Higher-spin symmetry and duality in (super)conformal field theory

Informations projet

HigherSpinCFT

N° de convention de subvention: 101107602

DOI

10.3030/101107602

Projet clôturé

Date de signature de la CE 3 Août 2023

Date de début 8 Avril 2024

Date de fin 7 Avril 2026

Financé au titre de

• Marie Skłodowska-Curie Actions (MSCA)

Coût total

Aucune donnée

Contribution de l’UE

€ 172 750,08

Coordonné par

ISTITUTO NAZIONALE DI FISICA NUCLEARE
Italy

Periodic Reporting for period 1 - HigherSpinCFT (Higher-spin symmetry and duality in (super)conformal field theory)

Période du rapport: 2024-04-08 au 2026-04-07

Résumé du contexte et des objectifs généraux du projet

Modern physics relies on mathematical frameworks that describe how nature behaves at its most fundamental level. Among the most important of these frameworks are conformal field theories (CFTs) and supersymmetry, which underpin our understanding of elementary particles, critical phenomena in materials, and aspects of quantum gravity. These theories also play a central role in the search for physics beyond the current Standard Model.

Despite their importance, many CFTs, especially in higher space-time dimensions, remain poorly understood. CFTs with extended symmetry (such as supersymmetry, higher-spin symmetry and duality invariance) have become a fertile research ground due to their links to string theory and their role as toy models for exploring questions that are otherwise inaccessible in field theories without supersymmetry. Superconformal field theories (SCFTs) have also influenced several branches of pure mathematics, including geometry, topology and integrable systems.

This project aims to develop new mathematical tools to formulate these highly symmetric quantum field theories across diverse space-time dimensions. By establishing general frameworks applicable to broad classes of theories, the research will provide new methods for modern theoretical and mathematical physics.

Travail effectué depuis le début du projet jusqu’à la fin de la période considérée dans le rapport et principaux résultats atteints jusqu’à présent

The research focused on three objectives:
(1) How N=1 superconformal symmetry constrains correlation functions of conserved higher-spin currents in four-dimensional (4D) N=1 SCFT in Minkowski spacetime. Specifically, we studied the most general form of two and three point functions, which are building blocks for understanding the dynamics of quantum field theories. Building on recent advances in the mathematical formalism of supersymmetry, we have introduced a formalism based on twistor-like auxiliary variables to represent tensorial structures as homogeneous polynomials. We also developed appropriate superspace techniques to enable a systematic implementation of conservation laws and superconformal symmetry constraints.

(2) Study of non-linear chiral form gauge field theories in diverse dimensions which are relevant for quantum electrodynamics. A major focus was the mathematical classification of Lorentz invariants of tensor fields, particularly the challenging problem of classifying the functionally independent invariants of a self-dual 5-form in ten space-time dimensions. These structures naturally arise in higher-derivative corrections to string effective actions and interacting chiral 4-form gauge field theories. Building on this classification, we analysed a broad class of 10D chiral 4-form theories, including conformally invariant models that generalise the recently discovered ModMax theory of non-linear electrodynamics. Our results revealed a fundamental difference between ten-dimensional theories and their four- and six-dimensional counterparts.

(3) The third line of research was aimed at revisiting the construction of 5D N =1 minimal gauged (AdS) supergravity deformed by higher-derivative corrections. By using conformal superspace techniques, we completed the construction of the three curvature-squared invariants (Weyl tensor squared, Ricci tensor squared, scalar curvature-squared) in gauged supergravity, allowing detailed study of their component structure.

JOURNAL PUBLICATIONS
1. Title: On non-linear chiral 4-form theories in D=10
https://link.springer.com/article/10.1007/JHEP02(2026)147; https://arxiv.org/abs/2509.14351.

2. Title: Some remarks on invariants
https://iopscience.iop.org/article/10.1088/1751-8121/ae3bb8; https://arxiv.org/abs/2509.14350.

3. Title: On five-dimensional curvature squared supergravity and holography
https://www.matrix-inst.org.au/2024-matrix-annals/; https://arxiv.org/abs/2504.10856

4. Title: Three-point functions of higher-spin supercurrents in 4D N=1 SCFT: General formalism for arbitrary superspins
https://journals.aps.org/prd/abstract/10.1103/PhysRevD.110.085013; https://arxiv.org/abs/2407.17106

5. Title: Components of curvature-squared invariants of minimal supergravity in five dimensions
https://link.springer.com/article/10.1007/JHEP07(2024)221

Progrès au-delà de l’état des connaissances et impact potentiel prévu (y compris l’impact socio-économique et les conséquences sociétales plus larges du projet jusqu’à présent)

The results from this project are expected to advance our fundamental understanding of how (super)conformal symmetries in D > 2 space-time dimensions constrain the structure of interactions and dynamics in quantum field theory and gravity. Specifically:
(i) The formalisms used to study three-point correlation functions of conserved higher-spin currents in 4D N=1 SCFT (and its generalisation to three-dimensional case) should find broad applications ranging from the use of bootstrap approaches in SCFT to the study of higher-spin theories.

(ii) Mathematical classifications of Lorentz invariants of tensor fields in different space-time dimensions; in particular, of a self-dual 5-form field in ten space-time dimensions (the 10D analogue of Maxwell two-form field in 4D) can be used to understand properties of conformal deformations of tensor field theories in higher dimensions.

(iii) The results on component structure of curvature-squared invariants of 5D N=1 minimal gauged (AdS) supergravity deformed by higher-derivative corrections (using superconformal methods) should find applications in the theory of black holes, new applications to holography corrected by curvature-squared terms and AdS/CFT.

On a broader level, the expected impact is primarily scientific and long term. By addressing fundamental questions about symmetry and the structure of quantum theories, the project will help support major international efforts to deepen our understanding of quantum matter, particle physics and gravity. The project will also advance mathematical techniques used across theoretical physics and may contribute to the knowledge base underpinning future scientific and technological innovation.