Geometrical quantization of bosonic string with Wess-Zumino term on genus-<span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi></math></span> Riemann surface

Yu-liang Liu; Su-qing Chen; Guang-jiong Ni

doi:10.1103/PhysRevD.41.472

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Geometrical quantization of bosonic string with Wess-Zumino term on genus- $g$ Riemann surface

Yu-liang Liu and Su-qing Chen

Guang-jiong Ni

Physics Department, Fudan University, Shanghai, China

Chinese Center of Advanced Science and Technology (World Laboratory), P.O. Box 8730, Beijing, China
Physics Department, Fudan University, Shanghai, China

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Phys. Rev. D 41, 472 – Published 15 January, 1990

DOI: https://doi.org/10.1103/PhysRevD.41.472

Abstract

By combining the method of geometrical quantization and Krichever and Novikov algebra, we study the holomorphic structure of a bosonic string with Wess-Zumino term on a genus- $g$ Riemann surface $Σ$ and arrive at the conclusion that the curvature on a Kähler manifold is proportional to the central extension of Krichever and Novikov algebra on $Σ$ and vanishes at the critical dimension $d = 26 - \frac{(k d_{G})}{(C_{V} + k)}$ .

References (11)

M. J. Bowick and S. G. Rajeev, Phys. Rev. Lett. 58, 535 (1987) Nucl. Phys. B293, 348 (1987)
K. Pilch and N. P. Warner, MIT Report No. CTP-1457, 1987 (unpublished)
I. M. Krichever and S. P. Novikov, Funk. Anal. Pril. 21, 46 (1987) ibid.21, 47 (1987)
L. Bonora, M. Bregola, P. Catta-Ramusino, and M. Martellini, Phys. Lett. B 205, 53 (1988)
L. Bonora, M. Martellini, M. Rinaldi, and J. Russo, Phys. Lett. B 206, 444 (1988)
L. Bonora, M. Rinaldi, J. Russo, and K. Wu, Phys. Lett. B 208, 440 (1988)
Yu-liang Liu and Guang-jiong Ni, Phys. Lett. B 220, 99 (1989)
Miao Li, Phys. Lett. B 208, 89 (1988)
S. Kobayashi and K. Nomizu, Foundations of Differential Geometry (Interscience, New York, 1969)
D. Harari, D. K. Hong, P. Ramond, and V. G. J. Rodgers, Nucl. Phys. B294, 556 (1987)
J. Michelsson, Commun. Math. Phys. 112, 653 (1987)

[c1] M. J. Bowick and S. G. Rajeev, Phys. Rev. Lett. 58, 535 (1987) Nucl. Phys. B293, 348 (1987)

[c2] K. Pilch and N. P. Warner, MIT Report No. CTP-1457, 1987 (unpublished)

[c3] I. M. Krichever and S. P. Novikov, Funk. Anal. Pril. 21, 46 (1987) ibid.21, 47 (1987)

[c4] L. Bonora, M. Bregola, P. Catta-Ramusino, and M. Martellini, Phys. Lett. B 205, 53 (1988)

[c5] L. Bonora, M. Martellini, M. Rinaldi, and J. Russo, Phys. Lett. B 206, 444 (1988)

[c6] L. Bonora, M. Rinaldi, J. Russo, and K. Wu, Phys. Lett. B 208, 440 (1988)

[c7] Yu-liang Liu and Guang-jiong Ni, Phys. Lett. B 220, 99 (1989)

[c8] Miao Li, Phys. Lett. B 208, 89 (1988)

[c9] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry (Interscience, New York, 1969)

[c10] D. Harari, D. K. Hong, P. Ramond, and V. G. J. Rodgers, Nucl. Phys. B294, 556 (1987)

[c11] J. Michelsson, Commun. Math. Phys. 112, 653 (1987)

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Geometrical quantization of bosonic string with Wess-Zumino term on genus- $g$ Riemann surface

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Geometrical quantization of bosonic string with Wess-Zumino term on genus-g Riemann surface

Abstract

References (11)

Geometrical quantization of bosonic string with Wess-Zumino term on genus- $g$ Riemann surface