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We present a comprehensive analysis of 2-charge fuzzball solutions, that is, horizon-free non-singular solutions of IIB supergravity characterized by a curve on R^4. We propose a precise map that relates any given curve to a specific superposition of R ground states of the D1-D5 system. To test this proposal we compute the holographic 1-point functions associated with these solutions, namely the conserved charges and the vacuum expectation values of chiral primary operators of the boundary theory, and find perfect agreement within the approximations used. In particular, all kinematical constraints are satisfied and the proposal is compatible with dynamical constraints although detailed quantitative tests would require going beyond the leading supergravity approximation. We also discuss which geometries may be dual to a given R ground state. We present the general asymptotic form that such solutions must have and present exact solutions which have such asymptotics and therefore pass all kinematical constraints. Dynamical constraints would again require going beyond the leading supergravity approximation., Comment: 87 pages, begins with 10 page self contained summary of results;v2:JHEP version; v3: typos corrected, see in particular formula D.16

The correspondence between domain-wall and cosmological solutions of gravity coupled to scalar fields is explained. Any domain wall solution that admits a Killing spinor is shown to correspond to a cosmology that admits a pseudo-Killing spinor: whereas the Killing spinor obeys a Dirac-type equation with hermitian `mass'-matrix, the corresponding pseudo-Killing spinor obeys a Dirac-type equation with a anti-hermitian `mass'-matrix. We comment on some implications of (pseudo)supersymmetry., Comment: 11 pages, contribution to the proceedings of IRGAC 2006;v3: minor changes

We review the generalized Witten-Nester spinor stability argument for flat domain wall solutions of gravitational theories. Neither the field theory nor the solution need be supersymmetric. Nor is the space-time dimension restricted. We develop the non-trivial extension required for AdS-sliced domain walls and apply this to show that the recently proposed "Janus" solution of Type IIB supergravity is stable non-perturbatively for a broad class of deformations. Generalizations of this solution to arbitrary dimension and a simple curious linear dilaton solution of Type IIB supergravity are byproducts of this work., Comment: 37 pages, 3 figures, v2: minor corrections, references and acknowledgments added

We extend the correspondence between adS-supergravities and superconformal field theories on the adS boundary to a correspondence between gauged supergravities (typically with non-compact gauge groups) and quantum field theories on domain walls., Comment: Latex, 17 pages; v2:Important additions: (1) the validity of various approximations in the dual frame is discussed, (2) connection between the holographic energy/distance relation and the dual frame is made

We derive the Bekenstein-Hawking entropy formula for four and five dimensional non-supersymmetric black holes (which include the Schwarzchild ones) by counting microscopic states. This is achieved by first showing that these black holes are U-dual to the three-dimensional black hole of Banados-Teitelboim-Zanelli and then counting microscopic states of the latter following Carlip's approach. Higher than five dimensional black holes are also considered. We discuss the connection of our approach to the D-brane picture., Comment: Misprints corrected, discussion section expanded, some references added. Version to appear in Nucl. Phys. B. 29 pages, latex

We consider a series of duality transformations that leads to a constant shift in the harmonic functions appearing in the description of a configuration of branes. This way, for several intersections of branes, we can relate the original brane configuration which is asymptotically flat to a geometry of the type $adS_k \xx E^l \xx S^m$. The implications of our results for supersymmetry enhancement, M(atrix) theory at finite N, and for supergravity theories in diverse dimensions are discussed., Comment: 13 pages, Latex, references added

A new heterotic N=2 string with manifest target space supersymmetry is constructed by combining a conventional N=2 string in the right-moving sector and a Green-Schwarz-Berkovits type string in the left-moving sector. The corresponding sigma model is then obtained by turning on background fields for the massless excitations. We compute the beta functions and we partially check the OPE's of the superconformal algebra perturbatively in $\alpha'$, all in superspace. The resulting field equations describe N=1 self-dual supergravity., Comment: 32 pages, Latex, discussion in pages 10, 11 revised so that it is compatible with the complex structure chosen in Appendix A. Appendix A slightly expanded. Final version

We {\em derive} the exact configuration space path integral, together with the way how to evaluate it, from the Hamiltonian approach for any quantum mechanical system in flat spacetime whose Hamiltonian has at most two momentum operators. Starting from a given, covariant or non-covariant, Hamiltonian, we go from the time-discretized path integral to the continuum path integral by introducing Fourier modes. We prove that the limit $N \rightarrow \infty$ for the terms in the perturbation expansion (``Feynman graphs'') exists, by demonstrating that the series involved are uniformly convergent. {\em All} terms in the expansion of the exponent in $$ contribute to the propagator (even at order $\Delta t$!). However, in the time-discretized path integral the only effect of the terms with $\hat{H}^2$ and higher is to cancel terms which naively seem to vanish for $N \rightarrow \infty$, but, in fact, are nonvanishing. The final result is that the naive correspondence between the Hamiltonian and the Lagrangian approach is correct, after all. We explicitly work through the example of a point particle coupled to electromagnetism. We compute the propagator to order $(\Delta t)^2$ both with the Hamiltonian and the path integral approach and find agreement., Comment: 35 pages, ITP-SB-93-86