Cascading RG Flows from New Sasaki-Einstein Manifolds

In important recent developments, new Sasaki-Einstein spaces $Y^{p,q}$ and conformal gauge theories dual to $AdS_5\times Y^{p,q}$ have been constructed. We consider a stack of N D3-branes and M wrapped D5-branes at the apex of a cone over $Y^{p,q}$. Replacing the D-branes by their fluxes, we construct asymptotic solutions for all p and q in the form of warped products of the cone and $R^{3,1}$. We show that they describe cascading RG flows where N decreases logarithmically with the scale. The warp factor, which we determine explicitly, is a function of the radius of the cone and one of the coordinates on $Y^{p,q}$. We describe the RG cascades in the dual quiver gauge theories, and find an exact agreement between the supergravity and the field theory beta functions. We also discuss certain dibaryon operators and their dual wrapped D3-branes in the conformal case M=0.Comment: 22 pages, 6 figures; v2 minor corrections; v3 refs, orbifold discussion added; v4 more ref

PP Wave Limit and Enhanced Supersymmetry in Gauge Theories

We observe that the pp wave limit of $AdS_5\times M^5$ compactifications of type IIB string theory is universal, and maximally supersymmetric, as long as $M^5$ is smooth and preserves some supersymmetry. We investigate a specific case, $M^5=T^{1,1}$. The dual ${\cal N}=1$ SCFT, describing D3-branes at a conifold singularity, has operators that we identify with the oscillators of the light-cone string in the universal pp-wave background. The correspondence is remarkable in that it relies on the exact spectrum of anomalous dimensions in this CFT, along with the existence of certain exceptional series of operators whose dimensions are protected only in the limit of large `t Hooft coupling. We also briefly examine the singular case $M^5=S^5/Z_2$, for which the pp wave background becomes a $Z_2$ orbifold of the maximally supersymmetric background by reflection of 4 transverse coordinates. We find operators in the corresponding ${\cal N}=2$ SCFT with the right properties to describe both the untwisted and the twisted sectors of the closed string.Comment: 15 pages, LaTeX; v2: added more detail to a derivation, and a preprint number; v3: minor corrections, some remarks and references adde

Impact of analytic provenance in genome analysis

Many computational methods are available for assembly and annotation of newly sequenced microbial genomes. However, when new genomes are reported in the literature, there is frequently very little critical analysis of choices made during the sequence assembly and gene annotation stages. These choices have a direct impact on the biologically relevant products of a genomic analysis - for instance identification of common and differentiating regions among genomes in a comparison, or identification of enriched gene functional categories in a specific strain. Here, we examine the outcomes of different assembly and analysis steps in typical workflows in a comparison among strains of Vibrio vulnificus

Supersymmetry Breaking from a Calabi-Yau Singularity

We conjecture a geometric criterion for determining whether supersymmetry is spontaneously broken in certain string backgrounds. These backgrounds contain wrapped branes at Calabi-Yau singularites with obstructions to deformation of the complex structure. We motivate our conjecture with a particular example: the $Y^{2,1}$ quiver gauge theory corresponding to a cone over the first del Pezzo surface, $dP_1$. This setup can be analyzed using ordinary supersymmetric field theory methods, where we find that gaugino condensation drives a deformation of the chiral ring which has no solutions. We expect this breaking to be a general feature of any theory of branes at a singularity with a smaller number of possible deformations than independent anomaly-free fractional branes.Comment: 32 pages, 6 figures, latex, v2: minor changes, refs adde

Structures in the Gauge/Gravity Duality Cascade

We study corrections to the anomalous mass dimension and their effects in the Seiberg duality cascade in the Klebanov-Strassler throat, where $\mathcal{N}=1$ supersymmetric $SU(N+M)\times SU(N)$ gauge theory with bifundamental chiral superfields and a quartic tree level superpotential in four dimensions is dual to type IIB string theory on $AdS_5 \times T^{1,1}$ background. Analyzing the renormalization group flow of the couplings on the gauge theory side, we propose specific corrections to the anomalous mass dimension. Applying gauge/gravity duality, we then show that the corrections reveal structures on the supergravity side with steps appearing in the running of the fluxes and the metric. The "charges" at the steps provide a gravitational source for Seiberg duality transformations. The finiteness of these corrections suggests that the theory flows to a baryonic branch rather than to a confining branch. The cosmological implication of the duality cascade and the gauge/gravity duality on the brane inflationary scenario and the cosmic microwave background radiation is pointed out.Comment: v3: 40 pages, minor changes and typos fixe

