A simple approach to counterterms in N=8 supergravity
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Freedman_A simple (arxiv).pdf
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Author(s)
Elvang, Henriette
Freedman, Daniel Z.
Kiermaier, Michael
Date Issued
November 2010
Journal
Journal of High Energy Physics
Publisher
Springer-Verlag
Citation
Elvang, Henriette, Daniel Z. Freedman, and Michael Kiermaier. “A Simple Approach to Counterterms in N=8 Supergravity.” Journal of High Energy Physics 2010.11 (2010): p. 1-28. Web.
Version
Author's final manuscript
Abstract
We present a simple systematic method to study candidate counterterms in =8 supergravity. Complicated details of the counterterm operators are avoided because we work with the on-shell matrix elements they produce. All n-point matrix elements of an independent SUSY invariant operator of the form D 2k R n+... must be local and satisfy SUSY Ward identities. These are strong constraints, and we test directly whether or not matrix elements with these properties can be constructed. If not, then the operator does not have a supersymmetrization, and it is excluded as a potential counterterm. For n> 4, we find that R n, D 2 R n, D 4 R n, and D 6 R n are excluded as counterterms of MHV amplitudes, while only R n and D 2 R n are excluded at the NMHV level. As a consequence, for loop order L<7, there are no independent D 2k R n counterterms with n>4. If an operator is not ruled out, our method constructs an explicit superamplitude for its matrix elements. This is done for the 7-loop D 4 R 6 operator at the NMHV level and in other cases. We also initiate the study of counterterms without leading pure-graviton matrix elements, which can occur beyond the MHV level. The landscape of excluded/ allowed candidate counterterms is summarized in a colorful chart.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1007/jhep11(2010)016
