Anomaly of Tensionless String in Light-cone Gauge

Abstract

The classical tensionless string theory has the spacetime conformal symmetry. We expect and require that the quantum tensionless string theory has it too. In the BRST quantization method, the theory has no spacetime conformal anomaly in two dimensions. On the other hand, in the light-cone gauge quantization without the mode expansion, the theory in $D>3$ has the spacetime conformal anomaly in the traceless part of $[{\mathcal{J}}^{-I},{\mathcal{K}}^J]$ in some operator order. In this paper, we consider a tensionless closed bosonic string in the light-cone gauge and investigate the spacetime conformal anomaly in the theory with the mode expansion. The appearance of the spacetime conformal anomaly in the light-cone gauge is different between the case of $D>3$ and the case of $D=3$ and depends on the choice of the operator order. Therefore we must consider dangerous commutators in the spacetime conformal symmetry of $D>3$ and $D=3$ in each operator order separately. Specifically we calculate dangerous commutators, $[{\mathcal{J}}^{-I},{\mathcal{K}}^K]$ in $D>3$ and ${\tilde{\mathcal{K}}}^{-}\equiv -i[{\mathcal{J}}^{-},{\tilde{\mathcal{K}}}^{-}]$ and $[{\mathcal{J}}^{-},{\tilde{\mathcal{K}}}^{-}]$ in $D=3$, in two types of the operator order.

arXiv comment44 pages

References in corpus (21)

• AdS Dual of the Critical O(N) Vector Model
• An AdS_3 Dual for Minimal Model CFTs
• Higher Spin Gauge Theory and Holography: The Three-Point Functions
• Higher Spin Gauge Theories: Star-Product and AdS Space
• Symmetries of Holographic Minimal Models
• GCA in 2d
• Spacetime Geometry in Higher Spin Gravity
• Classical and Quantized Tensionless Strings
• On the Tensionless Limit of Bosonic Strings, Infinite Symmetries and Higher Spins
• Higher Spin Gravity with Matter in AdS_3 and Its CFT Dual
• On Higher Spin Gauge Theory and the Critical O(N) Model
• Higher spin gravity in 3D: black holes, global charges and thermodynamics
• Higher-Spin Theory and Space-Time Metamorphoses
• Anyons from Strings
• The Zero Tension Limit of The Virasoro Algebra and the Central Extension
• Tensionless p-branes with manifest conformal invariance
• AdS/CFT for 3D Higher-Spin Gravity Coupled to Matter Fields
• All Superparticles are BPS
• The Quantum 3D Superparticle
• The Mass Spectrum of the 2-dimensional Conformal String
• The Zero Tension Limit of Strings and Superstrings