Dibaryon Spectroscopy

The AdS/CFT correspondence relates dibaryons in superconformal gauge theories to holomorphic curves in Kaehler-Einstein surfaces. The degree of the holomorphic curves is proportional to the gauge theory conformal dimension of the dibaryons. Moreover, the number of holomorphic curves should match, in an appropriately defined sense, the number of dibaryons. Using AdS/CFT backgrounds built from the generalized conifolds of Gubser, Shatashvili, and Nekrasov (1999), we show that the gauge theory prediction for the dimension of dibaryonic operators does indeed match the degree of the corresponding holomorphic curves. For AdS/CFT backgrounds built from cones over del Pezzo surfaces, we are able to match the degree of the curves to the conformal dimension of dibaryons for the n'th del Pezzo surface, n=1,2,...,6. Also, for the del Pezzos and the A_k type generalized conifolds, for the dibaryons of smallest conformal dimension, we are able to match the number of holomorphic curves with the number of possible dibaryon operators from gauge theory.Comment: 30 pages, 6 figures, corrected refs; v3 typos correcte

New checks and subtleties for AdS/CFT and a-maximization

We provide a cross-check of AdS/CFT and a-charge maximization for a four dimensional $N$=1 SCFT with irrational R-charges. The gauge theory is the low energy effective theory of N D3-branes at the tip of the complex cone over the first del Pezzo surface. By carefully taking into account the subtle issue of flavor symmetry breaking at the fixed point, we show, using a-maximization, that this theory has in fact irrational central charge and R-charges. Our results perfectly match with those inherited from the recently discovered supergravity dual background. Along analogous lines, we make novel predictions for the still unknown AdS dual of the quiver theory for the second del Pezzo surface. This should flow to a SCFT with irrational charges, too. All of our results differ from previous findings in the literature and outline interesting subtleties in a-maximization and AdS/CFT techniques overlooked in the past.Comment: Latex, 16 pagex, 2 figures; v2, comments and a reference added; v3, typos correcte

Mirror Symmetry, Mirror Map and Applications to Calabi-Yau Hypersurfaces

Mirror Symmetry, Picard-Fuchs equations and instanton corrected Yukawa couplings are discussed within the framework of toric geometry. It allows to establish mirror symmetry of Calabi-Yau spaces for which the mirror manifold had been unavailable in previous constructions. Mirror maps and Yukawa couplings are explicitly given for several examples with two and three moduli.Comment: 59 pages. Some changes in the references, a few minor points have been clarifie

Obstructions to the Existence of Sasaki-Einstein Metrics

We describe two simple obstructions to the existence of Ricci-flat Kahler cone metrics on isolated Gorenstein singularities or, equivalently, to the existence of Sasaki-Einstein metrics on the links of these singularities. In particular, this also leads to new obstructions for Kahler-Einstein metrics on Fano orbifolds. We present several families of hypersurface singularities that are obstructed, including 3-fold and 4-fold singularities of ADE type that have been studied previously in the physics literature. We show that the AdS/CFT dual of one obstruction is that the R-charge of a gauge invariant chiral primary operator violates the unitarity bound.Comment: 35 pages, 1 figure; references and a footnote adde

Dibaryons from Exceptional Collections

We discuss aspects of the dictionary between brane configurations in del Pezzo geometries and dibaryons in the dual superconformal quiver gauge theories. The basis of fractional branes defining the quiver theory at the singularity has a K-theoretic dual exceptional collection of bundles which can be used to read off the spectrum of dibaryons in the weakly curved dual geometry. Our prescription identifies the R-charge R and all baryonic U(1) charges Q_I with divisors in the del Pezzo surface without any Weyl group ambiguity. As one application of the correspondence, we identify the cubic anomaly tr R Q_I Q_J as an intersection product for dibaryon charges in large-N superconformal gauge theories. Examples can be given for all del Pezzo surfaces using three- and four-block exceptional collections. Markov-type equations enforce consistency among anomaly equations for three-block collections.Comment: 47 pages, 11 figures, corrected ref