Mellin bootstrap for scalars in generic dimension
Abstract
We use the recently developed framework of the Mellin bootstrap to study perturbatively free scalar CFTs in arbitrary dimensions. This approach uses the crossingsymmetric Mellin space formulation of correlation functions to generate algebraic bootstrap equations by demanding that only physical operators contribute to the OPE. We find that there are no perturbatively interacting CFTs with only fundamental scalars in d > 6 dimensions (to at least second order in the perturbation). Our results can be seen as a modest step towards understanding the space of interacting CFTs in d > 6 and are consistent with the intuition that no such CFTs exist.
 Authors:

 Univ. of Michigan, Ann Arbor, MI (United States). Dept. of Physics and Leinweber Center for Theoretical Physics
 Publication Date:
 Research Org.:
 Univ. of Michigan, Ann Arbor, MI (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1507007
 Grant/Contract Number:
 FG0295ER40899
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 6; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal Field Theory; Field Theories in Higher Dimensions
Citation Formats
Golden, John, and Mayerson, Daniel R. Mellin bootstrap for scalars in generic dimension. United States: N. p., 2018.
Web. doi:10.1007/jhep06(2018)066.
Golden, John, & Mayerson, Daniel R. Mellin bootstrap for scalars in generic dimension. United States. doi:https://doi.org/10.1007/jhep06(2018)066
Golden, John, and Mayerson, Daniel R. Wed .
"Mellin bootstrap for scalars in generic dimension". United States. doi:https://doi.org/10.1007/jhep06(2018)066. https://www.osti.gov/servlets/purl/1507007.
@article{osti_1507007,
title = {Mellin bootstrap for scalars in generic dimension},
author = {Golden, John and Mayerson, Daniel R.},
abstractNote = {We use the recently developed framework of the Mellin bootstrap to study perturbatively free scalar CFTs in arbitrary dimensions. This approach uses the crossingsymmetric Mellin space formulation of correlation functions to generate algebraic bootstrap equations by demanding that only physical operators contribute to the OPE. We find that there are no perturbatively interacting CFTs with only fundamental scalars in d > 6 dimensions (to at least second order in the perturbation). Our results can be seen as a modest step towards understanding the space of interacting CFTs in d > 6 and are consistent with the intuition that no such CFTs exist.},
doi = {10.1007/jhep06(2018)066},
journal = {Journal of High Energy Physics (Online)},
number = 6,
volume = 2018,
place = {United States},
year = {2018},
month = {6}
}
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Works referencing / citing this record:
On Mellin amplitudes in SCFTs with eight supercharges
journal, July 2018
 Zhou, Xinan
 Journal of High Energy Physics, Vol. 2018, Issue 7
Scalar CFTs and their large N limits
journal, September 2018
 Rong, Junchen; Su, Ning
 Journal of High Energy Physics, Vol. 2018, Issue 9
On the PolyakovMellin bootstrap
journal, December 2018
 Gopakumar, Rajesh; Sinha, Aninda
 Journal of High Energy Physics, Vol. 2018, Issue 12