Continuum limit of fishnet graphs and AdS sigma model
Abstract We consider the continuum limit of 4d planar fishnet diagrams using integrable spin chain methods borrowed from the N $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory. These techniques give us control on the scaling dimensions of single-trace operators for all values of the coupling constant i...
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doaj-36b0ed7e4d194f3b9679044cd76d99ed2020-11-25T01:28:22ZengSpringerOpenJournal of High Energy Physics1029-84792019-01-012019114610.1007/JHEP01(2019)002Continuum limit of fishnet graphs and AdS sigma modelBenjamin Basso0De-liang Zhong1Laboratoire de Physique Théorique de l’ École Normale Supérieure, CNRS, Université PSL, Sorbonne Universités, Université Pierre et Marie CurieLaboratoire de Physique Théorique de l’ École Normale Supérieure, CNRS, Université PSL, Sorbonne Universités, Université Pierre et Marie CurieAbstract We consider the continuum limit of 4d planar fishnet diagrams using integrable spin chain methods borrowed from the N $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory. These techniques give us control on the scaling dimensions of single-trace operators for all values of the coupling constant in the fishnet theory. We use them to study the thermodynamical limit of the BMN operator corresponding to the spin chain ferromagnetic vacuum. We find that its scaling dimension exhibits a critical behaviour when the coupling constant approaches Zamolodchikov’s critical coupling. Analysis close to that point suggests that the continuum limit of the fishnet graphs is controlled by the two-dimensional AdS 5 non-linear sigma model. More generally, we present evidence that the fishnet diagrams define an integrable lattice regularization of the AdS 5 model. A system of massless TBA equations is derived for the tachyon energy by dualizing the TBA equations of the weakly coupled planar N $$ \mathcal{N} $$ = 4 SYM theory.http://link.springer.com/article/10.1007/JHEP01(2019)002Integrable Field TheoriesSigma ModelsAdS-CFT CorrespondenceConformal Field Theory |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Benjamin Basso De-liang Zhong |
spellingShingle |
Benjamin Basso De-liang Zhong Continuum limit of fishnet graphs and AdS sigma model Journal of High Energy Physics Integrable Field Theories Sigma Models AdS-CFT Correspondence Conformal Field Theory |
author_facet |
Benjamin Basso De-liang Zhong |
author_sort |
Benjamin Basso |
title |
Continuum limit of fishnet graphs and AdS sigma model |
title_short |
Continuum limit of fishnet graphs and AdS sigma model |
title_full |
Continuum limit of fishnet graphs and AdS sigma model |
title_fullStr |
Continuum limit of fishnet graphs and AdS sigma model |
title_full_unstemmed |
Continuum limit of fishnet graphs and AdS sigma model |
title_sort |
continuum limit of fishnet graphs and ads sigma model |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2019-01-01 |
description |
Abstract We consider the continuum limit of 4d planar fishnet diagrams using integrable spin chain methods borrowed from the N $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory. These techniques give us control on the scaling dimensions of single-trace operators for all values of the coupling constant in the fishnet theory. We use them to study the thermodynamical limit of the BMN operator corresponding to the spin chain ferromagnetic vacuum. We find that its scaling dimension exhibits a critical behaviour when the coupling constant approaches Zamolodchikov’s critical coupling. Analysis close to that point suggests that the continuum limit of the fishnet graphs is controlled by the two-dimensional AdS 5 non-linear sigma model. More generally, we present evidence that the fishnet diagrams define an integrable lattice regularization of the AdS 5 model. A system of massless TBA equations is derived for the tachyon energy by dualizing the TBA equations of the weakly coupled planar N $$ \mathcal{N} $$ = 4 SYM theory. |
topic |
Integrable Field Theories Sigma Models AdS-CFT Correspondence Conformal Field Theory |
url |
http://link.springer.com/article/10.1007/JHEP01(2019)002 |
work_keys_str_mv |
AT benjaminbasso continuumlimitoffishnetgraphsandadssigmamodel AT deliangzhong continuumlimitoffishnetgraphsandadssigmamodel |
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