Details
| Originalsprache | Englisch |
|---|---|
| Aufsatznummer | 132 |
| Seitenumfang | 17 |
| Fachzeitschrift | Journal of high energy physics |
| Jahrgang | 2023 |
| Ausgabenummer | 12 |
| Publikationsstatus | Veröffentlicht - 19 Dez. 2023 |
Abstract
Nicolai maps offer an alternative description of supersymmetric theories via nonlinear and nonlocal transformations characterized by the so-called ‘free-action’ and ‘determinant-matching’ conditions. The latter expresses the equality of the Jacobian determinant of the transformation with the one obtained by integrating out the fermions, which so far have been considered only to quadratic terms. We argue that such a restriction is not substantial, as Nicolai maps can be constructed for arbitrary nonlinear sigma models, which feature four-fermion interactions. The fermionic effective one-loop action then gets generalized to higher loops and the perturbative tree expansion of such Nicolai maps receives quantum corrections in the form of fermion loop decorations. The ‘free-action condition’ continues to hold for the classical map, but the ‘determinant-matching condition’ is extended to an infinite hierarchy in fermion loop order. After general considerations for sigma models in four dimensions, we specialize to the case of CPN symmetric spaces and construct the associated Nicolai map. These sigma models admit a formulation with only quadratic fermions via an auxiliary vector field, which does not simplify our analysis.
ASJC Scopus Sachgebiete
- Physik und Astronomie (insg.)
- Kern- und Hochenergiephysik
Zitieren
- Standard
- Harvard
- Apa
- Vancouver
- BibTex
- RIS
in: Journal of high energy physics, Jahrgang 2023, Nr. 12, 132, 19.12.2023.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Nicolai maps with four-fermion interactions
AU - Casarin, Lorenzo
AU - Lechtenfeld, Olaf
AU - Rupprecht, Maximilian
N1 - Funding Information: Article funded by SCOAP
PY - 2023/12/19
Y1 - 2023/12/19
N2 - Nicolai maps offer an alternative description of supersymmetric theories via nonlinear and nonlocal transformations characterized by the so-called ‘free-action’ and ‘determinant-matching’ conditions. The latter expresses the equality of the Jacobian determinant of the transformation with the one obtained by integrating out the fermions, which so far have been considered only to quadratic terms. We argue that such a restriction is not substantial, as Nicolai maps can be constructed for arbitrary nonlinear sigma models, which feature four-fermion interactions. The fermionic effective one-loop action then gets generalized to higher loops and the perturbative tree expansion of such Nicolai maps receives quantum corrections in the form of fermion loop decorations. The ‘free-action condition’ continues to hold for the classical map, but the ‘determinant-matching condition’ is extended to an infinite hierarchy in fermion loop order. After general considerations for sigma models in four dimensions, we specialize to the case of CPN symmetric spaces and construct the associated Nicolai map. These sigma models admit a formulation with only quadratic fermions via an auxiliary vector field, which does not simplify our analysis.
AB - Nicolai maps offer an alternative description of supersymmetric theories via nonlinear and nonlocal transformations characterized by the so-called ‘free-action’ and ‘determinant-matching’ conditions. The latter expresses the equality of the Jacobian determinant of the transformation with the one obtained by integrating out the fermions, which so far have been considered only to quadratic terms. We argue that such a restriction is not substantial, as Nicolai maps can be constructed for arbitrary nonlinear sigma models, which feature four-fermion interactions. The fermionic effective one-loop action then gets generalized to higher loops and the perturbative tree expansion of such Nicolai maps receives quantum corrections in the form of fermion loop decorations. The ‘free-action condition’ continues to hold for the classical map, but the ‘determinant-matching condition’ is extended to an infinite hierarchy in fermion loop order. After general considerations for sigma models in four dimensions, we specialize to the case of CPN symmetric spaces and construct the associated Nicolai map. These sigma models admit a formulation with only quadratic fermions via an auxiliary vector field, which does not simplify our analysis.
KW - Effective Field Theories
KW - Sigma Models
KW - Space-Time Symmetries
KW - Supersymmetric Gauge Theory
UR - http://www.scopus.com/inward/record.url?scp=85180248287&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2310.19946
DO - 10.48550/arXiv.2310.19946
M3 - Article
AN - SCOPUS:85180248287
VL - 2023
JO - Journal of high energy physics
JF - Journal of high energy physics
SN - 1029-8479
IS - 12
M1 - 132
ER -