Stability issues with baryons in AdS/CFT

We consider baryon vertices within the gauge/gravity correspondence for a class of curved backgrounds. The holographic description based on the N=4 SYM theory for SU(N) allows classical solutions representing bound states of k-quarks with k less than or equal to N. We construct the corresponding classical configurations and perform a stability analysis. We present the details for the theory at the conformal point and at finite temperature and show that there is a critical value of k, below which there is instability. This may also arise when the baryon reaches a critical size. We also extend our treatment to magnetically charged baryon vertices.Comment: v1: 22 Pages, 4 figures; v2: A reference corrected and a reference adde

Microscopic derivation of the Bekenstein-Hawking entropy formula for non-extremal black holes

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, late

Non-Abelian coset string backgrounds from asymptotic and initial data

We describe hierarchies of exact string backgrounds obtained as non-Abelian cosets of orthogonal groups and having a space--time realization in terms of gauged WZW models. For each member in these hierarchies, the target-space backgrounds are generated by the ``boundary'' backgrounds of the next member. We explicitly demonstrate that this property holds to all orders in $\alpha'$. It is a consequence of the existence of an integrable marginal operator build on, generically, non-Abelian parafermion bilinears. These are dressed with the dilaton supported by the extra radial dimension, whose asymptotic value defines the boundary. Depending on the hierarchy, this boundary can be time-like or space-like with, in the latter case, potential cosmological applications.Comment: 26 page

Toda fields of SO(3) hyper-Kahler metrics and free field realizations

The Eguchi-Hanson, Taub-NUT and Atiyah-Hitchin metrics are the only complete non-singular SO(3)-invariant hyper-Kahler metrics in four dimensions. The presence of a rotational SO(2) isometry allows for their unified treatment based on solutions of the 3-dim continual Toda equation. We determine the Toda potential in each case and examine the free field realization of the corresponding solutions, using infinite power series expansions. The Atiyah-Hitchin metric exhibits some unusual features attributed to topological properties of the group of area preserving diffeomorphisms. The construction of a descending series of SO(2)-invariant 4-dim regular hyper-Kahler metrics remains an interesting question.Comment: A few typos have been corrected; final versio

PP-waves from rotating and continuously distributed D3-branes

We study families of PP-wave solutions of type-IIB supergravity that have (light-cone) time dependent metrics and RR five-form fluxes. They arise as Penrose limits of supergravity solutions that correspond to rotating or continuous distributions of D3-branes. In general, the solutions preserve sixteen supersymmetries. On the dual field theory side these backgrounds describe the BMN limit of N=4 SYM when some scalars in the field theory have non-vanishing expectation values. We study the perturbative string spectrum and in several cases we are able to determine it exactly for the bosons as well as for the fermions. We find that there are special states for particular values of the light-cone constant P_+.Comment: 23 pages, Latex. v2: a few extra remarks and aesthetic changes, version to appear in JHE

String effects and field theory puzzles with supersymmetry

We investigate field theory puzzles occuring in the interplay between supersymmetry and duality in the presense of rotational isometries (also known as non-triholomorphic in hyper-Kahler geometry). We show that T-duality is always compatible with supersymmetry, provided that non-local world-sheet effects are properly taken into account. The underlying superconformal algebra remains the same, and T-duality simply relates local with non-local realizations of it. The non-local realizations have a natural description using parafermion variables of the corresponding conformal field theory. We also comment on the relevance of these ideas to a possible resolution of long standing problems in the quantum theory of black holes.Comment: 16 pages, Latex; contribution to the proceedings of the 5th Hellenic school and workshops on elementary particle physics, Corfu, 3-24 September 199

Generalized Duality and Singular Strings in Higher Dimensions

Deformations of gauged WZW actions are constructed for any pair $(G,H)$ by taking different embeddings of the gauge group $H\subset G$ as it acts on the left and right of the group element $g$. This leads to models that are dual to each other, generalizing the axial/vector duality of the two dimensional black hole manifold. The classical equations are completely solved for any pair $(G,H)$ and in particular for the anti de Sitter string based on $SO(d- 1,2)/SO(d-1,1)$ for which the normal modes are determined. Duality is demonstrated for models that have the same set of normal modes. Concentrating on $SO(2,2)/SO(2,1)$, the metric and dilaton fields of the $d=3$ string as well as some of the dual generalizations are obtained. They have curvature singularities and represent new singular solutions of Einstein's general relativity in three dimensions.Comment: 17 page

