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Hamiltonian BRST Quantization of the Conformal String
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abstract
We present a new formulation of the tensionless string ($T= 0$) where the space-time conformal symmetry is manifest. Using a Hamiltonian BRST scheme we quantize this {\em Conformal String} and find that it has critical dimension $D=2$. This is in keeping with our classical result that the model describes massless particles in this dimension. It is also consistent with our previous results which indicate that quantized conformally symmetric tensionless strings describe a topological phase away {}from $D=2$. We reach our result by demanding nilpotency of the BRST charge and consistency with the Jacobi identities. The derivation is presented in two different ways: in operator language and using mode expansions. Careful attention is payed to regularization, a crucial ingredient in our calculations.
Forward citations
Cited by 8 Pith papers
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BRST quantization of Carroll-Weyl gauged null strings
In the highest-weight representation, the Carroll-Weyl null string is anomalous for every target-space dimension because its three anomaly coefficients demand D=27, D=6, and D=4 simultaneously.
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Null-strings Gauged, Reloaded and Quantized, I: Canonical Quantization in the Light-Cone Gauge
Light-cone Schrödinger quantization of null-strings with Carroll-Weyl symmetry yields D-3 physical modes, a discrete spectrum, and no critical dimension.
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Null Strings Gauged and Reloaded, I: Null Strings Have Carroll-Weyl Gauge Symmetry
Null strings admit two Carroll-Weyl gauge scalings; the standard ILST action arises by fixing one of them, with the residual symmetry matching an overlooked partial gauge symmetry identified in prior work.
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Quantum Anomalies of Tensionless Bosonic Strings
A unified BRST analysis shows the flipped-vacuum anomaly fixes D=26 for the ILST null string, leaves a λ-family of critical dimensions for the hybrid string, and rules out the conformal and Carroll-Weyl strings.
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Path integral quantization of null bosonic strings with Carroll-Weyl ghosts
Null bosonic string quantization on Carrollian worldsheets requires an extra scalar ghost pair for Carroll-Weyl scaling, yielding a bcs system that alters the BRST complex and anomaly cancellation beyond the standard ...
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Null Strings Gauged and Reloaded, II: Consistent Classical Treatment of the Null Strings
Null strings exhibit an independent Carroll-Weyl gauge symmetry that necessitates an extended BMS₃ algebra of constraints.
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The conformal null string in $d+2$ and $d$ dimensions
The conformal null string reduces from d+2 to d dimensions via Dirac slices, with the Virasoro-su(1,1) algebra mapping to Carrollian-Weyl symmetry.
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Symmetries of tensionless strings
The scale transformation symmetry of tensionless strings has been treated in numerous prior classical and quantum studies.
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