Tensionless p-branes with manifest conformal invariance

Abstract

The quantization of the tensionless p-brane is discussed. Inspection of the constraint algebra reveals that the central extensions for the p-branes have a simple form. Using a Hamiltonian BRST scheme we find that the quantization is consistent in any space-time dimension while the quantization of the conformal tensionless p-brane gives a critical dimension $d=2$.Comment: 14 pages, no figure

Quantum 3D tensionless string in light-cone gauge

“…Here we don't discuss more. 44 The spacetime index in the light-cone base: {µ} = {+, −, I} and I = 2, · · · , D − 1.…”

“…where the subscript R in the right-hand side indicates the reordering into R-order 10 . In light-cone 9 We can obtain the R-ordering from the normal ordering in the tensionless limit T → 0. In detail, the string ground state |0 T of a tensile string with a tension T is annihilated by positive modes of right-moving and left-moving oscillators, {αn, αn; n > 0}.…”

“…In this paper, we investigate 3d tensionless bosonic closed string. It has been known by using BRST method that tensionless p-branes have no Lorentz anomaly in any dimensions and that conformal tensionless p-branes have the critical dimension for the space-time conformal symmetry, D = 2 [6,7,8,9]. And the mass spectrum also has been investigated in [10,11].…”

“…Furthermore it is verified by the calculation without the mode expansion that the dangerous commutator, [J −I , K J ], in the light-cone gauge of higher dimensions causes the anomaly in the Reference order, called R-order for short 5 [37,38,39]. Similarly, tensionless string theories with the supersymmetry [40,41,42,43] and theories of a higher dimensional object [44,45] are studied.…”

Tensionless Branes and the Null String Critical Dimension

“…Finally, we pay attention to the fact that in every one of the p subalgebras (at fixed a) of the constraint algebra, one can obtain non-trivial central extension and consequently -critical dimension (see Appendix). For example, taking string − like or W eyl ordering, one derives D = 25 + p, which appears to be critical dimension for the tensile p-brane [17], [16]. However, the considered quantum dynamical system is described by the f ull constraint algebra, where only trivial central extensions are possible.…”