arXiv subjects

Sebastian Mizera

Publications and source records attributed to Sebastian Mizera.

At least 19 recordsLinked to original sources

arXiv2026

SubTropica

We present SubTropica, a Mathematica package that performs symbolic integration of multi-polylogarithmic integrals using recent advances in tropical geometry. It focuses on the class of linearly-reducible Euler integrals, such as Feynman integrals, and expands them using a tropical subtraction scheme. The engine behind it is HyperIntica, a native Mathematica package for hyperlogarithm integration that can be used independently. This paper documents both packages and illustrates their usage on examples from across different physics applications. Additionally, we introduce an AI-driven library of Feynman integrals, which catalogs diagrams discussed in the literature and serves as a database for computed results. Its online version is available at: https://subtropi.ca and features a graphical user interface for diagram input and retrieval of records.

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arXiv2026

Precision asymptotics of string amplitudes

Recent work revealed a tension between the Gross-Mende analysis of the high-energy fixed-angle behavior of string amplitudes and the explicit numerical data. Motivated by this puzzle, we revisit the problem of classifying saddle-point geometries for the one-loop amplitude. We find an infinite family of complex saddles that dominate the high-energy regime. Using general constraints and matching to numerical data, we formulate a bootstrap problem that determines their multiplicities. This procedure yields a precise asymptotic expansion of the one-loop amplitude at high energies. The resulting oscillatory contributions lead to a much richer high-energy behavior than that predicted by the original Gross-Mende analysis.

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arXiv2025

The Unitary Architecture of Renormalization

We set up a bootstrap problem for renormalization. Working in the massless four-dimensional O$(N)$ model and the $\lambda \phi^4$ theory, we prove that unitarity leads to all-loop recursion relations between coefficients of scattering amplitudes with different multiplicities. These turn out to be equivalent to the identities imposed by renormalization of the coupling and the wavefunction through subleading logarithmic order, except with different initial conditions. Matching the initial conditions thus fixes the beta function and wavefunction anomalous dimension to these orders. We explain how to connect this new on-shell renormalization picture with the standard renormalized perturbation theory, highlighting a rich interplay between finiteness, dimensional regularization, and unitarity cuts.

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arXiv2025

The Unitarity Flow Conjecture: An On-shell Approach to the Renormalization Group

We propose that the broad architecture of the renormalization group flow in quantum field theories is, at least in part, fixed by unitarity. The precise statement is summarized in the Unitarity Flow Conjecture, which states that the non-linear $S$-matrix identities obtained by imposing unitarity imply those needed to derive the renormalization group equations. As a proof of principle, we verify this conjecture to all loops at the leading and subleading logarithmic order in the four-dimensional massless $\lambda\phi^4$ theory using on-shell techniques, without reference to any counterterms or Feynman diagrams.

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arXiv2025

One-loop four-graviton string amplitude at finite $\alpha'$

We evaluate the one-loop four-graviton scattering amplitude in type-II superstring theory exactly in $\alpha'$. This result is achieved by combining physical insights into the $i\varepsilon$ prescription in string theory with a new technical application of the Rademacher expansion of modular integrals. We provide an implementation of our formula in $\texttt{C++}$ and use it to study the behavior of the amplitude at finite $\alpha'$ and in different kinematic regimes. Our analysis reveals a tension between explicit computations and the saddle point analysis of Gross and Mende in the high-energy limit and suggests the presence of additional saddle points.

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arXiv2025

SOFIA: Singularities of Feynman Integrals Automatized

We introduce SOFIA, a Mathematica package that automatizes the computation of singularities of Feynman integrals, based on new theoretical understanding of their analytic structure. Given a Feynman diagram, SOFIA generates a list of potential singularities along with a candidate symbol alphabet. The package also provides a comprehensive set of tools for analyzing the analytic properties of Feynman integrals and related objects, such as cosmological and energy correlators. We showcase its capabilities by reproducing known results and predicting singularities and symbol alphabets of Feynman integrals at and beyond the high-precision frontier.

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arXiv2025

Records from the S-Matrix Marathon: Asymptotic Observables

These lectures introduce the notion of asymptotic observables, which are classes of measurable quantities predicted by quantum field theory. In gapped theories with trivial infrared dynamics, these include scattering amplitudes, expectation values of operators approaching infinity, inclusive cross sections, etc. We argue for a unified picture in which various asymptotic observables are related by analytic continuation embodying new versions of crossing symmetry. As an application, we discuss the exponentiation of infrared divergences for inclusive observables in Quantum Electrodynamics using time-folded contours. Finally, we outline prospects for a systematic study of analyticity properties of asymptotic observables using the Fourier-Bros-Iagolnitzer transform. These notes are based on a series of lectures held during the S-Matrix Marathon workshop at the Institute for Advanced Study on 11-22 March 2024.

