Теория струн и скрытые измерения вселенной

87

Shamit Kachru (Stanford University), interview with author, August 19, 2008.

88

Ashoke Sen (Harish-Chandra Research Institute), interview with author, August 22, 2008.

89

Jacques Distler and Brian Greene, “Some Exact Results on the Superpotential from Calabi-Yau Compactifications,” Nuclear Physics В 309 (1988): 295–316.

90

Doron Gepner, “Yukawa Couplings for Calabi-Yau String Compactification,” Nuclear Physics В 311 (1988): 191–204.

91

Kachru, interview with author, August 19, 2008.

92

Paul Aspinwall (Duke University), interview with author, August 14, 2008.

93

Wolfgang Lerche, Cumrun Vafa, and Nicholas Warner, “Chiral Rings in N=2 Superconformal Theories,” Nuclear Physics В 324 (1989): 427–474.

94

В. R. Greene, C. Vafa, N. P. Warner, “Calabi-Yau Manifolds and Renormalization Group Flows,” Nuclear Physics В 324 (1989): 371–390.

95

Brian Greene (Columbia University), interview with author, March 11,2010.

96

Ibid.

97

Doron Gepner, interview with author, August 19, 2008.

98

B. R. Greene and M. R. Plesser, “Duality in Calabi-Yau Moduli Space,” Nuclear Physics В 338 (1990): 15–37.

99

Brian Greene, The Elegant Universe (New York: Vintage Books, 2000), p. 258.

100

Plesser, interview with author, September 19, 2008.

101

Greene, interview with author, March 11, 2010.

102

Greene, The Elegant Universe, p. 259.

103

Cumrun Vafa (Harvard University), interview with author, September 19, 2008.

104

Greene, interview with author, March 13, 2010.

105

Mark Gross (UCSD), interview with author, October 31, 2008.

106

Andreas Gathmann (University of Kaiserslautern), interview with author, August 25, 2008.

107

David Hilbert, “Mathematical Problems,” lecture, International Congress of Mathematicians, Paris, 1900,(html version prepared by David Joyce, Mathematics Department, Clark University, Worcester, Mass.).

108

Andreas Gathmann, “Mirror Principle I,” Mathematical Reviews, MR1621573, 1999.

109

David Cox (Amherst College), interview with author, June 13, 2008.

110

Andrew Strominger (Harvard University), interview with author, February 7, 2007.

111

Gross, interview with author, September 19, 2008.

112

Ibid.

113

Gross, interview with author, September 24, 2008.

114

Eric Zaslow (Northwestern University), interview with author, June 26, 2008.

115

Gross, interview with author, September 24, 2008.

116

Mark Gross, e-mail letter to author, September 29, 2008.

117

Strominger, interview with author, August 1, 2007.

118

Zaslow, interview with author, June 26, 2008.

119

Gross, interview with author, September 19, 2008.

120

Yan Soibelman (Kansas State University), interview with author, September 26, 2008.

121

Aspinwall, interview with author, June 23, 2008.

122

Michael Douglas (Stony Brook University), interview with author, August 20, 2008.

123

Aspinwall, interview with author, June 23, 2008.

124

Gross, interview with author, September 24, 2008.

125

Avi Loeb (Harvard University), interview with author, September 25,2008.

126

American Mathematical Society, “Interview with Heisuke Hironaka,” Notices of the AMS 52, no. 9 (October 2005): 1,015.

127

Steve Nadis, “Cosmic Inflation Comes of Age,” Astronomy (April 2002).

128

Andrew Strominger, “String Theory, Black Holes, and the Fundamental Laws of Nature,” lecture, Harvard University, Cambridge, Mass., April 4, 2007.

129

Ibid.

130

Hirosi Ooguri (California Institute of Technology), interview with author, October 8, 2008.

131

Strominger, lecture.

132

Andrew Strominger and Cumrun Vafa, “Microscopic Origin of the Bekenstein-Hawking Entropy,” Physics Letters В 379 (June 27, 1996): 99-104.

133

Andrew Strominger, quoted in Gary Taubes, “Black Holes and Beyond,” Science Watch, May/June 1999, http://archive.sciencewatch.com/may-june99/sw_may-june99_page3.htm.

134

Hirosi Ooguri, interview with author, October 8, 2008.

135

Strominger, quoted in Taubes, “Black Holes and Beyond.”

136

Xi Yin (Harvard University), interview with author, October 14, 2008.

137

Ibid.

138

Xi Yin, interview with author, October 22, 2008.

139

Frederik Denef (Harvard University), interview with author, August 26, 2008.

140

Xi Yin, interview with author, October 14, 2008.

141

Aaron Simons, interview with author, February 9, 2007.

142

Ibid.

143

J. M. Maldacena, A. Strominger, and E. Witten, “Black Hole Entropy in M-Theory” Journal of High Energy Physics 9712 (1997), http://arxiv.org/PS_cache/hepth/pdf/9711/9711053vl.pdf.

144

Juan Maldacena (IAS), interview with author, September 4, 2008.

145

Hirosi Ooguri, Andrew Strominger, and Cumrun Vafa, “Black Hole Attractors and the Topological String,” Physical Review D 70 (2004).

146

Cumrun Vafa (Harvard University), interviewwith author, September 26, 2008.

147