Properties of the є-expansion, Lagrange inversion and associahedra and the O (1) model
Abstract We discuss properties of the є-expansion in d = 4 − є dimensions. Using Lagrange inversion we write down an exact expression for the value of the Wilson-Fisher fixed point coupling order by order in є in terms of the beta function coefficients. The є-expansion is combinatoric in the sense t...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-04-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP04(2020)072 |
| Summary: | Abstract We discuss properties of the є-expansion in d = 4 − є dimensions. Using Lagrange inversion we write down an exact expression for the value of the Wilson-Fisher fixed point coupling order by order in є in terms of the beta function coefficients. The є-expansion is combinatoric in the sense that the Wilson-Fisher fixed point coupling at each order depends on the beta function coefficients via Bell polynomials. Using certain properties of Lagrange inversion we then argue that the є-expansion of the Wilson-Fisher fixed point coupling equally well can be viewed as a geometric expansion which is controlled by the facial structure of associahedra. We then write down an exact expression for the value of anomalous dimensions at the Wilson-Fisher fixed point order by order in є in terms of the coefficients of the beta function and anomalous dimensions. We finally use our general results to compute the values for the Wilson-fisher fixed point coupling and critical exponents for the scalar O (1) symmetric model to O(є 7). |
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| ISSN: | 1029-8479 |