Abstract
Recently, a careful canonical quantisation of the theory of closed bosonic tensionless strings has resulted in the discovery of three separate vacua and hence three different quantum theories that emerge from this single classical tensionless theory. In this note, we perform lightcone quantisation with the aim of determination of the critical dimension of these three inequivalent quantum theories. The satisfying conclusion of a rather long and tedious calculation is that one of vacua does not lead to any constraint on the number of dimensions, while the other two give D = 26. This implies that all three quantum tensionless theories can be thought of as consistent sub-sectors of quantum tensile bosonic closed string theory.
Highlights
The classical theory of tensionless or null strings [1] is well understood
Recently, a careful canonical quantisation of the theory of closed bosonic tensionless strings has resulted in the discovery of three separate vacua and three different quantum theories that emerge from this single classical tensionless theory
Through the process of lightcone quantisation and the closure of the Lorentz algebra in the background, we asked in which dimensions the quantum tensionless bosonic string theory was consistent
Summary
Where Xμ are space-time co-ordinates and the string worldsheet coordinates are σ0,1 ≡. For V α = (1,0), the residual symmetry transformation that still keeps the gauge fixed action invariant are (τ,σ) → (τ f (σ)+g(σ),f (σ)), where the functions f (σ),g(σ) can be arbitrary. We can invert the above expressions to find an expansion of the EM tensor in terms of the modes of the BMS algebra:. Where xμ and pμ are real, and the mode coefficients Aμn and Bnμ have to satisfy the reality condition (Xμ = (Xμ)∗). The induced vacuum is named from the induced representations of the BMS algebra under which it transforms. This can be thought of as the limit of the tensile vacuum.
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