Interacting CFTs for all couplings: thermal versus entanglement entropy at large N

Abstract

In this paper, I calculate the large N limit of marginal O(N) models with non-polynomial potentials in arbitrary odd dimensions d. This results in a new class of interacting pure conformal field theories (CFTs) in d = 3 + 4n for any n ∈ ℤ+. Similarly, in d = 3 + 4n I calculate the thermal entropy for all couplings on R2+4n × S1 for n = 0, 1, 2, 3. In 2+1 dimensions I find the strong-to-weak coupling ratio of the thermal entropy to be 4/5, matching recent results, and further extend this analysis to higher odd dimensions. Next, I calculated the vacuum entanglement entropy {s}_{textrm{EE}}^d on Sd−2 for all couplings in arbitrary odd d in the large N limit. I find the vacuum entanglement entropy on Sd−2 to be not only solvable but also constant for all couplings λ. Thus, in the large N limit, the vacuum entanglement entropy on Sd−2 for odd d is constant for all λ, in contrast to the thermal entropy which is shown to also be monotonically decreasing with λ in d = 3 + 4n.