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$\epsilon$-Expansions Near Three Dimensions from Conformal Field Theory · Around

2015

$\epsilon$-Expansions Near Three Dimensions from Conformal Field Theory

Basu, Pallab, Krishnan, Chethan

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We formally extend the CFT techniques introduced in arXiv:1505.00963, to $\phi^{\frac{2d_0}{d_0-2}}$ theory in $d=d_0-\epsilon$ dimensions and use it to compute anomalous dimensions near $d_0=3, 4$ in a unified manner.

We also do a similar analysis of the $O(N)$ model in three dimensions by developing a recursive combinatorial approach for OPE contractions.
Our results match precisely with low loop perturbative computations.
Finally, using 3-point correlators in the CFT, we comment on why the $\phi^3$ theory in $d_0=6$ is qualitatively different.

Built on

S. Ferrara, A. F. Grillo and R. Gatto, Manifestly conformal covariant operator-product expansion
1971
Earlier work this paper cites.
S. Ferrara, A. F. Grillo and R. Gatto, Tensor representations of conformal algebra and conformally covariant operator product expansion
1973
Earlier work this paper cites.
A. J. Macfarlane and G. Woo, Phi**3 Theory in Six-Dimensions and the Renormalization Group
1974
Earlier work this paper cites.

Similar

S. Ferrara, R. Gatto and A. F. Grillo, Properties of Partial Wave Amplitudes in Conformal Invariant Field Theories
1975
Cited alongside, same era.
O. F. de Alcantara Bonfim, J. E. Kirkham and A. J. McKane, Critical Exponents to Order ϵ 3 \epsilon^{3} for ϕ 3 \phi^{3} Models of Critical Phenomena in Six ϵ \epsilon -dimensions
1980
Cited alongside, same era.
S. Rychkov and Z. M. Tan, The Epsilon-Expansion from Conformal Field Theory
Original
Cited in the paper.
https://sites.google.com/site/slavarychkov/home
Cited in the paper.

Then

J. S. Hager, Six-loop renormalization group functions of O(n)-symmetric phi**6-theory and epsilon-expansions of tricritical exponents up to epsilon**3
2002
Later among the works it cites.
R. Rattazzi, V. S. Rychkov, E. Tonni and A. Vichi, JHEP 0812
Original
2014
Later among the works it cites.

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