Brane-anti-brane Democracy

We suggest a duality invariant formula for the entropy and temperature of non-extreme black holes in supersymmetric string theory. The entropy is given in terms of the duality invariant parameter of the deviation from extremality and 56 SU(8) covariant central charges. It interpolates between the entropies of Schwarzschild solution and extremal solutions with various amount of unbroken supersymmetries and therefore serves for classification of black holes in supersymmetric string theories. We introduce the second auxiliary 56 via E(7) symmetric constraint. The symmetric and antisymmetric combinations of these two multiplets are related via moduli to the corresponding two fundamental representations of E(7): brane and anti-brane "numbers." Using the CPT as well as C symmetry of the entropy formula and duality one can explain the mysterious simplicity of the non-extreme black hole area formula in terms of branes and anti-branes.Comment: LaTeX, 12 pages, no figure

N=8 Supergravity 4-point Amplitudes

We present the explicit expressions in N=8 supergravity for the bosonic 4-particle tree and 1-loop amplitudes including vectors and scalars. We also present the candidate 4-point UV divergences in a form of helicity amplitudes, corresponding to 3-loop manifestly N=8 supersymmetric and Lorentz covariant counterterm. This may shed some light on the 3-loop finiteness of N=8 SG and on a conjectured higher loop finiteness. We perform a supersymmetric deformation to complex momentum of the 4-point generating function including higher-loop counterterms and the 1-loop UV finite amplitudes. Using the explicit form of the scalar part of the 3-loop counterterm and of the 1-loop UV finite scalar 4-point amplitudes we find that they both have an unbroken E7 symmetry. We derive from E7 symmetry the low-energy theorem for the 1-loop n-point amplitudes.Comment: 23 p, 4 figure

Quantization of p-branes, D-p-branes and M-branes

Killing spinors of space-time BPS configurations play an important role in quantization of theories with the fermionic worldvolume local symmetry. We show here how it works for the GS superstring, BST supermembrane and M-5-brane. We show that the non-linear generalization of the (2,0) d=6 tensor supermultiplet action is the M-5-brane action in a Killing gauge. For D-p-branes the novel feature of quantization is that they can be quantized Lorentz covariantly, in particular, for D-0-brane a gauge exists where the action is covariant and free. We present a general condition on possible choice of gauges for the kappa-symmetric branes.Comment: 9 pages, Talk at STRINGS'97 Meeting, Amsterdam, The Netherlands, 16-21 Jun 199

E(7) Symmetric Area of the Black Hole Horizon

Extreme black holes with 1/8 of unbroken N=8 supersymmetry are characterized by the non-vanishing area of the horizon. The central charge matrix has four generic eigenvalues. The area is proportional to the square root of the invariant quartic form of $E_{7(7)}$. It vanishes in all cases when 1/4 or 1/2 of supersymmetry is unbroken. The supergravity non-renormalization theorem for the area of the horizon in N=8 case protects the unique U-duality invariant.Comment: a reference added, misprints remove

Black Hole Superpartners and Fixed Scalars

Some bosonic solutions of supergravities admit Killing spinors of unbroken supersymmetry. The anti-Killing spinors of broken supersymmetry can be used to generate the superpartners of stringy black holes. This has a consequent feedback on the metric and the graviphoton. We have found however that the fixed scalars for the black hole superpartners remain the same as for the original black holes. Possible phenomenological implications of this result are discussed.Comment: 6 pages, Late

General Static N=2 Black Holes

We find general static BPS black hole solutions for general N=2, d=4 supergravity theories with an arbitrary number of vector multiplets. These solutions are completely specified by the K\"ahler potential of the underlying special K\"ahler geometry and a set of constrained harmonic functions.Comment: Latex, 7 pages, typos corrected, version to appear in MPL

Supersymmetric Balance of Forces and Condensation of BPS States

Until now all known static multi black hole solutions described BPS states with charges of the same sign. Such solutions could not be related to flat directions in the space of BPS states. The total number of such states could not spontaneously increase because of the charge conservation. We show that there exist static BPS configurations which remain in equilibrium even if they consist of states with opposite electric (or magnetic) charges from vector multiplets. This is possible because of the exact cancellation between the Coulomb and scalar forces. In particular, in the theories with N=4 or N=2 supersymmetry there exist stable massless multi center configurations with vanishing total charge. Since such configurations have vanishing energy and charge independently of their number, they can be associated with flat directions in the space of all possible BPS states. For N=2 case this provides a realization of the idea that BPS condensates could relate to each other different vacua of the string theory.Comment: 19 pages, LaTe

Near Horizon Superspace

The adS_{p+2} x S^{d-p-2} geometry of the near horizon branes is promoted to a supergeometry: the solution of the supergravity constraints for the vielbein, connection and form superfields are found. This supergeometry can be used for the construction of new superconformal theories. We also discuss the Green-Schwarz action for a type IIB string on adS_5 x S_5.Comment: 11 pages, LaTe

Stationary Axion/Dilaton Solutions and Supersymmetry

We present a new set of supersymmetric stationary solutions of pure N=4,d=4 supergravity (and, hence, of low-energy effective string theory) that generalize (and include) the Israel-Wilson-Perj\'es solutions of Einstein-Maxwell theory. All solutions have 1/4 of the supersymmetries unbroken and some have 1/2. The full solution is determined by two arbitrary complex harmonic functions {\cal H}_{1,2} which transform as a doublet under SL(2,\R) S duality and N complex constants k^{(n)} that transform as an SO(N) vector. This set of solutions is, then, manifestly duality invariant. When the harmonic functions are chosen to have only one pole, all the general resulting point-like objects have supersymmetric rotating asymptotically Taub-NUT metrics with 1/2 or 1/4 of the supersymmetries unbroken. The static, asymptotically flat metrics describe supersymmetric extreme black holes. Only those breaking 3/4 of the supersymmetries have regular horizons. The stationary asymptotically flat metrics do not describe black holes when the angular momentum does not vanish, even in the case in which 3/4 of the supersymmetries are broken.Comment: A few comments added and alternative formulae for the horizon area with manifest moduli-independence and duality-invariance given. 36 page