Heavy-light bootstrap from Lorentzian inversion formula

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 C T → ∞. 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 [O H O L ] n ,J. 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.

More on heavy-light bootstrap up to double-stress-tensor

“…It is indeed found from holographic set-ups that the universal piece of heavy-light fourpoint function is the lowest-twist multi-stress-tensors [31,32], similar to the universality in CFT 2 imposed by Virasoro symmetry. Thus it would be interesting and important to utilize the developed lightcone bootstrap to study heavy-light four-point function from which the underlying CFT data can be extracted [33][34][35][36] and the evidence of the universality can be provided and understood [35]. This paper is a supplement to the previous paper [35] that bootstraps the heavy-light four-point function by using the Lorentzian inversion formula.…”

“…Thus it would be interesting and important to utilize the developed lightcone bootstrap to study heavy-light four-point function from which the underlying CFT data can be extracted [33][34][35][36] and the evidence of the universality can be provided and understood [35]. This paper is a supplement to the previous paper [35] that bootstraps the heavy-light four-point function by using the Lorentzian inversion formula. We discuss the large impact parameter regime of the Regge limit [37] for lowest-twist double-stress-tensor in the heavy-light four-point function, and more importantly, we extend the universality of the double-twist operators [O H O L ] n,J at the leading order O(µ) from large spin to finite spin and then tackle the ∆ L poles referred in [31,32,35,38].…”

“…This paper is a supplement to the previous paper [35] that bootstraps the heavy-light four-point function by using the Lorentzian inversion formula. We discuss the large impact parameter regime of the Regge limit [37] for lowest-twist double-stress-tensor in the heavy-light four-point function, and more importantly, we extend the universality of the double-twist operators [O H O L ] n,J at the leading order O(µ) from large spin to finite spin and then tackle the ∆ L poles referred in [31,32,35,38]. We also discuss the case in d = 2, showing the consistency with Virasoro identity block [21].…”

“…In this section, we review the set-up and the recent progress of bootstrapping heavy-light four-point function, moreover, we would like to comment on the mixing problem of heavylight bootstrap mentioned in [35] and argue that we do not need to worry about the mixing problem.…”

“…Then we can expand the resulting correlators in terms of µ around µ → 0. Another perspective is that we can start with large N expansion where the degenerate point is located at CT → ∞ and then we collect ∆H to reorganize the expansions in terms of µ [35].…”