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<p>Quantum field theory on two- and three-dimensional fuzzy anti-de Sitter spaces is introduced and studied. We find a complete set of solutions to the fuzzy Klein-Gordon equation and identify the commutative limit in which they reduce to classical scalar field modes. After introducing the noncommutative boundary via semi-classical states, the fuzzy modes are used to obtain the boundary two-point function. In both two and three dimensions, this gives an interesting two-parameter deformation of the conformal two-point function. For the fuzzy AdS<sub>2</sub>, the two-point function is given explicitly in terms of the Appell function <i>F</i><sub>1</sub>.</p>

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QFT on fuzzy AdS spaces: classical limit and boundary correlation functions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月8日

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  • Bojana Brkić,
  • Ilija Burić,
  • Maja Burić,
  • Dušan Ðorđević,
  • Duško Latas

摘要

Quantum field theory on two- and three-dimensional fuzzy anti-de Sitter spaces is introduced and studied. We find a complete set of solutions to the fuzzy Klein-Gordon equation and identify the commutative limit in which they reduce to classical scalar field modes. After introducing the noncommutative boundary via semi-classical states, the fuzzy modes are used to obtain the boundary two-point function. In both two and three dimensions, this gives an interesting two-parameter deformation of the conformal two-point function. For the fuzzy AdS2, the two-point function is given explicitly in terms of the Appell function F1.