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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2020-01-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP01(2020)081 |
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| Summary: | 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. |
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| ISSN: | 1029-8479 |