About

Professor Marcus B. Spradlin is a theoretical physicist specializing in string theory, duality, quantum gravity, and the mathematical aspects of quantum field theory. He holds an A.B. in Physics from Princeton University, earned in 1996 with summa cum laude honors, a Master of Advanced Study in Mathematics from the University of Cambridge obtained in 1997 with distinction, and a Ph.D. in Physics from Harvard University completed in 2001. At Brown University, he is affiliated with the Physics department and teaches a range of courses including Basic Physics, General Relativity, String Theory for Undergraduates, Classical Theoretical Physics, and Quantum Theory of Fields. His research focuses on advancing understanding in fundamental areas of theoretical physics, contributing to the development of concepts in string theory and related fields.

Research topics

• Mathematics
• Computer Science
• Physics
• Combinatorics
• Pure mathematics
• Quantum mechanics
• Mathematical analysis
• Mathematical physics
• Theoretical physics
• Discrete mathematics
• Algorithm
• Geometry

Selected publications

• Cluster Bootstrap for Cosmological Correlators

  arXiv (Cornell University) · 2026-03-09

  articleOpen access

  We show that cosmological wavefunction coefficients associated with $n$-site chain and loop graphs for a cubic scalar theory in de Sitter spacetime have symbol alphabets given by subsets of $A_{2n{-}2}$ and $B_{2n{-}1}$ cluster variables, respectively, and satisfy the associated cluster adjacency properties. The key step in proving this is identifying a precise connection between graph "tubings" that appear in the kinematic flow equation and polygon "triangulations" that encode the combinatorics of cluster compatibility. Our results imply that cosmological wavefunction coefficients in a general power-law FRW cosmology satisfy cluster adjacency to all orders in the $ε$ expansion. We use this information as bootstrap input to show that de Sitter symbols for $n \leq 4$ are uniquely determined by simple physical constraints.

  PublisherOA PDF

• de Sitter Wavefunction from Quadrangular Polylogarithms: Chain Graphs

  arXiv (Cornell University) · 2026-05-07

  preprintOpen access

  We present an explicit formula for the $n$-site chain graph contribution to the cosmological wavefunction for conformally coupled $ϕ^3$ theory in de Sitter space. Our result relies on the recent finding that the symbol of this function satisfies total compatibility with respect to the $A_{2n-2}$ cluster algebra, and that Rudenko's quadrangular polylogarithms provide, by construction, a complete basis for such functions. We prove our formula by directly relating a recursive set of differential equations satisfied by these wavefunction coefficients to a recursive coproduct formula for quadrangular polylogarithms.

  PublisherDOI

• Landau Analysis of One-Cycle Negative Geometries

  arXiv (Cornell University) · 2026-04-24

  preprintOpen access

  We use geometric Landau analysis to determine the singularity structure of four-point, one-cycle negative geometries in $\mathcal{N}=4$ super-Yang-Mills theory, which represent certain contributions to the logarithm of the four-point amplitude or equivalently the normalized quadrangular Wilson loop with a Lagrangian insertion. By analyzing the relevant Landau diagrams recursively, we prove that this quantity has singularities only at $z=-1,0$ and $\infty$ to all loop orders. This represents a first step towards obtaining a non-perturbative resummation for this quantity at next-to-leading order in the expansion over cycles.

  PublisherDOI

• Symbol alphabets in QCD and flag cluster algebras

  Journal of High Energy Physics · 2026-03-12 · 2 citations

  articleOpen accessCorresponding

  A bstract The full 245-letter symbol alphabet for all planar massless two-loop six-point Feynman integrals was recently determined in arXiv:2412.19884 and arXiv:2501.01847. In a parallel mathematical development, it was shown in arXiv:2408.14956 that there is an embedding of the cluster algebra associated to the partial flag variety $$ {\mathcal{Fl}}_{2,n-2;n} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Fl</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mi>n</mml:mi> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> <mml:mo>;</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:msub> </mml:math> , which describes the kinematics of n massless particles, into that of the Grassmannian Gr( n –2, 2 n –4). In this paper we connect these developments by showing that most of the rational symbol letters can be expressed in terms of flag cluster variables, and that all of the algebraic symbol letters arise from infinite mutation sequences.

  PublisherOA PDFDOI

• de Sitter Wavefunction from Quadrangular Polylogarithms: Chain Graphs

  ArXiv.org · 2026-05-07

  articleOpen access

  We present an explicit formula for the $n$-site chain graph contribution to the cosmological wavefunction for conformally coupled $ϕ^3$ theory in de Sitter space. Our result relies on the recent finding that the symbol of this function satisfies total compatibility with respect to the $A_{2n-2}$ cluster algebra, and that Rudenko's quadrangular polylogarithms provide, by construction, a complete basis for such functions. We prove our formula by directly relating a recursive set of differential equations satisfied by these wavefunction coefficients to a recursive coproduct formula for quadrangular polylogarithms.

