Ramzi R. Khuri

Entropy of 4D Extremal Black Holes

We derive the Bekenstein-Hawking entropy formula for four-dimensional Reissner- Nordstrom extremal black holes in type II string theory. The derivation is performed in two separate (T-dual) weak coupling pictures. One uses a type IIB bound state problem of D5- and D1-branes, while the other uses a bound state problem of D0- and D4-branes with macroscopic fundamental type IIA strings. In both cases, the D-brane systems are also bound to a Kaluza-Klein monopole, which then yields the four-dimensional black hole at strong coupling.

Four-dimensional string/string duality

We present supersymmetric soliton solutions of the four-dimensional heterotic string corresponding to monopoles, strings and domain walls. These solutions admit the D = 10 interpretation of a fivebrane wrapped around 5, 4 or 3 of the 6 toroidally compactified dimensions and are arguably exact to all orders in α′. The solitonic string solution exhibits an SL(2, Z) strong/weak coupling duality which however corresponds to an SL(2, Z) target space duality of the fundamental string.

Supersymmetry and dual string solitons

Abstract We present new classes of string-like soliton solutions in (N = 1; D = 10), (N = 2; D = 6) and (N = 4; D = 4) heterotic string theory. Connections are made between the solution-generating subgroup of the T-duality group of the compactification and the number of spacetime supersymmetries broken. Analogous solutions are also noted in (N = 1,2; D = 4) compactifications, where a different form of supersymmetry breaking arises.

Branes, times and dualities

Abstract Dualities link M-theory, the 10+1-dimensional strong coupling limit of the IIA string, to other 11-dimensional theories in signatures 9+2 and 6+5, and to type II string theories in all 10-dimensional signatures. We study the Freund-Rubin-type compactifications and brane-type solutions of these theories, and find that branes with various world-volume signatures are possible. For example, the 9+2-dimensional M ∗ theory has membrane-type solutions with world-volumes of signature (3,0) and (1,2), and a solitonic solution with world-volume signature (5,1).

A non-supersymmetric dyonic extreme Reissner-Nordström black hole

Abstract We present a dyonic embedding of the extreme Reissner-Nordstrom black hole in N = 4 and N = 8 supergravity that breaks all supersymmetries.

M-theory on a Calabi-Yau manifold

Abstract We compactify M -theory on a Calabi-Yau manifold to five dimensions by wrapping the membrane and fivebrane solitons of the eleven-dimensional supergravity limit around Calabi-Yau two-cycles and four-cycles, respectively. We identify the perturbative and non-perturbative BPS states thus obtained with those of heterotic string theory compactified on K 3 × S 1 . Quantum aspects of the five-dimensional theory are discussed.

Remark on string solitons

We derive an exact stringlike soliton solution of [ital D]=10 heterotic string theory. The solution possesses SU(2)[times]SU(2) instanton structure in the eight-dimensional space transverse to the world sheet of the soliton.

Some instanton solutions in string theory

Abstract In recent work Rey presented an exterior instanton solution for the massless fields in the low-energy limit of heterotic string theory to lowest order in α ′. We extend this solution to O ( α ′) in bosonic string theory and present several related solutions. For the spherically symmetric solution, the corresponding Weyl invariant sigma model is the product of a Wess-Zumino-Witten model and a one-dimensional conformal field theory. An exact solution is then obtained by fixing the metric and antisymmetric tensor field in their lowest order form and rescaling the dilation order by order in α ′.

New black hole, string and membrane solutions of the four-dimensional heterotic string

Abstract We present solutions of the low-energy four-dimensional heterotic string corresponding to p-branes with p=0, 1, 2, which are characterized by a mass per unit p-volume, M p+1 , and topological “magnetic” charge, gp+1. In the extremal limit, √2ϰ M p+1 =g p+1 , they reduce to the recently discovered nonsingular supersymmetric monopole, string and domain wall solutions. A novel feature is that the solutions involve both the dilaton and the modulus fields. In particular, the effective scalar coupling to the Maxwell field, e−αφFμνFμν, gives rise to a new string black hole with α=√3, in contrast to the pure dilaton black hole solution which has α=1. This means that electric/magnetic duality in D=4 may be seen as a consequence of string/fivebrane duality in D=10.

Worldvolume theories, holography, duality and time

Abstract Duality transformations involving compactifications on timelike as well as spacelike circles link M-theory, the 10 + 1-dimensional strong coupling limit of IIA string theory, to other 11-dimensional theories in signatures 9 + 2 and 6 + 5 and to type II string theories in all 10-dimensional signatures. These theories have BPS branes of various world-volume signatures, and here we construct the world-volume theories for these branes, which in each case have 16 supersymmetries. For the generalised D-branes of the various type II string theories, these are always supersymmetric Yang–Mills theories with 16 supersymmetries, and we show that these all arise from compactifications of the supersymmetric Yang–Mills theories in 9 + 1 or 5 + 5 dimensions. We discuss the geometry of the brane solutions and, for the cases in which the world-volume theories are superconformally invariant, we propose holographically dual string or M theories in constant curvature backgrounds. For product space solutions X×Y , there is in general a conformal field theory associated with the boundary of X and another with the boundary of Y .