PP-waves and logarithmic conformal field theories

We provide a world-sheet interpretation to the plane wave limit of a large class of exact supergravity backgrounds in terms of logarithmic conformal field theories. As an illustrative example, we consider the two-dimensional conformal field theory of the coset model SU(2)_N/U(1) times a free time-like boson U(1)_{-N}, which admits a space-time interpretation as a three-dimensional plane wave solution by taking a correlated limit \`a la Penrose. We show that upon a contraction of Saletan type, in which the parafermions of the compact coset model are combined with the free time-like boson, one obtains a novel logarithmic conformal field theory with central charge c=3. Our results are motivated at the classical level using Poisson brackets of the fields, but they are also explicitly demonstrated at the quantum level using exact operator product expansions. We perform several computations in this theory including the evaluation of the four-point functions involving primary fields and their logarithmic partners, which are identified. We also employ the extended conformal symmetries of the model to construct an infinite number of logarithmic operators. This analysis can be easily generalized to other exact conformal field theory backgrounds with a plane wave limit in the target space.Comment: 22 pages, Latex.v2: typos corrected and section 5 expanded to include the free field realization.v3: a few refs. added, NPB versio

Wilson loops from multicentre and rotating branes, mass gaps and phase structure in gauge theories

Within the AdS/CFT correspondence we use multicentre D3-brane metrics to investigate Wilson loops and compute the associated heavy quark-antiquark potentials for the strongly coupled SU(N) super-Yang-Mills gauge theory, when the gauge symmetry is broken by the expectation values of the scalar fields. For the case of a uniform distribution of D3-branes over a disc, we find that there exists a maximum separation beyond which there is no force between the quark and the antiquark, i.e. the screening is complete. We associate this phenomenon with the possible existence of a mass gap in the strongly coupled gauge theory. In the finite-temperature case, when the corresponding supergravity solution is a rotating D3-brane solution, there is a class of potentials interpolating between a Coulombic and a confining behaviour. However, above a certain critical value of the mass parameter, the potentials exhibit a behaviour characteristic of statistical systems undergoing phase transitions. The physical path preserves the concavity property of the potential and minimizes the energy. Using the same rotating-brane solutions, we also compute spatial Wilson loops, associated with the quark-antiquark potential in models of three-dimensional gauge theories at zero temperature, with similar results.Comment: 27 pages, latex, 7 figures; v2: no substantial changes, version to appear in Adv. Theor. Math. Phy

Four Dimensional Plane Wave String Solutions with Coset CFT Description

We present a number of D=4 bosonic and heterotic string solutions with a covariantly constant null Killing vector which, like the solution of Nappi and Witten (NW), correspond to (gauged) WZW models and thus have a direct conformal field theory interpretation. A class of exact plane wave solutions (which includes the NW solution) is constructed by `boosting' the twisted products of two D=2 `cosmological' or `black-hole' cosets of SL(2,R) and SU(2). We describe a general limiting procedure by which one can construct new solutions with a covariantly constant null Killing vector starting with known string backgrounds. By applying a non-abelian duality transformation to the NW model we find a D=4 solution which has a covariantly constant null Killing vector but is not a plane wave. Higher dimensional bosonic backgrounds with isometries can be interpreted as lower dimensional backgrounds with extra gauge fields. Some of them are at the same time solutions of the heterotic string theory. In particular, the NW model represents also a D=3 `gravi-electromagnetic' heterotic string plane wave. In addition to the (1,1) supersymmetric embeddings of bosonic solutions we construct a number of non-trivial (1,0) supersymmetric exact D=4 heterotic string plane wave solutions some of which are related (by a boost and analytic continuation) to limiting cases of D=4 heterotic black hole solutions.Comment: 36 pages, harvmac, THU-94/08, Imperial/TP/93-94/2