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We review a study of the semiclassical decay of macroscopic spinning strings in AdS_5 x S^5 as well as its dual gauge theory description. The conservation of the infinite tower of commuting charges in the semiclassical string sigma-model description of the process suggests that the decay channel of maximal probability should preserve integrability in the gauge theory., Comment: 8 pages, 6 figures; Contribution to the proceedings of the 37th International Symposium Ahrenshoop, Berlin, August 23-27, 2004

The gauge theory dual to the decay of an unstable D-particle in AdS is analysed in terms of coherent states. We discuss in detail how to count the number of particles in the decay product. We find, in agreement with the analysis in flat space, that the emission amplitude is suppressed as the mass of the radiated particles increases., Comment: 9 pages, 5 figures; Contribution to the proceedings of Strings '04, Paris. To appear in Comptes rendus - Physique

We study the effect of a magnetic field on N $$ \mathcal{N} $$ = 2 super-Yang-Mills on S 3 at strong coupling using the gauge/gravity correspondence. As in previous work that dealt with the theory in infinite volume, we find that increasing the magnetic field pushes the system into the confined phase. However, we in addition also find that, within the class of configurations with the same symmetry as those which describe the ground state at vanishing magnetic field, a mass gap appears in the spectrum. This suggests the existence of a new phase with so far unexplored symmetry structure. We provide suggestions for the physical properties of this phase.

We investigate N=2 super-Yang-Mills theory on a three sphere in the presence of an isospin chemical potential at strong coupling using the AdS/CFT correspondence. This system exhibits an instability for sufficiently large values of the chemical potential. In contrast to other related models, the first excitation to condense is not a vector meson but rather a scalar charged under the global SO(4) symmetry group. Furthermore, the spectrum of fluctuations exhibits an interesting cross-over behaviour as a function of the dimensionless temperature. We construct the new ground state of the non-linear theory., Comment: 29 pages

In holographic models of gauge theories with matter, there generically exists a first order phase transition in which mesons dissociate. We perform a careful analysis of the meson and quasi-particle spectra in the overheated resp. undercooled regimes close to the junction of the two phases. We show that all overheated finite meson masses eventually become infinitely degenerate, which implies that any connection to the quasi-particle spectrum is more subtle than previously suggested. For the Sakai-Sugimoto model no smooth connection between these spectra is possible., Comment: 23 pages, 21 figures

We analyze the effect of an isospin chemical potential \mu_I in the Sakai-Sugimoto model, which is the string dual of a confining gauge theory related to large N_c QCD, at temperatures below the chiral symmetry restoration temperature. For small chemical potentials we show that the results agree with expectations from the low-energy chiral Lagrangian, and the charged pion condenses. When the chemical potential reaches a critical value \mu_I = \mu_{crit} ~ 1.7 m_{\rho}, the lowest vector meson (the "rho meson") becomes massless, and it condenses (in addition to the pion condensate) for \mu_I > \mu_{crit}. This spontaneously breaks the rotational symmetry, as well as a residual U(1) flavor symmetry. We numerically construct the resulting new ground state for \mu_I > \mu_{crit}., Comment: 33 pages, 7 figures; v2: references added, minor corrections; v3: added footnote about other possible condensate

We discuss the Zamolodchikov-Faddeev algebra for the superstring sigma-model on AdS_5 x S^5. We find the canonical su(2|2)^2 invariant S-matrix satisfying the standard Yang-Baxter and crossing symmetry equations. Its near-plane-wave expansion matches exactly the leading order term recently obtained by the direct perturbative computation. We also show that the S-matrix obtained by Beisert in the gauge theory framework does not satisfy the standard Yang-Baxter equation, and, as a consequence, the corresponding ZF algebra is twisted. The S-matrices in gauge and string theories however are physically equivalent and related by a non-local transformation of the basis states which is explicitly constructed., 40 pages, v2: derivation of symmetries from the S-matrix and the Hopf algebra interpretation added, typos corrected, references added

Ideas about a duality between gauge fields and strings have been around for many decades. During the last ten years, these ideas have taken a much more concrete mathematical form. String descriptions of the strongly coupled dynamics of semi-realistic gauge theories, exhibiting confinement and chiral symmetry breaking, are now available. These provide remarkably simple ways to compute properties of the strongly coupled quark-gluon fluid phase, and also shed new light on various phenomenological models of hadron fragmentation. We present a review and highlight some exciting recent developments., Comment: Lectures presented by KP at the 45th Winter School on Theoretical Physics, February 2007, Schladming, Austria; v3: minor corrections, typos fixed, references added

We analyze the psu(2,2|4) supersymmetry algebra of a superstring propagating in the AdS_5 x S^5 background in the uniform light-cone gauge. We consider the off-shell theory by relaxing the level-matching condition and take the limit of infinite light-cone momentum, which decompactifies the string world-sheet. We focus on the psu(2|2)+psu(2|2) subalgebra which leaves the light-cone Hamiltonian invariant and show that it undergoes extension by a central element which is expressed in terms of the level-matching operator. This result is in agreement with the conjectured symmetry algebra of the dynamic S-matrix in the dual N=4 gauge theory., 30 pages, one figure

We use the uniform light-cone gauge to derive an exact gauge-fixed Lagrangian and light-cone Hamiltonian for the Green-Schwarz superstring in AdS5xS5. We then quantize the theory perturbatively in the near plane-wave limit, and compute the leading 1/J correction to a generic string state from the rank-1 subsectors. These investigations enable us to propose a new set of light-cone Bethe equations for the quantum string. The equations have a simple form and yield the correct spinning string and flat space limits. Finally, we clarify the notion of closed sectors in string theory by proving the existence of perturbative effective string Hamiltonians which are direct analogues of (all loop) dilatation operators in the dual N=4 gauge theory., Comment: 59 pages, no figures. v2: typos fixed. v3: more typos fixed, published version

Unstable D-particles in type-IIB string theory correspond to sphaleron solutions in the dual gauge theory. We construct an explicit time-dependent solution for the sphaleron decay on S^3 x R, as well as the coherent state corresponding to the decay product. We develop a method to count the number of bulk particles in the AdS/CFT setup. When applied to our coherent state, the naive number operator O^\dagger O is shown to be inappropriate, even in the large-N limit. The reason is that the final state consists of a large number of particles. By computing all probabilities for finding multi-particle states in the coherent state, we deduce the bulk particle content of the final state of the sphaleron decay. The qualitative features of this spectrum are compared with the results expected from the gravity side, and agreement is found., 17 pages, 5 figures; v2: minor additions to the text, typos fixed, references added, version to appear in Phys. Rev. D

We study the semiclassical decay of macroscopic spinning strings in AdS_5 x S^5 through spontaneous splitting of the folded string worldsheet. Based on similar considerations in flat space this decay channel is expected to dominate the full quantum computation. The outgoing strings are uniquely specified by an infinite set of conserved (local) charges with a regular expansion in inverse powers of the initial angular momentum. We compute these charges and determine functional relations between them. Finally, a preliminary discussion of the corresponding calculation in the non-planar sector of the dual gauge theory is presented., Comment: 22 pages, 5 figures; v2: typo corrected