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Publication# 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, which already hints interesting physics. 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. This is a mirror version of the Z(2) bootstrap, where the 2d Ising CFT sits at a kink while all the other minimal models saturating the bound on the right. We further carry out dimensional continuation of the 2d S U(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 = infinity limit, where the non-WF kink sits at (Delta(phi), 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 = infinity.

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Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it - for example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on it - for example, both a latitude and longitude are required to locate a point on the surface of a sphere.

Phase transition

In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of matter: solid, liquid, and gas, and in rare cases, plasma. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as temperature or pressure.

Infinity

Infinity is something which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol . Since the time of the ancient Greeks, the philosophical nature of infinity was the subject of many discussions among philosophers. In the 17th century, with the introduction of the infinity symbol and the infinitesimal calculus, mathematicians began to work with infinite series and what some mathematicians (including l'Hôpital and Bernoulli) regarded as infinitely small quantities, but infinity continued to be associated with endless processes.