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<p>We study null <i>p</i>-branes, <i>p</i>-branes with a Carrollian <i>p</i>+1-dimensional worldvolume embedded in a generic <i>D</i>-dimensional flat Minkowski target space. This theory has a generalised BMS<sub><i>p</i>+1</sub> gauge symmetry. By fixing the light-cone gauge, the BMS symmetry is partly fixed, leaving <i>p</i> “momentum constraints” alongside <i>p</i>-dimensional area-preserving diffeomorphisms. We quantise the theory in the light-cone gauge via canonical quantisation and construct the physical Hilbert space by imposing the remaining constraints using sandwich conditions: the constraints must vanish when sandwiched between any two physical states. We show that solutions to the sandwich conditions are classified into <i>p</i> + 1 distinct classes, which we completely specify. In addition, we discuss special and interesting case of membranes in four dimensions and examine the physical implications of the quantised null <i>p</i>-brane and its associated physical Hilbert space.</p>

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Towards quantizing null p-branes: light-cone gauge analysis and physical Hilbert space

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月5日

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  • S. Dutta,
  • I. M. Rasulian,
  • M. M. Sheikh-Jabbari,
  • H. Yavartanoo

摘要

We study null p-branes, p-branes with a Carrollian p+1-dimensional worldvolume embedded in a generic D-dimensional flat Minkowski target space. This theory has a generalised BMSp+1 gauge symmetry. By fixing the light-cone gauge, the BMS symmetry is partly fixed, leaving p “momentum constraints” alongside p-dimensional area-preserving diffeomorphisms. We quantise the theory in the light-cone gauge via canonical quantisation and construct the physical Hilbert space by imposing the remaining constraints using sandwich conditions: the constraints must vanish when sandwiched between any two physical states. We show that solutions to the sandwich conditions are classified into p + 1 distinct classes, which we completely specify. In addition, we discuss special and interesting case of membranes in four dimensions and examine the physical implications of the quantised null p-brane and its associated physical Hilbert space.