Fermion-scalar conformal blocks

Iliesiu, Luca V.; Kos, Filip; Poland, David; Pufu, Silviu S.; Simmons-Duffin, David; Yacoby, Ran

doi:10.1007/jhep04(2016)074

Cited by 68 publications

(156 citation statements)

References 38 publications

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“…We observe a good agreement between the available estimates from the conformal bootstrap approach [35], the FRG [40] and our results. Finally, we would like to comment on the replica limit for our GNY model, N → 0, which has been argued to be applicable to the transition from a relativistic semi-metallic state to a diffusive metallic phase in a 3D Weyl semi-metal [23].…”

Section: A Chiral Ising Modelsupporting

confidence: 71%

Four-loop critical exponents for the Gross-Neveu-Yukawa models

et al. 2017

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We study the chiral Ising, the chiral XY, and the chiral Heisenberg models at four-loop order with the perturbative renormalization group in 4 − ϵ dimensions and compute critical exponents for the GrossNeveu-Yukawa fixed points to order Oðϵ 4 Þ. Further, we provide Padé estimates for the correlation length exponent, the boson and fermion anomalous dimension, as well as the leading correction to scaling exponent in 2 þ 1 dimensions. We also confirm the emergence of supersymmetric field theories at four loops for the chiral Ising and the chiral XY models with N ¼ 1=4 and N ¼ 1=2 fermions, respectively. Furthermore, applications of our results relevant to various quantum transitions in the context of Dirac and Weyl semimetals are discussed, including interaction-induced transitions in graphene and surface states of topological insulators.

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Section: A Chiral Ising Modelsupporting

confidence: 71%

Four-loop critical exponents for the Gross-Neveu-Yukawa models

et al. 2017

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“…Also limited progress has been made in the case where external operators carry spin, see e.g. [49][50][51][52][53][54][55].…”

Section: Jhep05(2017)027mentioning

confidence: 99%

A Mellin space approach to the conformal bootstrap

Gopakumar

Kaviraj

Sen

et al. 2017

J. High Energ. Phys.

173

285

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We describe in more detail our approach to the conformal bootstrap which uses the Mellin representation of CF T d four point functions and expands them in terms of crossing symmetric combinations of AdS d+1 Witten exchange functions. We consider arbitrary external scalar operators and set up the conditions for consistency with the operator product expansion. Namely, we demand cancellation of spurious powers (of the cross ratios, in position space) which translate into spurious poles in Mellin space. We discuss two contexts in which we can immediately apply this method by imposing the simplest set of constraint equations. The first is the epsilon expansion. We mostly focus on the Wilson-Fisher fixed point as studied in an epsilon expansion about d = 4. We reproduce Feynman diagram results for operator dimensions to O( 3 ) rather straightforwardly. This approach also yields new analytic predictions for OPE coefficients to the same order which fit nicely with recent numerical estimates for the Ising model (at = 1). We will also mention some leading order results for scalar theories near three and six dimensions. The second context is a large spin expansion, in any dimension, where we are able to reproduce and go a bit beyond some of the results recently obtained using the (double) light cone expansion. We also have a preliminary discussion about numerical implementation of the above bootstrap scheme in the absence of a small parameter.

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“…[12] and the further developments in ref. [13], CBs associated to the exchange of fermion operators in 3D have recently been computed [14]. In ref.…”

Section: Jhep02(2016)183mentioning

confidence: 99%

Seed conformal blocks in 4D CFT

Echeverri

Elkhidir

Karateev

et al. 2016

J. High Energ. Phys.

151

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We compute in closed analytical form the minimal set of "seed" conformal blocks associated to the exchange of generic mixed symmetry spinor/tensor operators in an arbitrary representation ( ,¯ ) of the Lorentz group in four dimensional conformal field theories. These blocks arise from 4-point functions involving two scalars, one (0, | −¯ |) and one (| −¯ |, 0) spinors or tensors. We directly solve the set of Casimir equations, that can elegantly be written in a compact form for any ( ,¯ ), by using an educated ansatz and reducing the problem to an algebraic linear system. Various details on the form of the ansatz have been deduced by using the so called shadow formalism. The complexity of the conformal blocks depends on the value of p = | −¯ | and grows with p, in analogy to what happens to scalar conformal blocks in d even space-time dimensions as d increases. These results open the way to bootstrap 4-point functions involving arbitrary spinor/tensor operators in four dimensional conformal field theories.

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Fermion-scalar conformal blocks

Cited by 68 publications

References 38 publications

Four-loop critical exponents for the Gross-Neveu-Yukawa models

Four-loop critical exponents for the Gross-Neveu-Yukawa models

A Mellin space approach to the conformal bootstrap

Seed conformal blocks in 4D CFT

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