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 Tk as well as large spin double-twist operators {left[{mathcal{O}}_H{mathcal{O}}_Lright]}_{n^{prime },{J}^{prime }} . In this way, we also propose an algorithm to bootstrap the heavy- light 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-stress- tensor. 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 double- stress-tensor OPE coefficient. Exact expressions of lowest-twist double-stress-tensor OPE coefficients in d = 6, 8, 10 are also obtained as further examples.
Highlights
Directly studying strongly-coupled CFT is a hard task, recent developments of conformal bootstrap make it achievable
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 apply the Lorentzian inversion formula to heavylight four-point functions back and forth, and we surprisingly find that the Lorentzian inversion formula can shed light on the above questions
Summary
The conformal block is the solution of the quadratic Casimir equation. In d = 4, the closed form of conformal block for scalar four-point function O1O2O3O4 is known. The conformal block (2.4) is symmetric under (z → z, z → z). In general dimensions, the exact solutions are hard to come by. Compare the leading term of conformal block (2.6) (specifying d = 4) with the exact. ∆−J −2 block in d = 4 (2.4), it is obvious that the terms with z 2 are missing in the expansion (2.6). (2.6) is referred to as power laws in [15], because it only contains the essential terms with power z(∆−J)/2. The coefficients Bna,,bm can be obtained by solving quadratic Casimir equation, see, e.g. The coefficients Bna,,bm can be obtained by solving quadratic Casimir equation, see, e.g. [15] and appendix A.1
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