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<p>We study a two-matrix toy model with a BFSS-like interaction term using the collective field formalism. The main technical simplification is obtained by gauge-fixing first, and integrating out the off-diagonal elements, before changing to the collective field variable. We show that the resulting (2 + 1)-dimensional collective field action has novel features with respect to non-locality, and that we need to add a mass term to get a time-local potential. As is expected, one recovers the single matrix quantum mechanical collective field Hamiltonian in the proper limit.</p>

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Collective field theory of gauged multi-matrix models: integrating out off-diagonal strings

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月17日

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  • Suddhasattwa Brahma,
  • Robert Brandenberger,
  • Keshav Dasgupta,
  • Yue Lei,
  • Julia Pasiecznik

摘要

We study a two-matrix toy model with a BFSS-like interaction term using the collective field formalism. The main technical simplification is obtained by gauge-fixing first, and integrating out the off-diagonal elements, before changing to the collective field variable. We show that the resulting (2 + 1)-dimensional collective field action has novel features with respect to non-locality, and that we need to add a mass term to get a time-local potential. As is expected, one recovers the single matrix quantum mechanical collective field Hamiltonian in the proper limit.