Elliptic Genera of Symmetric Products and Second Quantized Strings

被引:0
作者
Robbert Dijkgraaf
Gregory Moore
Erik Verlinde
Herman Verlinde
机构
[1] Mathematics Dept,
[2] Univ. of Amsterdam,undefined
[3] 1018 TV Amsterdam,undefined
[4] The Netherlands,undefined
[5] Physics Dept,undefined
[6] Yale University,undefined
[7] New Haven,undefined
[8] CT 06520,undefined
[9] USA,undefined
[10] Theory Division,undefined
[11] CERN,undefined
[12] CH-1211 Geneva 23,undefined
[13] Switzerland and Inst. for Theor. Physics,undefined
[14] University of Utrecht,undefined
[15] 3508 TA Utrecht,undefined
[16] The Netherlands,undefined
[17] Inst. for Theor. Physics,undefined
[18] Univ. of Amsterdam,undefined
[19] 1018 XE Amsterdam,undefined
[20] The Netherlands,undefined
来源
Communications in Mathematical Physics | 1997年 / 185卷
关键词
Elliptic Genus; Symmetric Product; Quantized String;
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摘要
In this note we prove an identity that equates the elliptic genus partition function of a supersymmetric sigma model on the N-fold symmetric product \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} of a manifold M to the partition function of a second quantized string theory on the space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}. The generating function of these elliptic genera is shown to be (almost) an automorphic form for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}. In the context of D-brane dynamics, this result gives a precise computation of the free energy of a gas of D-strings inside a higher-dimensional brane.
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页码:197 / 209
页数:12
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