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arxiv: 2606.05978 · v1 · pith:E5ZKN7ELnew · submitted 2026-06-04 · ✦ hep-th · gr-qc

Lecture notes: Introduction to the Off-shell Double Copy Program

Eric Lescano This is my paper

Pith reviewed 2026-06-28 00:25 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords off-shell double copysingle copyT-dualityYang-Mills theorygravitygauge-gravity relations
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The pith

The off-shell double copy maps gauge theory fields to gravitational fields without first imposing equations of motion.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

These lecture notes review the basic structures of gauge theories and gravity to prepare for the off-shell single and double copy. The notes close by reinterpreting the copies inside T-duality-invariant frameworks. A reader would care because the approach supplies a systematic route from simpler gauge-theory data to gravitational results. The presentation requires only classical field theory and targets master's and PhD students.

Core claim

The single and double copy admit consistent off-shell formulations that relate the fields and actions of Yang-Mills theory to those of gravity, and these formulations admit reinterpretation within T-duality-invariant language.

What carries the argument

The off-shell double copy, which builds gravitational configurations from gauge-theory data at the level of the fields and action before any on-shell restriction is applied.

Load-bearing premise

The relations that connect gauge and gravity fields continue to hold when written in off-shell form and inside T-duality-invariant language.

What would settle it

An explicit gauge-theory configuration whose off-shell double copy fails to satisfy the gravitational equations of motion would falsify the framework.

read the original abstract

The present notes are based on a series of lectures prepared for an introductory eight-class course on the modern framework of the off-shell double copy. The course was held from April 16 to May 4, 2026, at Universidad de Buenos Aires (UBA). These lectures, aimed at PhD and master's students, are self-contained and require only a basic knowledge of classical field theory. The main goal is to review the fundamental concepts of gauge and gravitational theories in order to explore the off-shell frameworks of the single and double copy. In the final part of the course, we explore modern approaches to reinterpreting the single and double copy within T-duality-invariant frameworks.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 0 minor

Summary. The manuscript consists of lecture notes from an eight-class introductory course on the off-shell double copy program held at Universidad de Buenos Aires in 2026. It reviews fundamental concepts of gauge and gravitational theories to introduce the single and double copy frameworks, concluding with modern reinterpretations in T-duality-invariant settings. The notes are presented as self-contained for PhD and master's students assuming only basic classical field theory knowledge, with no original derivations or research claims advanced.

Significance. If the exposition accurately and clearly covers the reviewed material, the notes could provide a useful pedagogical entry point for graduate students into off-shell double copy constructions. The self-contained structure and focus on foundational concepts are positive features for teaching purposes, though the absence of new results limits broader research impact.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive evaluation of the lecture notes and for the recommendation to accept. The manuscript is accurately described as self-contained introductory material based on an eight-class course, with no original research claims.

Circularity Check

0 steps flagged

Lecture notes are purely expository; no derivations or claims to analyze

full rationale

The manuscript consists of lecture notes whose stated purpose is pedagogical review of existing concepts in gauge and gravitational theories, the off-shell single/double copy, and T-duality frameworks. No original theorem, derivation chain, fitted parameter, or load-bearing claim is advanced. The document is self-contained against external benchmarks by design and contains no equations or steps that reduce to their own inputs by construction. No self-citation load-bearing, ansatz smuggling, or renaming of results occurs because no such scientific claims exist.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Lecture notes introduce no new free parameters, axioms, or invented entities; they review existing frameworks.

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