  PublisherOA PDF

• Split-helicity tree amplitudes and flag cluster algebras

  Journal of High Energy Physics · 2026-05-12

  articleOpen access

  A bstract Recent work has uncovered a connection between the symbol letters of general massless scattering and (permutations of) cluster variables of partial flag varieties. In this paper we explore the cluster adjacency of tree-level gluon amplitudes, specifically focusing on split-helicity amplitudes which can be written in closed form in terms of zigzag diagrams. We check in several cases, and conjecture in general, that the poles in each term satisfy cluster adjacency under a set of permutations that is built from arc permutations of the corresponding zigzag.

  PublisherOA PDFDOI

• Large deformations of Tr(Φ3) and the world at infinity

  Journal of High Energy Physics · 2026-01-12

  articleOpen access

  A bstract The amplitudes of the non-linear sigma model can be obtained from those of Tr(Φ 3 ) theory by sending the kinematic (Mandelstam) variables to infinity in a certain direction. In this paper we characterize the behavior of Tr(Φ 3 ) amplitudes under a general class of large kinematic shifts called g -vector shifts. The objects that live in this world at infinity retain certain key amplitude-like properties, most notably factorization, and admit descriptions in terms of polytopes, but they are not generally amplitudes of any cognizable theory. We identify particular g -vector shifts that lead at infinity to mixed amplitudes involving two pions and any number of scalars, allowing us to provide polytopal descriptions of these amplitudes.

  PublisherOA PDFDOI

• Cluster Bootstrap for Cosmological Correlators

  Open MIND · 2026-03-09

  preprint

  We show that cosmological wavefunction coefficients associated with $n$-site chain and loop graphs for a cubic scalar theory in de Sitter spacetime have symbol alphabets given by subsets of $A_{2n{-}2}$ and $B_{2n{-}1}$ cluster variables, respectively, and satisfy the associated cluster adjacency properties. The key step in proving this is identifying a precise connection between graph "tubings" that appear in the kinematic flow equation and polygon "triangulations" that encode the combinatorics of cluster compatibility. Our results imply that cosmological wavefunction coefficients in a general power-law FRW cosmology satisfy cluster adjacency to all orders in the $ε$ expansion. We use this information as bootstrap input to show that de Sitter symbols for $n \leq 4$ are uniquely determined by simple physical constraints.

  DOI

• Landau Analysis of One-Cycle Negative Geometries

  ArXiv.org · 2026-04-24

  articleOpen access

  We use geometric Landau analysis to determine the singularity structure of four-point, one-cycle negative geometries in $\mathcal{N}=4$ super-Yang-Mills theory, which represent certain contributions to the logarithm of the four-point amplitude or equivalently the normalized quadrangular Wilson loop with a Lagrangian insertion. By analyzing the relevant Landau diagrams recursively, we prove that this quantity has singularities only at $z=-1,0$ and $\infty$ to all loop orders. This represents a first step towards obtaining a non-perturbative resummation for this quantity at next-to-leading order in the expansion over cycles.

  PublisherOA PDF

• Large deformations of Tr($Φ^3$) and the world at infinity

  ArXiv.org · 2025-04-15

  preprintOpen access

  The amplitudes of the non-linear sigma model can be obtained from those of Tr($Φ^3$) theory by sending the kinematic (Mandelstam) variables to infinity in a certain direction. In this paper we characterize the behavior of Tr($Φ^3$) amplitudes under a general class of large kinematic shifts called $g$-vector shifts. The objects that live in this world at infinity retain certain key amplitude-like properties, most notably factorization, and admit descriptions in terms of polytopes, but they are not generally amplitudes of any cognizable theory. We identify particular $g$-vector shifts that lead at infinity to mixed amplitudes involving two pions and any number of scalars, allowing us to provide polytopal descriptions of these amplitudes.

  PublisherOA PDFDOI

Recent grants

• String Theory Applications to Particle and Gravitational Physics

  NSF · $120k · 2006–2009

Frequent coauthors

• Anastasia Volovich

  240 shared

• Akshay Yelleshpur Srikant

  Brown University

  33 shared

• Jorge Mago

  Brown University

  26 shared

• Luke Lippstreu

  Brown University

  23 shared

• John Golden

  Los Alamos National Laboratory

  22 shared

• Cristian Vergu

  University of Copenhagen

  21 shared

• Anders Schreiber

  Max Planck Institute for Physics

  20 shared

• Maud Baylac

  Laboratoire de Physique Subatomique et de Cosmologie

  20 shared

Education

• B.A.

  Princeton University

  1996

• M.A.

  University of Cambridge

  1997

• Ph.D.

  Harvard University

  2001