Engineering Papers⌕ Search
Home/Archive/DOE OSTI

DOE OSTI · 2417789

The stratification of rigidity

Bourjaily, Jacob L.·Kalyanapuram, Nikhil
View original source ↗Read source document ↗Export metadata ↓

Abstract

We show that a master integrand basis exists for all planar, two-loop amplitudes in massless four-dimensional theories which is fully stratified by rigidity — with each integrand being either pure and strictly polylogarithmic or (pure and) strictly elliptic-polylogarithmic, with each of the later involving a single elliptic curve. Such integrands can be said to have definite rigidity.

Explore related subjects

1/N Expansion79 ASTRONOMY AND ASTROPHYSICSDifferential and Algebraic GeometryPhysicsScattering Amplitudes

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Bourjaily, Jacob L., Kalyanapuram, Nikhil. 2022-11-15. The stratification of rigidity. https://doi.org/10.1007/jhep11(2022)084

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related reports

DOE OSTI2025

All loop scattering for all multiplicity

We study the recently introduced curve integral formalism that defines a new family of formulas for the scattering amplitudes of the colored scalar trϕ 3 theory. We find that the curve integral manifests a very surprising fact about these amplitudes: the dependence on the number of particles, n, and the loop order, L, is effectively decoupled in these formulas. We derive the curve integrals at tree-level for all n. We then show that, for higher loop-order, it suffices to study the curve integrals for L-loop tadpole-like amplitudes, which have just one particle per color trace-factor. By combining these tadpole-like formulas with the tree-level results, we find formulas for the all n amplitudes at L loops. We illustrate this result by giving explicit curve integrals for all the amplitudes in the theory, including the non-planar amplitudes, through to two loops, for all n.

1/N Expansion↗
DOE OSTI2025

All loop scattering as a counting problem

Abstract This is the first in a series of papers presenting a new understanding of scattering amplitudes based on fundamentally combinatorial ideas in the kinematic space of the scattering data. We study the simplest theory of colored scalar particles with cubic interactions, at all loop orders and to all orders in the topological ’t Hooft expansion. We find novel integral formulas for the amplitudes of this theory, with no trace of the conventional sum over Feynman diagrams, but instead determined by a beautifully simple counting problem attached to any order of the topological expansion. These results represent a significant step forward in the decade-long quest to formulate the fundamental physics of the real world in a radically new language, where the rules of spacetime and quantum mechanics, as reflected in the principles of locality and unitarity, are seen to emerge from deeper mathematical structures.

1/N Expansion↗
DOE OSTI2025

Supersymmetry breaking in SYK and the black hole spectrum

The spectrum and dynamics of near-extremal black holes is strongly modified by quantum effects at low temperatures. When the extremal limit does not preserve any supersymmetry, the density of states goes to zero at extremality and no extremal black holes remain. However, when the extremal limit is supersymmetric, a large microscopic degeneracy survives and there is a gap to the first excited black hole visible from gravity. In this article we study large N quantum mechanical models where supersymmetry is explicitly broken, allowing us to interpolate between these two qualitatively different pictures. We propose and analyze deformations of N = 2 SYK models with such a pattern of (super) symmetry breaking which violate the U(1) R-symmetry. These models feature a lifting of the BPS degeneracy and a closing of the spectral gap, and we further show that the large N soft effective action is given by a modification of the N = 2 Schwarzian theory in which the U(1) R mode becomes massive.

1/N Expansion↗