to an additional constant of motion for color-charged point particles moving in it, implying integrability of the equation of motion. These are the gauge theory counterparts to the Carter constant and the integrability of the geodesic equation in a Kerr background.