Solution of the self-dual Φ4 QFT-model on four-dimensional Moyal space
Abstract Previously the exact solution of the planar sector of the self-dual Φ4-model on 4-dimensional Moyal space was established up to the solution of a Fredholm integral equation. This paper solves, for any coupling constant λ > − 1 π $$ \frac{1}{\uppi} $$ , the Fredholm equation in terms of a...
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SpringerOpen
2020-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2020)081 |
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| author | Harald Grosse Alexander Hock Raimar Wulkenhaar |
| author_facet | Harald Grosse Alexander Hock Raimar Wulkenhaar |
| author_sort | Harald Grosse |
| collection | DOAJ |
| description | Abstract Previously the exact solution of the planar sector of the self-dual Φ4-model on 4-dimensional Moyal space was established up to the solution of a Fredholm integral equation. This paper solves, for any coupling constant λ > − 1 π $$ \frac{1}{\uppi} $$ , the Fredholm equation in terms of a hypergeometric function and thus completes the construction of the planar sector of the model. We prove that the interacting model has spectral dimension 4 − 2 arcsin λπ π $$ \frac{\arcsin \left(\uplambda \uppi \right)}{\uppi} $$ for |λ| < 1 π $$ \frac{1}{\uppi} $$ . It is this dimension drop which for λ > 0 avoids the triviality problem of the matricial Φ 4 4 $$ {\varPhi}_4^4 $$ -model. We also establish the power series approximation of the Fredholm solution to all orders in λ. The appearing functions are hyperlogarithms defined by iterated integrals, here of alternating letters 0 and −1. We identify the renormalisation parameter which gives the same normalisation as the ribbon graph expansion. |
| format | Article |
| id | doaj-art-241252b62bdf410f86acd4dae2ca6dcd |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-241252b62bdf410f86acd4dae2ca6dcd2025-01-26T12:11:38ZengSpringerOpenJournal of High Energy Physics1029-84792020-01-012020111710.1007/JHEP01(2020)081Solution of the self-dual Φ4 QFT-model on four-dimensional Moyal spaceHarald Grosse0Alexander Hock1Raimar Wulkenhaar2Fakultät für Physik, Universität WienMathematisches Institut der Westfälischen Wilhelms-UniversitätMathematisches Institut der Westfälischen Wilhelms-UniversitätAbstract Previously the exact solution of the planar sector of the self-dual Φ4-model on 4-dimensional Moyal space was established up to the solution of a Fredholm integral equation. This paper solves, for any coupling constant λ > − 1 π $$ \frac{1}{\uppi} $$ , the Fredholm equation in terms of a hypergeometric function and thus completes the construction of the planar sector of the model. We prove that the interacting model has spectral dimension 4 − 2 arcsin λπ π $$ \frac{\arcsin \left(\uplambda \uppi \right)}{\uppi} $$ for |λ| < 1 π $$ \frac{1}{\uppi} $$ . It is this dimension drop which for λ > 0 avoids the triviality problem of the matricial Φ 4 4 $$ {\varPhi}_4^4 $$ -model. We also establish the power series approximation of the Fredholm solution to all orders in λ. The appearing functions are hyperlogarithms defined by iterated integrals, here of alternating letters 0 and −1. We identify the renormalisation parameter which gives the same normalisation as the ribbon graph expansion.https://doi.org/10.1007/JHEP01(2020)081Integrable Field TheoriesMatrix ModelsNon-Commutative Geometry |
| spellingShingle | Harald Grosse Alexander Hock Raimar Wulkenhaar Solution of the self-dual Φ4 QFT-model on four-dimensional Moyal space Journal of High Energy Physics Integrable Field Theories Matrix Models Non-Commutative Geometry |
| title | Solution of the self-dual Φ4 QFT-model on four-dimensional Moyal space |
| title_full | Solution of the self-dual Φ4 QFT-model on four-dimensional Moyal space |
| title_fullStr | Solution of the self-dual Φ4 QFT-model on four-dimensional Moyal space |
| title_full_unstemmed | Solution of the self-dual Φ4 QFT-model on four-dimensional Moyal space |
| title_short | Solution of the self-dual Φ4 QFT-model on four-dimensional Moyal space |
| title_sort | solution of the self dual φ4 qft model on four dimensional moyal space |
| topic | Integrable Field Theories Matrix Models Non-Commutative Geometry |
| url | https://doi.org/10.1007/JHEP01(2020)081 |
| work_keys_str_mv | AT haraldgrosse solutionoftheselfdualph4qftmodelonfourdimensionalmoyalspace AT alexanderhock solutionoftheselfdualph4qftmodelonfourdimensionalmoyalspace AT raimarwulkenhaar solutionoftheselfdualph4qftmodelonfourdimensionalmoyalspace |