Twisted Homotopy Algebras: Supersymmetric Twists, Spontaneous Symmetry Breaking, Anomalies and Localisation

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Borsten, Leron, Jonsson, Simon, Kanakaris, Dimitri, Kim, Hyungrok
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866918331643068416
author Borsten, Leron
Jonsson, Simon
Kanakaris, Dimitri
Kim, Hyungrok
author_facet Borsten, Leron
Jonsson, Simon
Kanakaris, Dimitri
Kim, Hyungrok
contents Twisting and classical background fields are two foundational techniques in supersymmetric quantum field theory, central to developments ranging from the Higgs mechanism to topological twisting and supersymmetric localisation. While traditionally treated as distinct procedures, they appear on an equal footing in the homotopy-algebraic approach to quantum field theory. In this work, we formalise this connection by interpreting both twisting and the introduction of classical backgrounds as instances of twisting curved quantum $L_\infty$-superalgebras. Using the language of homotopy algebras and the Batalin-Vilkovisky formalism, we provide a unified algebraic framework that encompasses topological/holomorphic twists, spontaneous symmetry breaking, computation of anomalies, and supersymmetric localisation à la Festuccia--Seiberg. As a byproduct, we introduce a notion of twisting for quantum $L_\infty$-algebras and a homotopy-algebraic reformulation of the one-particle-irreducible effective action.
format Preprint
id arxiv_https___arxiv_org_abs_2508_05134
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Twisted Homotopy Algebras: Supersymmetric Twists, Spontaneous Symmetry Breaking, Anomalies and Localisation
Borsten, Leron
Jonsson, Simon
Kanakaris, Dimitri
Kim, Hyungrok
High Energy Physics - Theory
Mathematical Physics
17B81 (Primary), 81T60, 81T50, 81T12 (Secondary)
Twisting and classical background fields are two foundational techniques in supersymmetric quantum field theory, central to developments ranging from the Higgs mechanism to topological twisting and supersymmetric localisation. While traditionally treated as distinct procedures, they appear on an equal footing in the homotopy-algebraic approach to quantum field theory. In this work, we formalise this connection by interpreting both twisting and the introduction of classical backgrounds as instances of twisting curved quantum $L_\infty$-superalgebras. Using the language of homotopy algebras and the Batalin-Vilkovisky formalism, we provide a unified algebraic framework that encompasses topological/holomorphic twists, spontaneous symmetry breaking, computation of anomalies, and supersymmetric localisation à la Festuccia--Seiberg. As a byproduct, we introduce a notion of twisting for quantum $L_\infty$-algebras and a homotopy-algebraic reformulation of the one-particle-irreducible effective action.
title Twisted Homotopy Algebras: Supersymmetric Twists, Spontaneous Symmetry Breaking, Anomalies and Localisation
topic High Energy Physics - Theory
Mathematical Physics
17B81 (Primary), 81T60, 81T50, 81T12 (Secondary)
url https://arxiv.org/abs/2508.05134