The Modular Duality of Specific Heat on Genus g Riemann Surface

YAN Jun; HU Shi-Ke

Chinese Physics C> 1993, Vol. 17> Issue(6) : 534-537

The Modular Duality of Specific Heat on Genus g Riemann Surface

YAN Jun ^, ,
HU Shi-Ke

Department of Physics,Sichuan University,Chengdu 610064

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Abstract：
The free energy on genus g Riemann surface is derived by introducing two-dimensional scalar field and using Vafa's operator approach.The modular duality relation of specific heat is also obtained.

References

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E.Alvarez and M. Osorio ，Nucl.Phys.，B304 (1988)，327.[2]B.McClain and B. Roth,Comm.Math. Phys.，111 (1987)，539.[3]Y. Leblanc, Phys.Rev. Lett.、64 (1990).831.[4]E. Alvarez and M.Osorio , Phys.Rev.D40 (1989)，1150.[5]Yan Jun, Li Jiannan and Hu Shike Chin.Phys.Lett.，9 (1989) 425.[6]Yan Jun, Li liannan and Hu Shike Chin.Phys.Lett.，8 (1990) 381.[7]颜骏、胡诗可，高能物理与核物理，5 (1991), 414.[8]J. Atick and E. Witten, Nucl. Phys.，B310 (1988)，291.[9]C. Vafa, Phys. Lett.，B190 (1987)，47.[10]P. Murphy and S. Sen, Phys. Lett.，B233 (1989)，322.[11]L. Gaume, G. Moore and C. Vafa, Comm. Math. Phys.，106 (1986)，1.[12]D. Mumford, Tata lectures on theta (I)，(Birkhauser-1983).[13]A. Giveon, E. Rabinovici and G. Veneziano, Nucl. Phys.，B322 (1989)，167.

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YAN Jun and HU Shi-Ke. The Modular Duality of Specific Heat on Genus g Riemann Surface[J]. Chinese Physics C, 1993, 17(6): 534-537.

YAN Jun and HU Shi-Ke. The Modular Duality of Specific Heat on Genus g Riemann Surface[J]. Chinese Physics C, 1993, 17(6): 534-537. shu

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Received: 1900-01-01
Revised: 1900-01-01

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The Modular Duality of Specific Heat on Genus g Riemann Surface

YAN Jun ^,
HU Shi-Ke

Corresponding author: YAN Jun,

Department of Physics,Sichuan University,Chengdu 610064

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1993-06-05

Abstract: The free energy on genus g Riemann surface is derived by introducing two-dimensional scalar field and using Vafa's operator approach.The modular duality relation of specific heat is also obtained.