Notes on conformal theory with nonprimary energy-momentum tensor that applies to the Nambu-Goto string

Abstract

I investigate the higher-derivative conformal theory which shows how the Nambu-Goto and Polyakov strings can be told apart. Its energy-momentum tensor is conserved, traceless but does not belong to the conformal family of the unit operator. To implement conformal invariance in this case, I develop the new technique that explicitly accounts for the quantum equation of motion and results in singular products. I show that the conformal transformations generated by such a nonprimary energy-momentum tensor form a Lie algebra with a central extension which in the path-integral formalism gives a logarithmically divergent contribution to the central charge. I demonstrate how the logarithmic divergence is canceled in the string susceptibility and reproduce the previously obtained deviation from KPZ-DDK at one loop.

16 pages 2 figures; v2: polished; v3: enlarged to 20 pages 3 figures, to appear in JHEP

References in corpus (2)

• The use of Pauli-Villars' regularization in string theory
• Private life of the Liouville field that causes new anomalies in the Nambu-Goto string

Cited by in corpus (3)

• Exact quantum conformal symmetry, its spontaneous breakdown, and gravitational Weyl anomaly
• Opus on conformal symmetry of the Nambu-Goto versus Polyakov strings
• Pauli-Villars' regularization of ghosts in path-integral string formulation