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 $N=\infty$.

arXiv comment16+3 pages

References in corpus (37)

• "Deconfined" quantum critical points
• Bounding scalar operator dimensions in 4D CFT
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Solving the 3D Ising Model with the Conformal Bootstrap
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Precision Islands in the Ising and $O(N)$ Models
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Deconfined quantum critical points: symmetries and dualities
• Bootstrapping the O(N) Vector Models
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Carving Out the Space of 4D CFTs
• Bootstrapping Conformal Field Theories with the Extremal Functional Method
• Walking, Weak first-order transitions, and Complex CFTs
• Scaling in the Fan of an Unconventional Quantum Critical Point
• Continuous quantum phase transition between an antiferromagnet and a valence-bond-solid in two dimensions; evidence for logarithmic corrections to scaling
• Universal Constraints on Conformal Operator Dimensions
• Emergent $SO(5)$ Symmetry at the Néel to Valence-Bond-Solid Transition
• Bootstrapping the O(N) Archipelago
• Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models
• Carving out OPE space and precise $O(2)$ model critical exponents
• Conformal Field Theories in Fractional Dimensions
• A Cheap Alternative to the Lattice?
• Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$
• Unitarity violation at the Wilson-Fisher fixed point in 4-epsilon dimensions
• Improved bounds for CFT's with global symmetries
• Conformal Bootstrap Dashing Hopes of Emergent Symmetry
• A theory of deconfined pseudo-criticality
• Approaching conformal window of $O(n)\times O(m)$ symmetric Landau-Ginzburg models from conformal bootstrap
• Note on Wess-Zumino-Witten models and quasiuniversality in 2+1 dimensions
• Bootstrapping Mixed Correlators in Three-Dimensional Cubic Theories
• Scalar CFTs and Their Large N Limits
• Bootstrapping the Minimal 3D SCFT
• Analytic and Numerical Bootstrap of CFTs with $O(m)\times O(n)$ Global Symmetry in 3D
• Searching for gauge theories with the conformal bootstrap
• Bootstrapping MN and Tetragonal CFTs in Three Dimensions

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