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arXiv2025

Rademacher expansion of modular integrals

We develop a method to evaluate integrals of non-holomorphic modular functions over the fundamental domain of the torus with modular parameter $\tau$ analytically. It proceeds in two steps: first the integral is transformed to a Lorentzian contour by the same strategy that leads to the Lorentzian inversion formula in CFT, and then we apply a two-dimensional version of the Rademacher expansion. This computes the integral in terms of an expansion sensitive to the singular behaviour of the integrand near all the Lorentzian cusps $\tau \to i \infty$, $\bar{\tau} \to x \in \mathbb{Q}$. We apply this technique to a variety of examples such as the evaluation of string one-loop partition functions, where it leads to the first analytic formula for the cosmological constants of the bosonic string and the $\mathrm{SO}(16) \times \mathrm{SO}(16)$ string.

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arXiv2024

Records from the S-Matrix Marathon: Gravitational Physics from Scattering Amplitudes

These lecture notes explain how classical gravitational physics emerges from scattering amplitudes. We emphasize the role of different kinematic regimes in probing various aspects of bound and unbound problems, as illustrated by the Hydrogen atom example. Classical predictions of General Relativity, such as the Shapiro time delay and perihelion precession, emerge from these considerations. We also explain a number of recent approaches to probing black hole physics from the perspective of amplitudes, including applications of worldline effective field theory in astrophysics, predictions of gravitational waveforms, and the hierarchical three-body problem. These notes are based on a series of lectures held during the S-Matrix Marathon workshop at the Institute for Advanced Study on 11--22 March 2024.

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arXiv2024

Records from the S-Matrix Marathon: Tasty Bits of Several Complex Variables

We will cover the basics of several complex variables in 4 lectures: Basic properties of holomorphic functions in several variables, the notion of pseudoconvexity, CR functions and CR geometry, and the $\bar\partial$-problem. The main underlying idea is to connect various characterizations of domains of holomorphy, that is, the natural domains of definition for holomorphic functions. In the process we will connect the function theory on the domain to geometric properties of the boundary, and discuss the relationship between the boundary values and the functions themselves and extension of holomorphic functions from subspaces. These notes are based on a series of lectures held during the S-Matrix Marathon workshop at the Institute for Advanced Study on 11-22 March 2024.

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arXiv2024

Records from the S-Matrix Marathon: A Timeless History of Time

By directly probing the initial conditions of our universe, cosmological surveys offer us a unique observational handle on quantum field theory in curved spacetime with dynamical gravity and might even allow us to glean information about a full theory of quantum gravity. Here we report on recent progress to study the natural observables in the problem, namely cosmological correlators. After setting the stage, we review results from three different approaches. First, we present the in-out formalism as an interesting alternative to the well-known in-in formalism and stress some of its advantages, such as the derivation of recursion relations, correlators cutting rules and a proposal for a de Sitter scattering matrix. Second, we tackle the important open problem of constructing effective theories in curved spacetime, which generally requires an open quantum system approach. Third, we provide an executive summary of general properties of the field-theoretic wavefunction that follow from symmetries, unitarity, causality and locality. We describe how these properties can be leveraged to bootstrap all tree-level results and we discuss loop contributions. These notes are based on a series of lectures held during the S-Matrix Marathon workshop at the Institute for Advanced Study on 11-22 March 2024.

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arXiv2024

Records from the S-Matrix Marathon: Observables in Expanding Universes

Observables in expanding universes are crucial to understand the physics of the early universe. In these lectures, we review some recent progress in understanding their mathematical structure and extract the physics encoded in them. After discussing the most salient features of an expanding background and their consequences for defining an observable, we focus on the so-called Bunch--Davies wavefunctional. We analyze its analytic properties on general grounds and introduce an integral representation for it in perturbation theory for a special class of scalar toy models. We discuss both the diagrammatics associated to the usual Feynman rules and combinatorial rules on the graphs, which generate a representation free of spurious poles. Such combinatorial rules find their origin in the combinatorics of the cosmological polytopes of which we provide a gentle introduction to its definition and its main features. Finally, the combinatorics of the cosmological polytopes turns out to determine the combinatorics of a special class of nestohedra that encode the asymptotic behaviour of the cosmological integrals. We provide a general description of such structures and behaviour, which is of crucial importance to understand the infrared divergences which plague observables in an expanding background. These notes are based on a series of lectures held during the S-Matrix Marathon workshop at the Institute for Advanced Study on 11--22 March 2024.

