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 $C_T\to \infty$. 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 $[{\mathcal{O}}_H{\mathcal{O}}_L{]}_{n^{\prime },J^{\prime }}$. 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.

arXiv commentLatex, 43 pages, typo corrected, rewritten more clearly, refs arranged more appropriately

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Cited by in corpus (21)

• Proper time to the black hole singularity from thermal one-point functions
• Holographic thermal correlators from supersymmetric instantons
• Gravitational orbits, double-twist mirage, and many-body scars
• Holographic Correlators at Finite Temperature
• Thermalization in Large-N CFTs
• Black hole bulk-cone singularities
• Model-Dependence of Minimal-Twist OPEs in $d>2$ Holographic CFTs
• ISCOs in AdS/CFT
• Exact thermal correlators of holographic $CFT$s
• On Local and Integrated Stress-Tensor Commutators
• Multi-stress tensors and next-to-leading singularities in the Regge limit
• $d>2$ Stress-Tensor OPE near a Line
• Mixed Correlator Dispersive CFT Sum Rules
• CFT correlators, $\mathcal{W}$-algebras and Generalized Catalan Numbers
• Factorized lightcone expansion of conformal blocks
• Newton vs. Coulomb in AdS/CFT and the Weak Gravity Conjecture
• Approximate Symmetries in $d=4$ CFTs with an Einstein Gravity Dual
• More on Heavy-Light Bootstrap up to Double-Stress-Tensor
• Toward Null State Equations in $d>2$
• Resummation of Multi-Stress Tensors in Higher Dimensions
• Operator product expansions and recoil