Bootstrapping conformal QED3 and deconfined quantum critical point

Li, Zhijin

doi:10.1007/jhep11(2022)005

Cited by 12 publications

(3 citation statements)

References 78 publications

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“…For instance, QED 3 with N f fermions is believed to stop being conformal below some N crit f . It has been difficult to precisely bootstrap this theory [35][36][37][38][39]. It is possible that a sharp signature for this theory could be found by bootstrapping a large set of correlators, which could be made feasible using our method.…”

Section: Discussionmentioning

confidence: 99%

Upper critical dimension of the 3-state Potts model

Chester¹,

Su²

2022

Preprint

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We consider the 3-state Potts model in d ≥ 2 dimensions. For d less than the upper critical dimension dcrit, the model has a critical and a tricritical fixed point. In d = 2, these fixed points are described by minimal models, and so are exactly solvable. For d > 2, however, strong coupling makes them difficult to study and there is no consensus on the value of dcrit. We use the numerical conformal bootstrap to compute critical exponents of both the critical and tricritical fixed points for general d. In d = 2 our results match the expected values, and as we increase d we find that the critical exponents of each fixed point get closer until they merge near dcrit 2.5.

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Section: Discussionmentioning

confidence: 99%

Upper critical dimension of the 3-state Potts model

Chester¹,

Su²

2022

Preprint

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“…It has been known since [20] 3D, the O(N ) vector bootstrap bounds show sharp kinks (type I) which are saturated by the 3D critical O(N ) vector models. Moreover, in [21] the author observed that besides the type I kinks, the 3D O(N ) vector bootstrap bounds also show another family of kinks (type II) which approach the free fermion bilinear in the large N limit. The type II kinks appear in general dimensions [18], and the kink in Fig.…”

Section: O(n ) Vector Crossing Equations In 1dmentioning

confidence: 99%

“…For instance, the 3D O(N ) vector bootstrap bounds have two types of kinks [20,21]. The type I kinks with an O(N ) vector scalar φ near a free boson ∆ φ = 1 2 are related to the critical O(N ) vector model [20], while the type II kinks with ∆ φ near free fermion bilinears also appear in general dimensions and show close relation with conformal gauge theories [18,21].…”

Section: Introductionmentioning

confidence: 99%

Large $N$ analytical functional bootstrap I: 1D CFTs and total positivity

Li¹

2023

Preprint

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We initiate the analytical functional bootstrap study of conformal field theories with large N limits. In this first paper we particularly focus on the 1D O(N ) vector bootstrap. We obtain a remarkably simple bootstrap equation from the O(N ) vector crossing equations in the large N limit. The bootstrap bound is saturated by the generalized free field theory.We study the analytical extremal functionals of this crossing equation, for which the total positivity of the SL(2, R) conformal block plays a critical role. We prove the SL(2, R) conformal block is totally positive for large scaling dimension ∆ and show that the total positivity is violated below a critical value ∆ * TP ≈ 0.32315626. The conformal block forms a surprisingly sophisticated mathematical structure, which for instance can violate total positivity at the order 10 −5654 for a normal value ∆ = 0.1627! We construct a series of analytical functionals {α M } which satisfy the bootstrap positive conditions up to a range ∆ Λ M . The functionals {α M } have a trivial large M limit. Surprisingly, due to total positivity, they can approach the large M limit in a way consistent with the bootstrap positive conditions for arbitrarily high Λ M , therefore proving the bootstrap bound analytically. Our result provides a concrete example to illustrate how the analytical properties of the conformal block lead to nontrivial bootstrap bounds. We expect this work paves the way for large N analytical functional bootstrap in higher dimensions.

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Non-Abelian currents bootstrap

He,

Rong,

et al. 2024

J. High Energ. Phys.

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We initiate the study of correlation functions of non-Abelian spin-1 conserved current in three-dimensional conformal field theories using numerical conformal bootstrap. We discuss the general framework and apply it to the particular cases of SU(N) and O(N) global symmetry. In both cases, we obtain general bounds on operator dimensions. In the large-N limit our bounds show features in correspondence of the expected position of fermionic QED3 in three dimensions, as well as other interesting theories. By imposing gaps inspired by the spectrum of QED3 at large-N, we manage to restrict the plane of certain operator dimensions to a small island, where QED3 must live.

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Bootstrapping conformal QED3 and deconfined quantum critical point

Cited by 12 publications

References 78 publications

Upper critical dimension of the 3-state Potts model

Upper critical dimension of the 3-state Potts model

Large $N$ analytical functional bootstrap I: 1D CFTs and total positivity

Non-Abelian currents bootstrap

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