Crossing antisymmetric Polyakov blocks + dispersion relation

Kaviraj, Apratim

doi:10.1007/jhep01(2022)005

Cited by 10 publications

(4 citation statements)

References 43 publications

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“…Let us first examine the constraints for m = 3. 16 Thus we observe a pattern of signs whereby the higher spins all have the same sign. This automatically implies a chain of inequalities, for instance: 17 From here it is clear that the contribution from c ′ 0,0 will be ∼ O( 103 ) times bigger than the higher spin contributions.…”

Section: D1 Motivating Ltdmentioning

confidence: 69%

Positivity, low twist dominance and CSDR for CFTs

Bissi

Sinha

2023

SciPost Phys.

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We consider a crossing symmetric dispersion relation (CSDR) for CFT four point correlation with identical scalar operators, which is manifestly symmetric under the cross-ratios u,vu,v interchange. This representation has several features in common with the CSDR for quantum field theories. It enables a study of the expansion of the correlation function around u=v=1/4u=v=1/4, which is used in the numerical conformal bootstrap program. We elucidate several remarkable features of the dispersive representation using the four point correlation function of \Phi_{1,2}Φ1,2 operators in 2d minimal models as a test-bed. When the dimension of the external scalar operator (\Delta_\sigmaΔσ) is less than \frac{1}{2}12, the CSDR gets contribution from only a single tower of global primary operators with the second tower being projected out. We find that there is a notion of low twist dominance (LTD) which, as a function of \Delta_\sigmaΔσ, is maximized near the 2d Ising model as well as the non-unitary Yang-Lee model. The CSDR and LTD further explain positivity of the Taylor expansion coefficients of the correlation function around the crossing symmetric point and lead to universal predictions for specific ratios of these coefficients. These results carry over to the epsilon expansion in 4-\epsilon4−ϵ dimensions. We also conduct a preliminary investigation of geometric function theory ideas, namely the Bieberbach-Rogosinski bounds.

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Section: D1 Motivating Ltdmentioning

confidence: 69%

Positivity, low twist dominance and CSDR for CFTs

Bissi

Sinha

2023

SciPost Phys.

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“…Further progress using large spin perturbation theory was made in [137]. Some preliminary attempts using the crossing symmetric dispersion was made in [138]. Unlike the epsilon expansion, even to go to the second subleading order in 1/N is challenging since one needs to resum the contriubtion of an infinite number of operators.…”

Section: Open Questionsmentioning

confidence: 99%

Selected Topics in Analytic Conformal Bootstrap: A Guided Journey

Bissi¹,

Sinha²,

Zhou³

2022

Preprint

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This review aims to offer a pedagogical introduction to the analytic conformal bootstrap program via a journey through selected topics. We review analytic methods which include the large spin perturbation theory, Mellin space methods and the Lorentzian inversion formula. These techniques are applied to a variety of topics ranging from large-N theories, to the epsilon expansion and holographic superconformal correlators, and are demonstrated in a large number of explicit examples.

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“…Numerical methods have led to high precision measurements of critical exponents of conformal field theories (CFTs) such as the 3D Ising [5][6][7][8] and the O(N ) models [9][10][11], while analytical methods have proven essential to the study of quantum gravity in Anti-de Sitter (AdS) spacetime [12][13][14][15][16][17][18] and perturbative CFTs [19,20]. In recent years, with the introduction of analytic functionals [21][22][23][24][25][26][27][28] and dispersion relation methods [29][30][31][32][33][34][35], the gap between numerics and analytics has greatly narrowed revealing new horizons for the bootstrap program. This paper builds upon this bridge by introducing new analytic dispersive functionals for correlators with unequal external scalar operators.…”

Section: Jhep03(2022)032mentioning

confidence: 99%

Mixed correlator dispersive CFT sum rules

Trinh

2022

J. High Energ. Phys.

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Conformal field theory (CFT) dispersion relations reconstruct correlators in terms of their double discontinuity. When applied to the crossing equation, such dispersive transforms lead to sum rules that suppress the double-twist sector of the spectrum and enjoy positivity properties at large twist. In this paper, we construct dispersive CFT functionals for correlators of unequal scalar operators in position- and Mellin-space. We then evaluate these functionals in the Regge limit to construct mixed correlator holographic CFT functionals which probe scalar particle scattering in Anti-de Sitter spacetime. Finally, we test properties of these dispersive sum rules when applied to the 3D Ising model, and we use truncated sum rules to find approximate solutions to the crossing equation.

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Crossing antisymmetric Polyakov blocks + dispersion relation

Cited by 10 publications

References 43 publications

Positivity, low twist dominance and CSDR for CFTs

Positivity, low twist dominance and CSDR for CFTs

Selected Topics in Analytic Conformal Bootstrap: A Guided Journey

Mixed correlator dispersive CFT sum rules

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