Abstract
By considering the renormalization group flow between N coupled Ising models in the UV and the cubic fixed point in the IR, we study the large N behavior of the cubic fixed points in three dimensions. We derive a diagrammatic expansion for the 1/N corrections to correlation functions. Leading large N corrections to conformal dimensions at the cubic fixed point are then evaluated using numeric conformal bootstrap data for the 3d Ising model.
Highlights
JHEP09(2021)071 field theories [18, 19]
By considering the renormalization group flow between N coupled Ising models in the UV and the cubic fixed point in the IR, we study the large N behavior of the cubic fixed points in three dimensions
In this work we studied the large N limit of the cubic fixed point
Summary
Let us introduce source fields Ji(x) and Ki(x) coupled to i(x) and Oi(x) respectively, where Oi(x) is some other local operator in the 3d Ising model. Let us begin by defining the generating functional for correlators of i(x) and Oi(x): Zλ,μ[Ji, Ki] = =. The HubbardStratonovich trick allows us to rewriting the cubic coupling using an auxiliary field: ddx λ −. We have used the fact that each Ising model is decoupled when λ = μ = 0 to factor the correlator. Each expectation value in (2.3) is the generating functional for correlators of (x) and O(x) in a single Ising model: ZIsing[Ji + φ, Ki] = exp ddx (Ji(x) + φ(x)) i(x) + Ki(x)Oi(x)
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