Global aspects of the harmonic gauge in bosonic string theory

• Published in: Nuclear physics. B 1988-08, Vol.306 (1), p.77-112
• Main Authors: Freedman, D.Z., Latorre, J.I., Pilch, K.
• Format: Article
• Language: English
• ISSN: 0550-3213; 1873-1562
• DOI: 10.1016/0550-3213(88)90172-1

The standard expression for the measure on Teichmüller space for the bosonic string on higher genus Riemann surfaces is transformed into a new expression which is exactly the ratio of determinants of the Faddeev-Popov method in the harmonic gauge. The new formula for the measure is checked by explicit computation for the sphere and torus. The measure can be expressed as a functional integral over ghosts and associated fields which incorporate the global geometry of the world-sheet. Measures for these fields are complete measures including zero modes, and the symmetry associated with the latter is gauge-fixed. A summary is given of a recently completed mathematical proof that a version of the harmonic gauge determines a globally defined slice in the space of metrics on Riemann surfaces of genus greater than one. Some clarification is given of the peculiar conformal properties of the harmonic gauge, namely the nonvanishing of the stress tensor component T z Z . As a pedagogical matter, the difference between the change of variables method conventionally used to obtain the string measure and the Faddeev-Popov method is clarified.