The conformal bootstrap: Theory, numerical techniques, and applications

Poland, David; Rychkov, Slava; Vichi, Alessandro

doi:10.1103/revmodphys.91.015002

Cited by 678 publications

(1,117 citation statements)

References 405 publications

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“…Tremendous progress has been witnessed in looking for DQCP in models . Recently, largescale QMC simulations [37] of microscopic fermion models obtained critical exponents that are consistent with the conformal bootstrap bounds [38][39][40], providing further support of DQCP with emergent SO(5) symmetry.…”

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confidence: 55%

“…Moreover, to the best of our knowledge, our MQMC simulation is the first sign-problem-free QMC study of the critical exponents in 2+1D N = 1 chiral-XY universality class, which provides a benchmark for the analytical calculation and numerical simulations in the future. It is also desired to derive quasi-rigorous bounds of critical exponents from conformal bootstrap calculations [38][39][40], which is deferred to the future, and see whether the QMC results of criti-cal exponents η and ν are consistent with the conformal bounds.…”

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confidence: 99%

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Fermion-induced quantum critical point in Dirac semimetals: A sign-problem-free quantum Monte Carlo study

Yao

2020

Phys. Rev. B

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According to Landau criterion, a phase transition should be first order when cubic terms of order parameters are allowed in its effective Ginzburg-Landau free energy. Recently, it was shown by renormalization group (RG) analysis that continuous transition can happen at putatively first-order Z3 transitions in 2D Dirac semimetals and such non-Landau phase transitions were dubbed "fermioninduced quantum critical points"(FIQCP) [Li et al., Nature Communications 8, 314 (2017)]. The RG analysis, controlled by the 1/N expansion with N the number of flavors of four-component Dirac fermions, shows that FIQCP occurs for N ≥ Nc. Previous QMC simulations of a microscopic model of SU(N ) fermions on the honeycomb lattice showed that FIQCP occurs at the transition between Dirac semimetals and Kekule-VBS for N ≥ 2. However, precise value of the lower bound Nc has not been established. Especially, the case of N = 1 has not been explored by studying microscopic models so far. Here, by introducing a generalized SU(N ) fermion model with N = 1 (namely spinless fermions on the honeycomb lattice), we perform large-scale sign-problem-free Majorana quantum Monte Carlo simulations and find convincing evidence of FIQCP for N = 1. Consequently, our results suggest that FIQCP can occur in 2D Dirac semimetals for all positive integers N ≥ 1.

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confidence: 55%

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confidence: 99%

Fermion-induced quantum critical point in Dirac semimetals: A sign-problem-free quantum Monte Carlo study

Yao

2020

Phys. Rev. B

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“…The last decade has seen a revival of interests in Conformal Field Theory (CFT) in higher dimensions with recent advances of numerical techniques applied to conformal bootstrap programme [1] (see e.g. [2][3][4] for reviews). Correlation functions are severely constrained by conformal symmetry and completely fixed up to three-point functions.…”

Section: Contentsmentioning

confidence: 99%

The gravity dual of Lorentzian OPE blocks

Chen

Kobayashi

et al. 2020

J. High Energ. Phys.

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We consider the operator product expansion (OPE) structure of scalar primary operators in a generic Lorentzian CFT and its dual description in a gravitational theory with one extra dimension. The OPE can be decomposed into certain bi-local operators transforming as the irreducible representations under conformal group, called the OPE blocks. We show the OPE block is given by integrating a higher spin field along a geodesic in the Lorentzian AdS space-time when the two operators are space-like separated. When the two operators are time-like separated however, we find the OPE block has a peculiar representation where the dual gravitational theory is not defined on the AdS space-time but on a hyperboloid with an additional time coordinate and Minkowski space-time on its boundary. This differs from the surface Witten diagram proposal for the time-like OPE block, but in two dimensions we reproduce it consistently using a kinematical duality between a pair of time-like separated points and space-like ones.

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“…A very general and successful method for studying superconformal field theories is the conformal bootstrap [9,10]. 2 It was initially developed without having supersymmetry in mind, but its application to SCFTs followed soon after [15,16].…”

Section: Introductionmentioning

confidence: 99%

Differential operators for superconformal correlation functions

Manenti

2020

J. High Energ. Phys.

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We present a systematic method to expand in components four dimensional superconformal multiplets. The results cover all possible N = 1 multiplets and some cases of interest for N = 2. As an application of the formalism we prove that certain N = 2 spinning chiral operators (also known as "exotic" chiral primaries) do not admit a consistent three-point function with the stress tensor and therefore cannot be present in any local SCFT. This extends a previous proof in the literature which only applies to certain classes of theories. To each superdescendant we associate a superconformally covariant differential operator, which can then be applied to any correlator in superspace. In the case of threepoint functions, we introduce a convenient representation of the differential operators that considerably simplifies their action. As a consequence it is possible to efficiently obtain the linear relations between the OPE coefficients of the operators in the same superconformal multiplet and in turn streamline the computation of superconformal blocks. We also introduce a Mathematica package to work with four dimensional superspace. 23 7. Conclusions25 Appendix A. Details on notation and conventions 26 -1 -Appendix B. Acting on different points 28 Appendix C. Superspace expansion 29 Appendix D. Some identities for the superspace derivatives 30 References 32 In[11]:= chi = Compare[ChiralDp[tOφφb, η2, θ3, x3], variables → Array[C,4]] 20 In the package the derivatives ChiralD represent the derivatives D. When acting on the t use ChiralD instead (D =[esc]scD[esc]). Also note that, when acting on the t, the operators D are sent to D and D to D. See (4.8). 21 In more complicated applications it is better to separate the various orders in θ3 andθ3 and act on each piece only with the operators inside ChiralD (like ∂η∂ θ , ∂η∂xθ etc. . .) that do not give zero when the θ's are suppressed. In the documentation of the package there is a worked out example. 22 See (2.11). 23 This instruction will generate an error but it can be ignored. It can be avoided by replacing the C[i]'s with variables consisting in a single Symbol. It comes up because there is an automatic routine that sets ConstQ to true for the variables in variables, which works only if they are Symbols. This is not an issue because ConstQ[C[i]] is true by default after SUSY3pf is called.

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The conformal bootstrap: Theory, numerical techniques, and applications

Cited by 678 publications

References 405 publications

Fermion-induced quantum critical point in Dirac semimetals: A sign-problem-free quantum Monte Carlo study

Fermion-induced quantum critical point in Dirac semimetals: A sign-problem-free quantum Monte Carlo study

The gravity dual of Lorentzian OPE blocks

Differential operators for superconformal correlation functions

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