Speaker
Description
We study multiscalar theories with $\text{O}(N) \times \text{O}(2)$ symmetry. These models have a stable fixed point in $d$ dimensions if $N$ is greater than some critical value $N_c(d)$. The expectation is that at this critical value $N_c(d)$ a merger between the stable and unstable fixed point occurs and that for $N < N_c(d)$ the fixed points move off into the complex plane. Previous estimates of this critical value from perturbative and non-perturbative renormalization group methods have produced mutually incompatible results. We use numerical conformal bootstrap methods to constrain $N_c(d)$ for $3 \leq d < 4$. Our results show that $N_c > 3.78$ for $d = 3$. This favors the scenario that the models that are physically relevant to the description of frustrated magnets where $N = 2,3$ and $d=3$, do not have a stable fixed point, indicating a first-order transition. We also find evidence for the merger-and-annihilation scenario being responsible for the disappearance of this fixed point in the form of the square root behavior of $\Delta_{SS}$ as $N_c$ is approached from above. Our result highlights the utility of modern algorithms for the numerical conformal bootstrap.
Link to publication (if applicable)
https://arxiv.org/abs/2405.19411
