A simple approach to counterterms in N=8 supergravity
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 2...
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| Format: | Article |
| Language: | en_US |
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Springer-Verlag
2012
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| Online Access: | http://hdl.handle.net/1721.1/71191 https://orcid.org/0000-0001-8408-1941 |
| _version_ | 1811072860533293056 |
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| author | Elvang, Henriette Freedman, Daniel Z. Kiermaier, Michael |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Elvang, Henriette Freedman, Daniel Z. Kiermaier, Michael |
| author_sort | Elvang, Henriette |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T09:17:34Z |
| format | Article |
| id | mit-1721.1/71191 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T09:17:34Z |
| publishDate | 2012 |
| publisher | Springer-Verlag |
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| spelling | mit-1721.1/711912022-09-26T11:11:56Z A simple approach to counterterms in N=8 supergravity Elvang, Henriette Freedman, Daniel Z. Kiermaier, Michael Massachusetts Institute of Technology. Center for Theoretical Physics Massachusetts Institute of Technology. Department of Mathematics Freedman, Daniel Z. Freedman, Daniel Z. 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. United States. Dept. of Energy (grant DE-FG02- 95ER40899 ) National Science Foundation (U.S.) (NSF grant PHY-0503584) National Science Foundation (U.S.) (grant No. PHY-0600465) United States. Dept. of Energy (cooperative research agreement DE-FG-0205FR41360) National Science Foundation (U.S.) (NSF grant PHY-0756966) 2012-06-21T17:14:26Z 2012-06-21T17:14:26Z 2010-11 2010-09 Article http://purl.org/eprint/type/JournalArticle 1126-6708 1029-8479 http://hdl.handle.net/1721.1/71191 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. https://orcid.org/0000-0001-8408-1941 en_US http://dx.doi.org/10.1007/jhep11(2010)016 Journal of High Energy Physics Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Springer-Verlag arXiv |
| spellingShingle | Elvang, Henriette Freedman, Daniel Z. Kiermaier, Michael A simple approach to counterterms in N=8 supergravity |
| title | A simple approach to counterterms in N=8 supergravity |
| title_full | A simple approach to counterterms in N=8 supergravity |
| title_fullStr | A simple approach to counterterms in N=8 supergravity |
| title_full_unstemmed | A simple approach to counterterms in N=8 supergravity |
| title_short | A simple approach to counterterms in N=8 supergravity |
| title_sort | simple approach to counterterms in n 8 supergravity |
| url | http://hdl.handle.net/1721.1/71191 https://orcid.org/0000-0001-8408-1941 |
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