Analytic and numerical bootstrap of CFTs with $O(m)\times O(n)$ global  symmetry in 3D

Henriksson, Johan; Kousvos, Stefanos R.; Stergiou, A.

doi:10.21468/scipostphys.9.3.035

Cited by 49 publications

(77 citation statements)

References 70 publications

(272 reference statements)

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“…The piecewise definition of the Ω transforms in the regions u < v and u > v may appear awkward at first, but it is in fact dictated by analyticity -the expressions in the two different domains are the analytic continuations of each other. 12 We show this in detail in appendix A.1, and give the gist of the argument here. Take for example (2.21) for u < v and analytically continue it in z,z outside of the region u < v. The singularities of the kernel K B (u, v; u , v ) move in the space of w,w and we are forced to deform the contour C − × C + to avoid the singularities.…”

Section: Jhep05(2021)243mentioning

confidence: 99%

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Dispersive CFT sum rules

Caron-Huot

Mazáč

Rastelli

et al. 2021

J. High Energ. Phys.

175

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We give a unified treatment of dispersive sum rules for four-point correlators in conformal field theory. We call a sum rule “dispersive” if it has double zeros at all double-twist operators above a fixed twist gap. Dispersive sum rules have their conceptual origin in Lorentzian kinematics and absorptive physics (the notion of double discontinuity). They have been discussed using three seemingly different methods: analytic functionals dual to double-twist operators, dispersion relations in position space, and dispersion relations in Mellin space. We show that these three approaches can be mapped into one another and lead to completely equivalent sum rules. A central idea of our discussion is a fully nonperturbative expansion of the correlator as a sum over Polyakov-Regge blocks. Unlike the usual OPE sum, the Polyakov-Regge expansion utilizes the data of two separate channels, while having (term by term) good Regge behavior in the third channel. We construct sum rules which are non-negative above the double-twist gap; they have the physical interpretation of a subtracted version of “superconvergence” sum rules. We expect dispersive sum rules to be a very useful tool to study expansions around mean-field theory, and to constrain the low-energy description of holographic CFTs with a large gap. We give examples of the first kind of applications, notably we exhibit a candidate extremal functional for the spin-two gap problem.

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Section: Jhep05(2021)243mentioning

confidence: 99%

“…(2.25) 12 The theta function term in (2.20), (2.21) only applies literally when u, v are real and non-negative.…”

Section: Jhep05(2021)243mentioning

confidence: 99%

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Dispersive CFT sum rules

Caron-Huot

Mazáč

Rastelli

et al. 2021

J. High Energ. Phys.

175

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“…Interesting CFTs usually sit at"kinks" of the bootstrap curve, such as the Ising model [14], the three dimensional O(N ) vector models [15] and many Wilson-Fisher CFTs with flavor symmetry groups to be subgroups of O(N ) [16][17][18][19][20]. Sometimes bootstrap curves shows more than one kink [19-23] 1 .…”

Section: Introductionmentioning

confidence: 99%

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

Rong

2021

SciPost Phys.

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It is well established that the O(N)O(N) Wilson-Fisher (WF) CFT sits at a kink of the numerical bounds from bootstrapping four point function of O(N)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)O(N) numerical bounds. Different from the O(N)O(N) WF kinks that exist for arbitary NN in 2<d<42<d<4 dimensions, the non-WF kinks exist in arbitrary dimensions but only for a large enough N>N_c(d)N>Nc(d) in a given dimension dd. 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)O(4) bootstrap in 2d, where the non-WF kink turns out to be the SU(2)_1SU(2)1 Wess-Zumino-Witten (WZW) model, and all the SU(2)_{k>2}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_2Z2 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 SU(2)_1SU(2)1 kink towards the 3d SO(5)SO(5) deconfined phase transition. We find the kink disappears at around d=2.7d=2.7 dimensions indicating the SO(5)SO(5) deconfined phase transition is weakly first order. The second interesting observation is, the O(2)O(2) bootstrap bound does not show any kink in 2d (N_c=2Nc=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=\inftyN=∞ limit, where the non-WF kink sits at (\Delta_\phi, \Delta_T)=(d-1, 2d)(Δϕ,ΔT)=(d−1,2d) in dd 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 NN, in a similar fashion as O(N)O(N) WF CFTs originating from free boson at N=\inftyN=∞.

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“…[26]), where now the operator X acts as the Hubbard-Stratonovich auxiliary field. Specifically, we use the analytic conformal bootstrap method of large spin perturbation theory, developed in [27][28][29][30], to compute m −1 corrections to scaling dimensions and OPE coefficients. This expansion is valid for all spacetime dimensions d ∈ (2,4].…”

Section: Introductionmentioning

confidence: 99%

Perturbative and nonperturbative studies of CFTs with MN global symmetry

Henriksson

Stergiou

2021

SciPost Phys.

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Fixed points in three dimensions described by conformal field theories with \ensuremath{M N}_{m,n} = O(m)^n\rtimes S_nMNm,n=O(m)n⋊Sn global symmetry have extensive applications in critical phenomena. Associated experimental data for m=n=2m=n=2 suggest the existence of two non-trivial fixed points, while the \varepsilonε expansion predicts only one, resulting in a puzzling state of affairs. A recent numerical conformal bootstrap study has found two kinks for small values of the parameters mm and nn, with critical exponents in good agreement with experimental determinations in the m=n=2m=n=2 case. In this paper we investigate the fate of the corresponding fixed points as we vary the parameters mm and nn. We find that one family of kinks approaches a perturbative limit as mm increases, and using large spin perturbation theory we construct a large mm expansion that fits well with the numerical data. This new expansion, akin to the large NN expansion of critical O(N)O(N) models, is compatible with the fixed point found in the \varepsilonε expansion. For the other family of kinks, we find that it persists only for n=2n=2, where for large mm it approaches a non-perturbative limit with \Delta_\phi\approx 0.75Δϕ≈0.75. We investigate the spectrum in the case \ensuremath{M N}_{100,2}MN100,2 and find consistency with expectations from the lightcone bootstrap.

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Analytic and numerical bootstrap of CFTs with $O(m)\times O(n)$ global symmetry in 3D

Cited by 49 publications

References 70 publications

Dispersive CFT sum rules

Dispersive CFT sum rules

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

Perturbative and nonperturbative studies of CFTs with MN global symmetry

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