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arXiv2024

Lorentzian contours for tree-level string amplitudes

We engineer compact contours on the moduli spaces of genus-zero Riemann surfaces that achieve analytic continuation from Euclidean to Lorentzian worldsheets. These generalized Pochhammer contours are based on the combinatorics of associahedra and make the analytic properties of tree-level amplitudes entirely manifest for any number and type of external strings. We use them in practice to perform first numerical computations of open and closed string amplitudes directly in the physical kinematics for $n=4,5,6,7,8,9$. We provide a code that allows anyone to do such computations.

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arXiv2024

Regge Limit of One-Loop String Amplitudes

We study the high-energy limit of $2 \to 2$ one-loop string amplitudes at fixed momentum transfer. For the closed string, the high-energy behaviour of the amplitudes can be determined from Regge theory just like in field theory, as was first discussed by Amati, Ciafaloni and Veneziano. However, field theory intuition partially breaks down for the open-string amplitude, where amplitudes can exhibit surprising asymptotics in the high-energy limit depending on the topology of the diagram. We call this phenomenon Regge attenuation. We extract Regge limits by a combination of unitarity cuts and saddle-point analysis. We show that the leading contribution of the planar open-string amplitude is sufficiently simple that we can extract it at any loop order. This allows us to resum the genus expansion in a certain limit and demonstrate that the leading Regge trajectory remains linear in that limit.

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arXiv2024

Cutting-Edge Tools for Cutting Edges

We review different notions of cuts appearing throughout the literature on scattering amplitudes. Despite similar names, such as unitarity cuts or generalized cuts, they often represent distinct computations and distinct physics. We consolidate this knowledge, summarize how cuts are used in various computational strategies, and explain their relations to other quantities including imaginary parts, discontinuities, and monodromies. Differences and nuances are illustrated on explicit examples.

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arXiv2024

Language Models as Science Tutors

NLP has recently made exciting progress toward training language models (LMs) with strong scientific problem-solving skills. However, model development has not focused on real-life use-cases of LMs for science, including applications in education that require processing long scientific documents. To address this, we introduce TutorEval and TutorChat. TutorEval is a diverse question-answering benchmark consisting of questions about long chapters from STEM textbooks, written by experts. TutorEval helps measure real-life usability of LMs as scientific assistants, and it is the first benchmark combining long contexts, free-form generation, and multi-disciplinary scientific knowledge. Moreover, we show that fine-tuning base models with existing dialogue datasets leads to poor performance on TutorEval. Therefore, we create TutorChat, a dataset of 80,000 long synthetic dialogues about textbooks. We use TutorChat to fine-tune Llemma models with 7B and 34B parameters. These LM tutors specialized in math have a 32K-token context window, and they excel at TutorEval while performing strongly on GSM8K and MATH. Our datasets build on open-source materials, and we release our models, data, and evaluations.

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arXiv2023

Principal Landau Determinants

We reformulate the Landau analysis of Feynman integrals with the aim of advancing the state of the art in modern particle-physics computations. We contribute new algorithms for computing Landau singularities, using tools from polyhedral geometry and symbolic/numerical elimination. Inspired by the work of Gelfand, Kapranov, and Zelevinsky (GKZ) on generalized Euler integrals, we define the principal Landau determinant of a Feynman diagram. We illustrate with a number of examples that this algebraic formalism allows to compute many components of the Landau singular locus. We adapt the GKZ framework by carefully specializing Euler integrals to Feynman integrals. For instance, ultraviolet and infrared singularities are detected as irreducible components of an incidence variety, which project dominantly to the kinematic space. We compute principal Landau determinants for the infinite families of one-loop and banana diagrams with different mass configurations, and for a range of cutting-edge Standard Model processes. Our algorithms build on the Julia package Landau.jl and are implemented in the new open-source package PLD.jl available at https://mathrepo.mis.mpg.de/PLD/.

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arXiv2023

Landau Singularities Revisited: Computational Algebraic Geometry for Feynman Integrals

We reformulate the analysis of singularities of Feynman integrals in a way that can be practically applied to perturbative computations in the Standard Model in dimensional regularization. After highlighting issues in the textbook treatment of Landau singularities, we develop an algorithm for classifying and computing them using techniques from computational algebraic geometry. We introduce an algebraic variety called the principal Landau determinant, which captures the singularities even in the presence of massless particles or UV/IR divergences. We illustrate this for 114 example diagrams, including a cutting-edge 2-loop 5-point non-planar QCD process with multiple mass scales. The algorithms introduced in this work are implemented in the open-source Julia package PLD.jl available at https://mathrepo.mis.mpg.de/PLD/.

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