Nonabelian gauge field and dual description of fuzzy sphere

In matrix models, higher dimensional D-branes are obtained by imposing a noncommutative relation to coordinates of lower dimensional D-branes. On the other hand, a dual description of this noncommutative space is provided by higher dimensional D-branes with gauge fields. Fuzzy spheres can appear as a configuration of lower dimensional D-branes in a constant R-R field strength background. In this paper, we consider a dual description of higher dimensional fuzzy spheres by introducing nonabelian gauge fields on higher dimensional spherical D-branes. By using the Born-Infeld action, we show that a fuzzy $2k$-sphere and spherical D$2k$-branes with a nonabelian gauge field whose Chern character is nontrivial are the same objects when $n$ is large. We discuss a relationship between the noncommutative geometry and nonabelian gauge fields. Nonabelian gauge fields are represented by noncommutative matrices including the coordinate dependence. A similarity to the quantum Hall system is also studied.Comment: 28 page

On The Pomeron at Large 't Hooft Coupling

We begin the process of unitarizing the Pomeron at large 't Hooft coupling. We do so first in the conformal regime, which applies to good accuracy to a number of real and toy problems in QCD. We rewrite the conformal Pomeron in the $J$-plane and transverse position space, and then work out the eikonal approximation to multiple Pomeron exchange. This is done in the context of a more general treatment of the complex $J$-plane and the geometric consequences of conformal invariance. The methods required are direct generalizations of our previous work on single Pomeron exchange and on multiple graviton exchange in AdS space, and should form a starting point for other investigations. We consider unitarity and saturation in the conformal regime, noting elastic and absorptive effects, and exploring where different processes dominate. Our methods extend to confining theories and we briefly consider the Pomeron kernel in this context. Though there is important model dependence that requires detailed consideration, the eikonal approximation indicates that the Froissart bound is generically both satisfied and saturated.Comment: 63 pages, 7 figures; published version: references updated and several typos correcte

The baryon vertex with magnetic flux

In this letter we generalise the baryon vertex configuration of AdS/CFT by adding a suitable instantonic magnetic field on its worldvolume, dissolving D-string charge. A careful analysis of the configuration shows that there is an upper bound on the number of dissolved strings. This should be a manifestation of the stringy exclusion principle. We provide a microscopical description of this configuration in terms of a dielectric effect for the dissolved strings.Comment: 17 pages, 2 figures. V2: reference added. V3: version to appear in JHE

Glueballs of Super Yang-Mills from Wrapped Branes

In this paper we study qualitative features of glueballs in N=1 SYM for models of wrapped branes in IIA and IIB backgrounds. The scalar mode, 0++ is found to be a mixture of the dilaton and the internal part of the metric. We carry out the numerical study of the IIB background. The potential found exhibits a mass gap and produces a discrete spectrum without any cut-off. We propose a regularization procedure needed to make these states normalizable.Comment: 22 pages plus a appendixes, 2 figure

Relating branes and matrices

We construct a general map between a Dp-brane with magnetic flux and a matrix configuration of D0-branes, by showing how one can rewrite the boundary state of the Dp-brane in terms of its D0-brane constituents. This map gives a simple prescription for constructing the matrices of fuzzy spaces corresponding to branes of arbitrary shape and topology. Since we explicitly identify the D0-brane degrees of freedom on the brane, we also derive the D0-brane charge of the brane in a very direct way including the A-genus term. As a check on our formalism, we use our map to derive the abelian-Born-Infeld equations of motion from the action of the D0-brane matrices.Comment: 28 pages, Late

