Massive String States as Extreme Black Holes

  • Published 1997


We consider the Schwarz-Sen spectrum of elementary electrically charged massive NR = 1=2 states of the four-dimensional heterotic string and show them to correspond to extreme black hole solutions with scalar-Maxwell parameter a = p 3 or 1 according as NL = 1 or NL > 1. The solitonic magnetically charged spectrum conjectured by Schwarz and Sen on the basis of string/ vebrane duality is also described by extreme black holes. PACS numbers: 11.17+y, 11.10.Kk JUNE 1994 y Research supported in part by NSF Grant PHY-9106593 The idea that elementary particles might behave like black holes is not a new one [1]. Intuitively, one might expect that a pointlike object whose mass exceeds the Planck mass, and whose Compton wavelength is therefore less than its Schwarzschild radius, would exhibit an event horizon. In the absence of a consistent quantum theory of gravity, however, such notions would always remain rather vague. Superstring theory, on the other hand, not only predicts such massive states but may provide us with a consistent framework in which to discuss them. The purpose of the present paper is to con rm the claim [2] that certain massive excitations of four-dimensional superstrings are indeed black holes. Our results thus complement those of [3] where it is suggested that all black holes are single string states. Of course, non-extreme black holes would be unstable due to the Hawking e ect. To describe stable elementary particles, therefore, we must focus on extreme black holes whose masses saturate a Bogomol'nyi bound. Speci cally, we shall consider the four-dimensional heterotic string obtained by toroidal compacti cation. At a generic point in the moduli space of vacuum con gurations the unbroken gauge symmetry is U(1) and the low energy e ective eld theory is described by N = 4 supergravity coupled to 22 abelian vector multiplets. A recent paper [2] showed that this theory exhibits both electrically and magnetically charged black hole solutions corresponding to scalar-Maxwell parameter a = 0; 1; p 3. In other words, by choosing appropriate combinations of dilaton and moduli elds to be the scalar eld and appropriate combinations of the eld strengths and their duals to be the Maxwell eld F , the eld equations can be consistently truncated to a form given by the Lagrangian L = 1 32 p g R 1 2 (@ ) 1 4 e a F 2 (1) for these three values of a. The bound between the black hole ADM mass m, and the electric charge Q = R e a ~ F=8 , where a tilda denotes the dual, is given by

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@inproceedings{1997MassiveSS, title={Massive String States as Extreme Black Holes}, author={}, year={1997} }