Abstract
Pure CFTs have vanishing β-function at any value of the coupling. One example of a pure CFT is the O(N) Wess-Zumino model in 2+1 dimensions in the large N limit. This model can be analytically solved at finite temperature for any value of the coupling, and we find that its entropy density at strong coupling is exactly equal to frac{31}{35} of the non-interacting Stefan-Boltzmann result. We show that a large class of theories with equal numbers of N-component fermions and bosons, supersymmetric or not, for a large class of interactions, exhibit the same universal ratio. For unequal numbers of fermions and bosons we find that the strong-weak thermodynamic ratio is bounded to lie in between frac{4}{5} and 1.
Highlights
This model can be analytically solved at finite temperature for any value of the coupling, and we find that its entropy density at strong coupling is exactly equal to
For unequal numbers of fermions and bosons we find that the strong-weak thermodynamic ratio is bounded to lie in between
It is straightforward to show that these divergences are suppressed by 1/N, such that in the large N limit, the theory has vanishing β-function for all λ, which is a hallmark of pure CFTs
Summary
Let us consider the O(N) supersymmetric Wess-Zumino model [8] in 2+1 dimensions given by the superspace action. Introducing an auxiliary field σ = φcφc/N and its Lagrange multiplier ζ as 1 = DσDζei ζ(σ−φcφc/N), only the zero modes of σ, ζ contribute to the leading order large N result of the partition function. Where bosonic and fermionic sum-integrals in 3 − 2 dimensions are written as K =. Where the bosonic and fermionic thermal sum-integrals JB, JF in 2+1 dimensions are finite in the → 0 limit. For large N, the partition function may be evaluated exactly using the saddle points located at iζ = z∗, σ = σ∗ given by the solution of the non-perturbative coupled gap equations z∗ 3σ2. It is straightforward to verify that in the weak coupling limit λ → 0, the solution to these equations is mF = mB = 0, indicating vanishing thermal masses for both bosons and fermions. Bosons and fermions develop non-vanishing thermal masses.
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