Abstract
Zamolodchikov's famous analysis of the RG trajectory connecting successive minimal CFT models $M_p$ and $M_{p-1}$ for $p\gg 1$, is improved by including second order in coupling constant corrections. This allows to compute IR quantities with next to leading order accuracy of the $1/p$ expansion. We compute in particular, the beta function and the anomalous dimensions for certain classes of fields. As a result we are able to identify with a greater accuracy the IR limit of these fields with certain linear combination of the IR theory $M_{p-1}$. We discuss the relation of these results with Gaotto's recent RG domain wall proposal.
Highlights
The matrix of anomalous dimensions, does not receive 1/p or 1/p2 corrections
The beta function and the anomalous dimensions for certain classes of fields
In this paper we have found several four-point correlation functions in large p limit (see formulae (C.1))
Summary
With H0 being the UV CFT action density, φ a relevant local spinless field and λ the coupling constant. We calculate the β-function up to 1/p4 ∼ 4 corrections for the small values of the (renormalized) coupling constant (of order or smaller) As it will become quite clear later for this purpose one should evaluate the integral (1.7) in the special case φ1 = φ2 = φ and I(y) given by (1.12) with the accuracy ∼ 1/. For the integral outside these discs we will safely use the small limits of the correlation functions given in the appendix while inside the discs we’ll explore (exact in ) OPE. To calculate the four-point function in this region we apply the OPE (all the structure constants we use in this paper can be extracted from the general formula (A.5)). The shift of the central charge [4]
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