Non-Wilson-Fisher kinks of $O(N)$ numerical bootstrap: from the deconfined phase transition to a putative new family of CFTs

Abstract

It is well established that the $O(N)$ Wilson-Fisher (WF) CFT sits at a kink of the numerical bounds from bootstrapping four point function of $O(N)$ vector. Moving away from the WF kinks, there indeed exists another family of kinks (dubbed non-WF kinks) on the curve of $O(N)$ numerical bounds. Different from the $O(N)$ WF kinks that exist for arbitary $N$ in $2<d<4$ dimensions, the non-WF kinks exist in arbitrary dimensions but only for a large enough $N>N_c(d)$ in a given dimension $d$. In this paper we have achieved a thorough understanding for few special cases of these non-WF kinks. The first case is the $O(4)$ bootstrap in 2d, where the non-WF kink turns out to be the $SU(2{)}_1$ Wess-Zumino-Witten (WZW) model, and all the $SU(2{)}_{k>2}$ WZW models saturate the numerical bound on the left side of the kink. We further carry out dimensional continuation of the 2d $SU(2{)}_1$ kink towards the 3d $SO(5)$ deconfined phase transition. We find the kink disappears at around $d=2.7$ dimensions indicating the $SO(5)$ deconfined phase transition is weakly first order. The second interesting observation is, the $O(2)$ bootstrap bound does not show any kink in 2d ($N_c=2$), but is surprisingly saturated by the 2d free boson CFT (also called Luttinger liquid) all the way on the numerical curve. The last case is the $N=\infty$ limit, where the non-WF kink sits at $({\Delta }_{\varphi },{\Delta }_T)=(d-1,2d)$ in $d$ dimensions. We manage to write down its analytical four point function in arbitrary dimensions, which equals to the subtraction of correlation functions of a free fermion theory and generalized free theory. An important feature of this solution is the existence of a full tower of conserved higher spin current. We speculate that a new family of CFTs will emerge at non-WF kinks for finite $N$, in a similar fashion as $O(N)$ WF CFTs originating from free boson at $N=\infty$.

16+3 pages

References in corpus (10)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Scaling in the Fan of an Unconventional Quantum Critical Point
• Approaching conformal window of $O(n)\times O(m)$ symmetric Landau-Ginzburg models from conformal bootstrap
• Analytic and Numerical Bootstrap of CFTs with $O(m)\times O(n)$ Global Symmetry in 3D
• Searching for gauge theories with the conformal bootstrap

Cited by in corpus (20)

• Quantum Criticality and Spin Liquid Phase in the Shastry-Sutherland model
• The emergence of gapless quantum spin liquid from deconfined quantum critical point
• Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality
• New Developments in the Numerical Conformal Bootstrap
• A model of $d$-wave superconductivity, antiferromagnetism, and charge order on the square lattice
• Deconfined criticality and a gapless ${\mathbb{Z}}_2$ spin liquid in the square lattice antiferromagnet
• Conformal bootstrap bounds for the $U(1)$ Dirac spin liquid and $N=7$ Stiefel liquid
• Bootstrapping traceless symmetric $O(N)$ scalars
• Notes on Resonances and Unitarity from Celestial Amplitudes
• Perturbative and Nonperturbative Studies of CFTs with MN Global Symmetry
• Crossing antisymmetric Polyakov blocks + Dispersion relation
• A roadmap for bootstrapping critical gauge theories: decoupling operators of conformal field theories in $d>2$ dimensions
• Ising model close to $d=2$
• Bootstrapping Mixed MN Correlators in 3D
• Navigating through the O(N) archipelago
• Emergent self-duality in long range critical spin chain: from deconfined criticality to first order transition
• Equilibration of Topological Defects Near the Deconfined Quantum Multicritical Point
• Incompleteness of the large-$N$ analysis of the $O(N)$ models: Nonperturbative cuspy fixed points and their nontrivial homotopy at finite $N$
• Disturbing news about the $d=2+\epsilon$ expansion
• Conformal Bootstrap with Duality-Inspired Fusion Rule