Sphere free energy of scalar field theories with cubic interactions

Abstract

The dimensional continuation approach to calculating the free energy of $d$-dimensional Euclidean CFT on the round sphere $S^d$ has been used to develop its $4-\epsilon$ expansion for a number of well-known non-supersymmetric theories, such as the $O(N)$ model. The resulting estimate of the sphere free energy $F$ in the 3D Ising model has turned out to be in good agreement with the numerical value obtained using the fuzzy sphere regularization. In this paper, we develop the $6-\epsilon$ expansions for CFTs on $S^d$ described by scalar field theory with cubic interactions and use their resummations to estimate the values of $F$. In particular, we study the theories with purely imaginary coupling constants, which describe non-unitary universality classes arising when certain conformal minimal models are continued above two dimensions. The Yang-Lee model $M(2,5)$ is described by a field theory with one scalar field, while the $D$-series $M(3,8)$ model is described by two scalar fields. We also study the $OSp(1|2)$ symmetric cubic theory of one commuting and two anti-commuting scalar fields, which appears to describe the critical behavior of random spanning forests. In the course of our work, we revisit the calculations of beta functions of marginal operators containing the curvature. We also use another method for approximating $F$, which relies on perturbation theory around the bilocal action near the long-range/short-range crossover. The numerical values it gives for $F$ tend to be in good agreement with other available methods.

27 pages + appendices, 10 figures, v2: minor corrections, v3: updated references and numerics in Yang-Lee long-range approach, v4: minor corrections, updated to reflect published version

References in corpus (24)

• Towards a derivation of holographic entanglement entropy
• Seeing a c-theorem with holography
• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• On the Resolution of Singularities of Multiple Mellin-Barnes Integrals
• Critical exponents of the 3d Ising and related models from Conformal Bootstrap
• Bosonic Tensor Models at Large $N$ and Small $\epsilon$
• Bootstrapping $O(N)$ Vector Models in $4<d<6$
• The critical O(N) CFT: Methods and conformal data
• Five loop renormalization of ${\varphi }^3$ theory with applications to the Lee-Yang edge singularity and percolation theory
• Microscopic models of interacting Yang-Lee anyons
• Ferromagnetic phase transition for the spanning-forest model (q \to 0 limit of the Potts model) in three or more dimensions
• Irreversibility of the renormalization group flow in non-unitary quantum field theory
• Line of fixed points in a bosonic tensor model
• Critical exponents from five-loop scalar theory renormalization near six-dimensions
• Studying the 3d Ising surface CFTs on the fuzzy sphere
• AdS one-loop partition functions from bulk and edge characters
• MB Tools reloaded
• More on the cubic versus quartic interaction equivalence in the $O(N)$ model
• Ginzburg-Landau Description and Emergent Supersymmetry of the $(3,8)$ Minimal Model
• Long Range, Large Charge, Large $N$
• Free Energy on the Sphere for Non-Abelian Gauge Theories
• Critical Field Theories with OSp$(1|2M)$ Symmetry
• Testing the RG-flow $M(3,10)+{\varphi }_{1,7}\to M(3,8)$ with Hamiltonian Truncation
• Percolation transition for random forests in $d\ge 3$