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

Poisson-Lie T-Duality beyond the classical level and the renormalization group

In order to study quantum aspects of \s-models related by Poisson--Lie T-duality, we construct three- and two-dimensional models that correspond, in one of the dual faces, to deformations of $S^3$ and $S^2$. Their classical canonical equivalence is demonstrated by means of a generating functional, which we explicitly compute. We examine how they behave under the renormalization group and show that dually related models have the same 1-loop beta functions for the coupling and deformation parameters. We find non-trivial fixed points in the ultraviolet, where the theories do not become asymptotically free. This suggests that the limit of Poisson--Lie T-duality to the usual Abelian and non-Abelian T-dualities does not exist quantum mechanically, although it does so classically.Comment: 13 pages, latex; v2: references and a note are added. Version to appear in Phys. Lett.

Coset Models and Differential Geometry

String propagation on a curved background defines an embedding problem of surfaces in differential geometry. Using this, we show that in a wide class of backgrounds the classical dynamics of the physical degrees of freedom of the string involves 2-dim sigma-models corresponding to coset conformal field theories.Comment: 7 pages, latex;Contribution to the proceedings of the Conference in Imperial College, London, 5-10 July 1996 and the e--proceedings of the Conference in Argonne, IL, 27 June - 12 July 199

Branes for Higgs phases and exact conformal field theories

We consider multicenter supergravity solutions corresponding to Higgs phases of supersymmetric Yang-Mills theories with Z_N symmetric vacua. In certain energy regimes, we find a description in terms of a generalized wormhole solution that corresponds to the SL(2,R)/U(1) \times SU(2)/U(1) exact conformal field theory. We show that U-dualities map these backgrounds to purely gravitational ones and comment on the relation to the black holes arising from intersecting D1 and D5 branes. We also discuss supersymmetric properties of the various solutions and the relation to 2-dim solitons, on flat space, of the reduced axion-dilaton-gravity equations. Finally, we address the problem of understanding other supergravity solutions from the multicenter ones. As prototype examples we use rotating D3 branes and NS5 and D5 branes associated to non-Abelian duals of 4-dim hyper-Kahler metrics with SO(3) isometry.Comment: 14 pages, latex; v2: a few typos corrected and a reference added. Version to appear in JHE

Supersymmetric phases of finite-temperature strings II

It was recently proposed that there exist stable supersymmetric phases for finite temperature superstings. This issue was investigated using an effective supergravity which takes into account massive winding modes. Such a theory admits BPS solutions that do not suffer from Hagedorn-type instabilities. We extend several aspects of this work. First we restrict to the real-field sector of the theory and allow, in general, for unequal right and left winding fields. Then, by further specializing to type-II theories (IIA, IIB and a self-dual hybrid) we construct the most general 1/2-BPS solution and reveal several new features arising in various consistent truncations. In the heterotic case we investigate the general properties of the solution which is presented in a closed form in the limit of infinitely large left-winding field.Comment: 19 pages, latex. v2: clarifying remarks are added and a few typos are corrected, version to appear in JHE

Integrable deformations of the Gk1×Gk2/Gk1+k2G_{k_1} \times G_{k_2}/G_{k_1+k_2} coset CFTs

We study the effective action for the integrable $\lambda$-deformation of the $G_{k_1} \times G_{k_2}/G_{k_1+k_2}$ coset CFTs. For unequal levels theses models do not fall into the general discussion of $\lambda$-deformations of CFTs corresponding to symmetric spaces and have many attractive features. We show that the perturbation is driven by parafermion bilinears and we revisit the derivation of their algebra. We uncover a non-trivial symmetry of these models parametric space, which has not encountered before in the literature. Using field theoretical methods and the effective action we compute the exact in the deformation parameter $\beta$-function and explicitly demonstrate the existence of a fixed point in the IR corresponding to the $G_{k_1-k_2} \times G_{k_2}/G_{k_1}$ coset CFTs. The same result is verified using gravitational methods for $G=SU(2)$. We examine various limiting cases previously considered in the literature and found agreement.Comment: 1+23 pages, Latex; v2: NPB version; v3: Correcting a typo in Eqs. (2.21), (2.22

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