Properties of the є-expansion, Lagrange inversion and associahedra and the O (1) model

Thomas A. Ryttov*

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Abstrakt

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).

OriginalsprogEngelsk
Artikelnummer72
TidsskriftJournal of High Energy Physics (JHEP)
Vol/bind2020
Udgave nummer4
Antal sider16
ISSN1126-6708
DOI
StatusUdgivet - 14. apr. 2020

Bibliografisk note

17 pages, 2 figures

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