Mellin space bootstrap for global symmetry

Dey, Parijat; Kaviraj, Apratim; Sinha, Aninda

doi:10.1007/jhep07(2017)019

Cited by 91 publications

(130 citation statements)

References 133 publications

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121

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“…It is interesting to note that if we assume that the shadow relation ∆ σ = d − ∆ S,0 holds also at order N −1 , we can compute 46) in agreement with the literature value [19,29]. 7 Note that there is a typo in equation (4.21) of [23]. We thank the authors for sharing with us a file with the correct result.…”

Section: Cft-data For T and A At N −1supporting

confidence: 84%

“…We can eliminate f 1 (ξ) from the Casimir equation and put this in the D sat equation to get a single, third order differential equation for f 0 (ξ). This is an inhomogeneous differential equation, with inhomogeneous part determined by ξ 1−µ H (1) T ±A (1 − z, 1 − z) z 0 , which can be extracted from (D.7) 23 . Specifically, we find the equations:…”

Section: A Inversion Methodsmentioning

confidence: 99%

“…in the non-linear sigma model [50]. In three dimensions and at finite N , numeric conformal bootstrap provides results for some CFT-data to very high precision [13], as well as numeric estimates for a larger set of 18 See also [23] where this CFT-data, including scalar operators, were computed to order 3 using bootstrap in Mellin space. 19 Note that there is a typo in the definition of the parameter α in [17]; as pointed out in [15] Table 2: Evaluation of the truncated series in d = 3 for C J given in (3.54).…”

Section: Irrep Spinmentioning

confidence: 99%

“…The corrections to the corresponding central charges C T and C J were computed to order N −1 in [20] and [21], as summarized in [22]. The only other known subleading corrections to any OPE coefficients are the ones for the weakly broken currents in the T and A representations, which were computed to order N −1 in [23].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An alternative to diagrams for the critical O(N) model: dimensions and structure constants to order 1/N2

Alday

Henriksson

Loon

2020

J. High Energ. Phys.

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We apply the methods of modern analytic bootstrap to the critical O(N ) model in a 1/N expansion. At infinite N the model possesses higher spin symmetry which is weakly broken as we turn on 1/N . By studying consistency conditions for the correlator of four fundamental fields we derive the CFT-data for all the (broken) currents to order 1/N , and the CFT-data for the non-singlet currents to order 1/N 2 . To order 1/N our results are in perfect agreement with those in the literature. To order 1/N 2 we reproduce known results for anomalous dimensions and obtain a variety of new results for structure constants, including the global symmetry central charge C J to this order.

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Section: Cft-data For T and A At N −1supporting

confidence: 84%

Section: A Inversion Methodsmentioning

confidence: 99%

Section: Irrep Spinmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An alternative to diagrams for the critical O(N) model: dimensions and structure constants to order 1/N2

Alday

Henriksson

Loon

2020

J. High Energ. Phys.

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show abstract

“…[64][65][66][67][68][69][70][71][72][73][74][75][76][77][78][79]. Another approach is the analytic bootstrap, either together with the largespin expansion [80], or in its Mellin-space version [81][82][83][84]. Finally, ref.…”

Section: Jhep12(2017)054mentioning

confidence: 99%

Scaling dimensions in QED3 from the ϵ-expansion

Pietro

Stamou

2017

J. High Energ. Phys.

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Abstract:We study the fixed point that controls the IR dynamics of QED in d = 4 − 2 dimensions. We derive the scaling dimensions of four-fermion and bilinear operators beyond leading order in the -expansion. For the four-fermion operators, this requires the computation of a two-loop mixing that was not known before. We then extrapolate these scaling dimensions to d = 3 to estimate their value at the IR fixed point of QED 3 as function of the number of fermions N f . The next-to-leading order result for the four-fermion operators corrects significantly the leading one. Our best estimate at this order indicates that they do not cross marginality for any value of N f , which would imply that they cannot trigger a departure from the conformal phase. For the scaling dimensions of bilinear operators, we observe better convergence as we increase the order. In particular, the -expansion provides a convincing estimate for the dimension of the flavor-singlet scalar in the full range of N f .

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Spinning Mellin Bootstrap: Conformal Partial Waves, Crossing Kernels and Applications

Sleight

Taronna

2018

Fortschritte der Physik

153

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We study conformal partial waves (CPWs) in Mellin space with totally symmetric external operators of arbitrary integer spin. The exchanged spin is arbitrary, and includes mixed symmetry and (partially)-conserved representations. In a basis of CPWs recently introduced in arXiv:1702.08619, we find a remarkable factorisation of the external spin dependence in their Mellin representation. This property allows a relatively straightforward study of inversion formulae to extract OPE data from the Mellin representation of spinning 4pt correlators and in particular, to extract closed-form expressions for crossing kernels of spinning CPWs in terms of the hypergeometric function 4 F 3 . We consider numerous examples involving both arbitrary internal and external spins, and for both leading and sub-leading twist operators. As an application, working in general d we extract new results for O(1/N) anomalous dimensions of double-trace operators induced by double-trace deformations constructed from single-trace operators of generic twist and integer spin. In particular, we extract the anomalous dimensions of double-trace operators [O J ] n,l with O J a single-trace operator of integer spin J. 1 See however [48] for recent analytic results for the scalar-fermion bootstrap. 2 The Mellin space approach to the conformal bootstrap was initiated in [32,33,57] for external scalar operators. 1 of 77) www.advancedsciencenews.com www.fp-journal.org In §5.2.1 we apply our formalism to spinning correlators in arbitrary space-time dimensions, which also requires to consider mixed symmetry CPWs and their crossing kernels -which we derive. In particular, using the methods of §3 we first extract mean-field theory OPE coefficients for leading twist double-trace operators [O J ] 0,l built from a spin-J single-trace operator O J and a scalar operator . Combining the latter with the results for crossing kernels, we then obtain the anomalous dimensions of the doubletrace operators [O J ] 0,l induced by the double-trace flow (1.1) with l = 0. (3 The basis itself was originally obtained in the context of simplifying the kinematic map between bulk cubic couplings and 3pt conformal structures, so our proposed framework also lends itself nicely to studies of bulk physics. 4 Some of such nested formulas recently appeared in the literature in a different CFT basis. [62] For external scalars, such formulas were originally given in [29].

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Mellin space bootstrap for global symmetry

Cited by 91 publications

References 133 publications

An alternative to diagrams for the critical O(N) model: dimensions and structure constants to order 1/N2

An alternative to diagrams for the critical O(N) model: dimensions and structure constants to order 1/N2

Scaling dimensions in QED3 from the ϵ-expansion

Spinning Mellin Bootstrap: Conformal Partial Waves, Crossing Kernels and Applications

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