Abstract
In this paper we consider the collective field theory description of a single free massless scalar matrix theory in 2+1 dimensions. The collective fields are given by k-local operators obtained by tracing a product of k-matrices. For k = 2 and k = 3 we argue that the collective field packages the fields associated to a single and two Regge trajectories respectively. We also determine the coordinate transformation between the coordinates of the collective field theory and the bulk AdS space time. This is used to verify that the bulk equations of motion holds in the collective field theory description.
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Acknowledgments
RdMK would like to thank Antal Jevicki for very helpful discussions. RdMK is supported by a start up research fund of Huzhou University, a Zhejiang Province talent award and by a Changjiang Scholar award. PR is also supported by the South African Research Chairs Initiative of the Department of Science and Technology and the National Research Foundation. HJRVZ is supported in part by the “Quantum Technologies for Sustainable Development” grant from the National Institute for Theoretical and Computational Sciences of South Africa (NITHECS). RdMK and PR would like to thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the programme “Black holes: bridges between number theory and holographic quantum information” when work on this paper was initiated. This work was also supported by EPSRC Grant Number EP/R014604/1.
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de Mello Koch, R., Roy, P. & Van Zyl, H.J.R. Holography of a single free matrix. J. High Energ. Phys. 2024, 81 (2024). https://doi.org/10.1007/JHEP06(2024)081
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DOI: https://doi.org/10.1007/JHEP06(2024)081