Four Dimensional Black Holes in String Theory

Exact solutions of heterotic string theory corresponding to four-dimensional charge Q magnetic black holes are constructed as tensor products of an SU(2)/Z(2Q+2) WZW orbifold with a (0,1) supersymmetric SU(1,1)/U(1) WZW coset model. The spectrum is analyzed in some detail. ``Bad'' marginal operators are found which are argued to deform these theories to asymptotically flat black holes. Surprising behaviour is found for small values of Q, where low-energy field theory is inapplicable. At the minimal value Q=1, the theory degenerates. Renormalization group arguments are given that suggest the potential gravitational singularity of the low-energy field theory is resolved by a massive two-dimensional field theory. At Q=0, a stable, neutral ``remnant,'' of potential relevance to the black hole information paradox, is found.Comment: 37 pages + 1 figure (tar compressed and uuencoded

Some Remarks on Effective Range Formula in Potential Scattering

In this paper, we present different proofs of very recent results on the necessary as well as sufficient conditions on the decrease of the potential at infinity for the validity of effective range formulas in 3-D in low energy potential scattering (Andr\'e Martin, private communication, to appear. See Theorem 1 below). Our proofs are based on compact formulas for the phase-shifts. The sufficiency conditions are well-known since long. But the necessity of the same conditions for potentials keeping a constant sign at large distances are new. All these conditions are established here for dimension 3 and for all angular momenta $\ell \geq 0$

Duality Versus Supersymmetry and Compactification

We study the interplay between T-duality, compactification and supersymmetry. We prove that when the original configuration has unbroken space-time supersymmetries, the dual configuration also does if a special condition is met: the Killing spinors of the original configuration have to be independent on the coordinate which corresponds to the isometry direction of the bosonic fields used for duality. Examples of ``losers" (T-duals are not supersymmetric) and ``winners" (T-duals are supersymmetric) are given.Comment: LaTeX file, 19 pages, U. of Groningen Report UG-8/94, Stanford U. Report SU-ITP-94-19, QMW College Report QMW-PH-94-1

More on Four-Dimensional Extremal Black Holes

We consider an embedding of the extremal four-dimensional Reissner-Nordstr\"om black hole into type $IIB$ string theory. The equivalent type $IIB$ configuration, in the D-brane weak-coupling picture, is a bound state of D1- and D5-branes threaded by fundamental type $IIB$ strings. The bound state involves also a NSNS solitonic 5-brane, mimicking the role of the Kaluza-Klein magnetic monopole. The statistical entropy derived by counting the degeneracy of the BPS-saturated excitations of this bound state agrees perfectly with the (semiclassical) Bekenstein-Hawking formula.Comment: 19 pages, using Latex, no figure

Monopoles and Instantons in String Theory

In recent work, several classes of solitonic solutions of string theory with higher-membrane structure have been obtained. These solutions can be classified according to the symmetry possessed by the solitons in the subspace of the spacetime transverse to the membrane. Solitons with four-dimensional spherical symmetry represent instanton solutions in string theory, while those with three-dimensional spherical symmetry represent magnetic monopole-type solutions. For both of these classes, we discuss bosonic as well as heterotic solutions.Comment: 16 page

Kaluza-Klein and H-Dyons in String Theory

Kaluza-Klein monopole and H-monopole solutions, which are T-dual to each other, are the well-known solutions of string theory compactified on $T^6$. Since string theory in this case has an S-duality symmetry, we explicitly construct the corresponding dyonic solutions by expressing the $D = 4$ string effective action in a manifestly $SL(2, R)$ invariant form with an $SL(2, R)$ invariant constraint. The Schwarz-Sen charge spectrum, the BPS saturated mass formula as well as the stability of these states are discussed briefly.Comment: 15 pages, LaTeX, No figures, improved version to appear in Phys. Rev.

Extremal black holes as exact string solutions

We show that the leading order solution describing an extremal electrically charged black hole in string theory is, in fact, an exact solution to all orders in \a' when interpreted in a Kaluza-Klein fashion. This follows from the observation that it can be obtained via dimensional reduction from a five dimensional background which is proved to be an exact string solution.Comment: 13 pages, harvmac, Imperial/TP/93-94/51, UCSBTH-94-24 (references added

Exact SU(2)*U(1) Stringy Black Holes

Extreme magnetic dilaton black holes are promoted to exact solutions of heterotic string theory with unbroken supersymmetry. With account taken of alpha' corrections this is accomplished by supplementing the known solutions with SU(2) Yang-Mills vectors and scalars in addition to the already existing Abelian U(1) vector field. The solution has a simple analytic form and includes multi-black-holes. The issue of exactness of other black-hole-type solutions, including extreme dilaton electrically charged black holes and Taub-NUT solutions is discussed.Comment: 10 pages, SU-ITP-94-27 and QMW-PH-94-34 (version accepted for publication in Phys. Rev., contains a discussion of (4.1) supersymmetry of the black hole sigma model

Solution--Generating Transformations and the String Effective Action

We study exhaustively the solution-generating transformations (dualities) that occur in the context of the low-energy effective action of superstring theory. We first consider target-space duality (``T duality'') transformations in absence of vector fields. We find that for one isometry the full duality group is (SO^{\uparrow}(1,1))^{3} x D_{4}, the discrete part (D_{4}) being non-Abelian. We, then, include non-Abelian Yang--Mills fields and find the corresponding generalization of the T duality transformations. We study the \alpha^{\prime} corrections to these transformations and show that the T duality rules considerably simplify if the gauge group is embedded in the holonomy group. Next, in the case in which there are Abelian vector fields, we consider the duality group that includes the transformation introduced by Sen that rotates among themselves components of the metric, axion and vector field. Finally we list the duality symmetries of the Type II theories with one isometry.Comment: latex file, 42 pages (less if you use optional commands) No changes at all. Resubmited due to mailer problem

Curvature-corrected dilatonic black holes and black hole -- string transition

We investigate extremal charged black hole solutions in the four-dimensional string frame Gauss-Bonnet gravity with the Maxwell field and the dilaton. Without curvature corrections, the extremal electrically charged dilatonic black holes have singular horizon and zero Bekenstein entropy. When the Gauss-Bonnet term is switched on, the horizon radius expands to a finite value provided curvature corrections are strong enough. Below a certain threshold value of the Gauss-Bonnet coupling the extremal black hole solutions cease to exist. Since decreasing Gauss-Bonnet coupling corresponds to decreasing string coupling $g_s$, the situation can tentatively be interpreted as classical indication on the black hole -- string transition. Previously the extremal dilaton black holes were studied in the Einstein-frame version of the Gauss-Bonnet gravity. Here we work in the string frame version of this theory with the S-duality symmetric dilaton function as required by the heterotic string theory.Comment: 14 pages, 2 figure