Sparsity in the numerical six-point bootstrap, by Sebastian Harris
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SciPost Physics Home Authoring Refereeing Submit a manuscript About Sparsity in the numerical six-point bootstrap Sebastian Harris SciPost Phys. 19, 151 (2025) · published 10 December 2025 doi: 10.21468/SciPostPhys.19.6.151 pdf BiBTeX RIS Submissions/Reports Abstract The paper contributes to an ongoing effort to extend the conformal bootstrap beyond its traditional focus on systems of four-point correlation functions. Recently, it was demonstrated that semidefinite programming can be used to formulate a six-point generalisation of the numerical bootstrap, yielding qualitatively new, rigorous bounds on CFT data. However, the numerical six-point bootstrap requires solving SDPs involving infinite-dimensional matrices, which has so far limited its applicability and hindered scalability in early implementations. This work overcomes the challenges by using sparse matrix decompositions to exploit the banded structure of the underlying SDP. The result is a rewriting of one-dimensional six-point bootstrap problems as effectively two-dimensional standard mixed correlator four-point bootstrap computations. As application, novel bounds whose extremal correlators interpolate between the six-point functions of the generalised free fermion and boson are derived. The extremal interpolations are matched with perturbative deformations of the massive free boson in AdS$_2$. × TY - JOURPB - SciPost FoundationDO - 10.21468/SciPostPhys.19.6.151TI - Sparsity in the numerical six-point bootstrapPY - 2025/12/10UR - https://scipost.org/SciPostPhys.19.6.151JF - SciPost PhysicsJA - SciPost Phys.VL - 19IS - 6SP - 151A1 - Harris, SebastianAB - The paper contributes to an ongoing effort to extend the conformal bootstrap beyond its traditional focus on systems of four-point correlation functions. Recently, it was demonstrated that semidefinite programming can be used to formulate a six-point generalisation of the numerical bootstrap, yielding qualitatively new, rigorous bounds on CFT data. However, the numerical six-point bootstrap requires solving SDPs involving infinite-dimensional matrices, which has so far limited its applicability and hindered scalability in early implementations. This work overcomes the challenges by using sparse matrix decompositions to exploit the banded structure of the underlying SDP. The result is a rewriting of one-dimensional six-point bootstrap problems as effectively two-dimensional standard mixed correlator four-point bootstrap computations. As application, novel bounds whose extremal correlators interpolate between the six-point functions of the generalised free fermion and boson are derived. The extremal interpolations are matched with perturbative deformations of the massive free boson in AdS$_2$.ER - × @Article{10.21468/SciPostPhys.19.6.151, title={{Sparsity in the numerical six-point bootstrap}}, author={Sebastian Harris}, journal={SciPost Phys.}, volume={19}, pages={151}, year={2025}, publisher={SciPost}, doi={10.21468/SciPostPhys.19.6.151}, url={https://scipost.org/10.21468/SciPostPhys.19.6.151},} Ontology / Topics See full Ontology or Topics database. Conformal bootstrap Author / Affiliations: mappings to Contributors and Organizations See all Organizations. 1 2 Sebastian Harris 1 Deutsches Elektronen-Synchrotron / Deutsche Elektronen-Synchrotron DESY [DESY] 2 Universität Hamburg / University of Hamburg [UH] Funders for the research work leading to this publication Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG] Studienstiftung des Deutschen Volkes (through Organization: Studienstiftung des deutschen Volkes / German National Academic Foundation)