Towards a holographic dual of large-N_c QCD

We study N_f D6-brane probes in the supergravity background dual to N_c D4-branes compactified on a circle with supersymmetry-breaking boundary conditions. In the limit in which the resulting Kaluza--Klein modes decouple, the gauge theory reduces to non-supersymmetric, four-dimensional QCD with N_c colours and N_f << N_c flavours. As expected, this decoupling is not fully realised within the supergravity/Born--Infeld approximation. For N_f = 1 and massless quarks, m_q = 0, we exhibit spontaneous chiral symmetry breaking by a quark condensate, \neq 0, and find the associated massless `pion' in the spectrum. The latter becomes massive for m_q > 0, obeying the Gell-Mann--Oakes--Renner relation: M_pi^2= - m_q / \f_pi^2. In the case N_f > 1 we provide a holographic version of the Vafa--Witten theorem, which states that the U(N_f) flavour symmetry cannot be spontaneously broken. Further we find N_f^2 - 1 unexpectedly light pseudo-scalar mesons in the spectrum. We argue that these are not (pseudo) Goldstone bosons and speculate on the string mechanism responsible for their lightness. We then study the theory at finite temperature and exhibit a phase transition associated with a discontinuity in the chiral condensate. D6/anti-D6 pairs are also briefly discussed.Comment: 43 pages, LaTeX; v3: Scalar vs. pseudo-scalar nature of mesons clarified, references added. v4: Small change in Acknowledgment

Fluctuating Fuzzy Funnels

It is well known that a D-string ending on a D3, D5 or D7 brane is described in terms of a non-commutative fuzzy funnel geometry. In this article, we give a numerical study of the fluctuations about this leading geometry. This allows us to investigate issues related to the stability and moduli space of these solutions. We comment on the comparison to the linearized fluctuations in supergravity.Comment: 24 pages, 3 figures; v2 references added and correcte

Fuzzy Sphere Dynamics and Non-Abelian DBI in Curved Backgrounds

We consider the non-Abelian action for the dynamics of $N Dp'$-branes in the background of $M Dp$-branes, which parameterises a fuzzy sphere using the SU(2) algebra. We find that the curved background leads to collapsing solutions for the fuzzy sphere except when we have $D0$ branes in the $D6$ background, which is a realisation of the gravitational Myers effect. Furthermore we find the equations of motion in the Abelian and non-Abelian theories are identical in the large $N$ limit. By picking a specific ansatz we find that we can incorporate angular momentum into the action, although this imposes restriction upon the dimensionality of the background solutions. We also consider the case of non-Abelian non-BPS branes, and examine the resultant dynamics using world-volume symmetry transformations. We find that the fuzzy sphere always collapses but the solutions are sensitive to the combination of the two conserved charges and we can find expanding solutions with turning points. We go on to consider the coincident $NS$5-brane background, and again construct the non-Abelian theory for both BPS and non-BPS branes. In the latter case we must use symmetry arguments to find additional conserved charges on the world-volumes to solve the equations of motion. We find that in the Non-BPS case there is a turning solution for specific regions of the tachyon and radion fields. Finally we investigate the more general dynamics of fuzzy $\mathbb{S}^{2k}$ in the $Dp$-brane background, and find collapsing solutions in all cases.Comment: 49 pages, 3 figures, Latex; Version to appear in JHE

Notes on Giant Gravitons on PP-waves

We investigate the giant gravitons in the maximally supersymmetric IIB pp-wave from several viewpoints: (i) the dynamics of D3-branes, (ii) the world-sheet description and (iii) the correlation functions in the dual N=4 Yang-Mills theory. In particular, we derive the BPS equation of a D3-brane with magnetic flux, which is equivalent to multiple D-strings, and discuss the behavior of solutions in the presence of RR-flux. We find solutions which represent the excitations of the giant gravitons in that system.Comment: 25 pages, Latex, typos corrected, (minor) factors in eq.(2.11),(2.12),(2.16),(2.17) corrected, a footnote added, to appear in JHE

Squashed Giants: Bound States of Giant Gravitons

We consider giant gravitons in the maximally supersymmetric type IIB plane-wave, in the presence of a constant NSNS B-field background. We show that in response to the background B-field the giant graviton would take the shape of a deformed three-sphere, the size and shape of which depend on the B-field, and that the giant becomes classically unstable once the B-field is larger than a critical value B_{cr}. In particular, for the B-field which is (anti-)self-dual under the SO(4) isometry of the original giant S^3, the closed string metric is that of a round S^3, while the open string metric is a squashed three-sphere. The squashed giant can be interpreted as a bound state of a spherical three-brane and circular D-strings. We work out the spectrum of geometric fluctuations of the squashed giant and study its stability. We also comment on the gauge theory which lives on the brane (which is generically a noncommutative theory) and a possible dual gauge theory description of the deformed giant.Comment: Latex file, 32 pages, 6 .eps figures; v3: typos correcte