Scale and conformal invariance in 2d σ-models, with an application to N= 4 supersymmetry

Georgios Papadopoulos; Edward Witten

doi:10.1007/JHEP03(2025)056

Scale and conformal invariance in 2d σ-models, with an application to N= 4 supersymmetry

Georgios Papadopoulos^*, Edward Witten

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

By adapting previously known arguments concerning Ricci flow and the c-theorem, we give a direct proof that in a two-dimensional sigma-model with compact target space, scale invariance implies conformal invariance in perturbation theory. This argument, which applies to a general sigma-model constructed with a target space metric and B-field, is in accord with a more general proof in the literature that applies to arbitrary two-dimensional quantum field theories. Models with extended supersymmetry and a B-field are known to provide interesting test cases for the relation between scale invariance and conformal invariance in sigma-model perturbation theory. We give examples showing that in such models, the obstructions to conformal invariance suggested by general arguments can actually occur in models with target spaces that are not compact or complete. Thus compactness of the target space, or at least a suitable condition of completeness, is necessary as well as sufficient to ensure that scale invariance implies conformal invariance in models of this type.

Original language	English
Article number	56
Journal	Journal of High Energy Physics
Volume	2025
Issue number	3
DOIs	https://doi.org/10.1007/JHEP03(2025)056
Publication status	Published - Mar 2025

Keywords

Conformal Field Models in String Theory
Field Theories in Lower Dimensions
Scale and Conformal Symmetries
Sigma Models

Access to Document

10.1007/JHEP03(2025)056

Scale_Conformal_HKT12Accepted author manuscript, 514 KB

Cite this

@article{b1709badf4304d489bd2f9323825efec,

title = "Scale and conformal invariance in 2d σ-models, with an application to N= 4 supersymmetry",

abstract = "By adapting previously known arguments concerning Ricci flow and the c-theorem, we give a direct proof that in a two-dimensional sigma-model with compact target space, scale invariance implies conformal invariance in perturbation theory. This argument, which applies to a general sigma-model constructed with a target space metric and B-field, is in accord with a more general proof in the literature that applies to arbitrary two-dimensional quantum field theories. Models with extended supersymmetry and a B-field are known to provide interesting test cases for the relation between scale invariance and conformal invariance in sigma-model perturbation theory. We give examples showing that in such models, the obstructions to conformal invariance suggested by general arguments can actually occur in models with target spaces that are not compact or complete. Thus compactness of the target space, or at least a suitable condition of completeness, is necessary as well as sufficient to ensure that scale invariance implies conformal invariance in models of this type.",

keywords = "Conformal Field Models in String Theory, Field Theories in Lower Dimensions, Scale and Conformal Symmetries, Sigma Models",

author = "Georgios Papadopoulos and Edward Witten",

note = "Publisher Copyright: {\textcopyright} The Author(s) 2025.",

year = "2025",

month = mar,

doi = "10.1007/JHEP03(2025)056",

language = "English",

volume = "2025",

journal = "Journal of High Energy Physics",

issn = "1126-6708",

publisher = "IOP Publishing",

number = "3",

}

TY - JOUR

T1 - Scale and conformal invariance in 2d σ-models, with an application to N= 4 supersymmetry

AU - Papadopoulos, Georgios

AU - Witten, Edward

N1 - Publisher Copyright: © The Author(s) 2025.

PY - 2025/3

Y1 - 2025/3

N2 - By adapting previously known arguments concerning Ricci flow and the c-theorem, we give a direct proof that in a two-dimensional sigma-model with compact target space, scale invariance implies conformal invariance in perturbation theory. This argument, which applies to a general sigma-model constructed with a target space metric and B-field, is in accord with a more general proof in the literature that applies to arbitrary two-dimensional quantum field theories. Models with extended supersymmetry and a B-field are known to provide interesting test cases for the relation between scale invariance and conformal invariance in sigma-model perturbation theory. We give examples showing that in such models, the obstructions to conformal invariance suggested by general arguments can actually occur in models with target spaces that are not compact or complete. Thus compactness of the target space, or at least a suitable condition of completeness, is necessary as well as sufficient to ensure that scale invariance implies conformal invariance in models of this type.

AB - By adapting previously known arguments concerning Ricci flow and the c-theorem, we give a direct proof that in a two-dimensional sigma-model with compact target space, scale invariance implies conformal invariance in perturbation theory. This argument, which applies to a general sigma-model constructed with a target space metric and B-field, is in accord with a more general proof in the literature that applies to arbitrary two-dimensional quantum field theories. Models with extended supersymmetry and a B-field are known to provide interesting test cases for the relation between scale invariance and conformal invariance in sigma-model perturbation theory. We give examples showing that in such models, the obstructions to conformal invariance suggested by general arguments can actually occur in models with target spaces that are not compact or complete. Thus compactness of the target space, or at least a suitable condition of completeness, is necessary as well as sufficient to ensure that scale invariance implies conformal invariance in models of this type.

KW - Conformal Field Models in String Theory

KW - Field Theories in Lower Dimensions

KW - Scale and Conformal Symmetries

KW - Sigma Models

UR - http://www.scopus.com/inward/record.url?scp=86000783596&partnerID=8YFLogxK

U2 - 10.1007/JHEP03(2025)056

DO - 10.1007/JHEP03(2025)056

M3 - Article

AN - SCOPUS:86000783596

SN - 1126-6708

VL - 2025

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 3

M1 - 56

ER -

Scale and conformal invariance in 2d σ-models, with an application to N= 4 supersymmetry

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this