Heavy-light bootstrap from Lorentzian inversion formula
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Springer
Received: October 30, Revised: April 27, Accepted: June 12, Published: July 8,
2019 2020 2020 2020
Yue-Zhou Li Physics Department, Tianjin University, No. 135 Yaguan Road, Tianjin, China
E-mail: [email protected] Abstract: We study heavy-light four-point function by employing Lorentzian inversion formula, where the conformal dimension of heavy operator is as large as central charge CT → ∞. We implement the Lorentzian inversion formula back and forth to reveal the universality of the lowest-twist multi-stress-tensor T k as well as large spin double-twist operators [OH OL ]n0 ,J 0 . In this way, we also propose an algorithm to bootstrap the heavylight four-point function by extracting relevant OPE coefficients and anomalous dimensions. By following the algorithm, we exhibit the explicit results in d = 4 up to the triple-stresstensor. Moreover, general dimensional heavy-light bootstrap up to the double-stress-tensor is also discussed, and we present an infinite series representation of the lowest-twist doublestress-tensor OPE coefficient. Exact expressions of lowest-twist double-stress-tensor OPE coefficients in d = 6, 8, 10 are also obtained as further examples. Keywords: Conformal Field Theory, Field Theories in Higher Dimensions ArXiv ePrint: 1910.06357
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2020)046
JHEP07(2020)046
Heavy-light bootstrap from Lorentzian inversion formula
Contents 1 Introduction
1
2 Generalities 2.1 Conformal blocks 2.2 Lorentzian inversion formula 2.3 Heavy-light four-point function
4 4 5 6 9 9 9 11 12 13 15
4 Examples in four dimension up to T 3 4.1 O(µ) double-twist 4.2 Lowest-twist double-stress-tensor 4.3 O(µ2 ) double-twist and lowest-twist T 3
15 15 17 18
5 O(µ2 ) bootstrap in general dimension 5.1 A warm-up: free double-twist OPE 5.2 O(µ) double-twist 5.3 An infinite series of lowest-twist T 2
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6 Conclusion and future directions
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a,b and B ˜ a,b A Details of Bn,m n,m
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A.1 A.2
a,b Bn,m a,b ˜n,m B
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B More examples for double-stress-tensor
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Introduction
AdS/CFT correspondence (holography) serves as a bridge connecting gravity theories in anti-de Sitter (AdS) spacetime and strong-coupled CFT living in the AdS boundary [1–3], enabling us to exploit conformal field theories (CFT) with sparse spectrum [4] at strong coupling without referring to any specific CFT theories. On the other hand, although
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JHEP07(2020)046
3 Bootstrapping heavy-light: the algorithm 3.1 Lowest-twist multi-stress-tensor OPE 3.1.1 HLLH large spin behavior 3.1.2 Finding lowest-twist multi-stress-tensor 3.1.3 The universality 3.2 Comments on ∆L poles 3.3 The algorithm
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JHEP07(2020)046
directly studying strongly-coupled CFT is a hard task, recent developments of conformal bootstrap make it achievable. Conformal bootstrap utilizes the conformal symmetry, crossing symmetry, and sometimes other physical consistency conditions such as unitarity to explore the properties of conformal dimensions and operator pro
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