New results on superconformal quivers

All superconformal quivers are shown to satisfy the relation c = a and are thus good candidates for being the field theory living on D3 branes probing CY singularities. We systematically study 3 block and 4 block chiral quivers which admit a superconformal fixed point of the RG equation. Most of these theories are known to arise as living on D3 branes at a singular CY manifold, namely complex cones over del Pezzo surfaces. In the process we find a procedure of getting a new superconformal quiver from a known one. This procedure is termed "shrinking" and, in the 3 block case, leads to the discovery of two new models. Thus, the number of superconformal 3 block quivers is 16 rather than the previously known 14. We prove that this list exausts all the possibilities. We suggest that all rank 2 chiral quivers are either del Pezzo quivers or can be obtained by shrinking a del Pezzo quiver and verify this statement for all 4 block quivers, where a lot of "shrunk'' del Pezzo models exist.Comment: 51 pages, many figure

Gauge/Gravity Duality and Warped Resolved Conifold

We study supergravity backgrounds encoded through the gauge/string correspondence by the SU(N) \times SU(N) theory arising on N D3-branes on the conifold. As discussed in hep-th/9905104, the dynamics of this theory describes warped versions of both the singular and the resolved conifolds through different (symmetry breaking) vacua. We construct these supergravity solutions explicitly and match them with the gauge theory with different sets of vacuum expectation values of the bi-fundamental fields A_1, A_2, B_1, B_2. For the resolved conifold, we find a non-singular SU(2)\times U(1)\times U(1) symmetric warped solution produced by a stack of D3-branes localized at a point on the blown-up 2-sphere. It describes a smooth RG flow from AdS_5 \times T^{1,1} in the UV to AdS_5 \times S^5 in the IR, produced by giving a VEV to just one field, e.g. B_2. The presence of a condensate of baryonic operator det B_2 is confirmed using a Euclidean D3-brane wrapping a 4-cycle inside the resolved conifold. The Green's functions on the singular and resolved conifolds are central to our calculations and are discussed in some detail.Comment: 22 pages, 2 figures, v2 added note on wrapped euclidean D3 brane, other minor correction

A New Infinite Class of Quiver Gauge Theories

We construct a new infinite family of N=1 quiver gauge theories which can be Higgsed to the Y^{p,q} quiver gauge theories. The dual geometries are toric Calabi-Yau cones for which we give the toric data. We also discuss the action of Seiberg duality on these quivers, and explore the different Seiberg dual theories. We describe the relationship of these theories to five dimensional gauge theories on (p,q) 5-branes. Using the toric data, we specify some of the properties of the corresponding dual Sasaki-Einstein manifolds. These theories generically have algebraic R-charges which are not quadratic irrational numbers. The metrics for these manifolds still remain unknown.Comment: 29 pages, JHE

The Iliad’s big swoon: a case of innovation within the epic tradition

In book 5 of the Iliad Sarpedon suffers so greatly from a wound that his ‘‘ψυχή leaves him’. Rather than dying, however, Sarpedon lives to fight another day. This paper investigates the phrase τὸν δὲ λίπε ψυχή in extant archaic Greek poetry to gain a sense of its traditional referentiality and better assess the meaning of Sarpedon’s swoon. Finding that all other instances of the ψυχή leaving the body signify death, it suggests that the Iliad exploits a traditional unit of utterance to flag up the importance of Sarpedon to this version of the Troy story

The Volume of some Non-spherical Horizons and the AdS/CFT Correspondence

We calculate the volumes of a large class of Einstein manifolds, namely Sasaki-Einstein manifolds which are the bases of Ricci-flat affine cones described by polynomial embedding relations in C^n. These volumes are important because they allow us to extend and test the AdS/CFT correspondence. We use these volumes to extend the central charge calculation of Gubser (1998) to the generalized conifolds of Gubser, Shatashvili, and Nekrasov (1999). These volumes also allow one to quantize precisely the D-brane flux of the AdS supergravity solution. We end by demonstrating a relationship between the volumes of these Einstein spaces and the number of holomorphic polynomials (which correspond to chiral primary operators in the field theory dual) on the corresponding affine cone.Comment: 25 pp, LaTeX, 1 figure, v2: refs adde

Exceptional Collections and del Pezzo Gauge Theories

Stacks of D3-branes placed at the tip of a cone over a del Pezzo surface provide a way of geometrically engineering a small but rich class of gauge/gravity dualities. We develop tools for understanding the resulting quiver gauge theories using exceptional collections. We prove two important results for a general quiver gauge theory: 1) we show the ordering of the nodes can be determined up to cyclic permutation and 2) we derive a simple formula for the ranks of the gauge groups (at the conformal point) in terms of the numbers of bifundamentals. We also provide a detailed analysis of four node quivers, examining when precisely mutations of the exceptional collection are related to Seiberg duality.Comment: 26 pages, 1 figure; v2 footnote 2 amended; v3 ref adde

The Toric Phases of the Y^{p,q} Quivers

We construct all connected toric phases of the recently discovered $Y^{p,q}$ quivers and show their IR equivalence using Seiberg duality. We also compute the R and global U(1) charges for a generic toric phase of $Y^{p,q}$.Comment: 14 pages, 3 figure

Exceptional collections and D-branes probing toric singularities

We demonstrate that a strongly exceptional collection on a singular toric surface can be used to derive the gauge theory on a stack of D3-branes probing the Calabi-Yau singularity caused by the surface shrinking to zero size. A strongly exceptional collection, i.e., an ordered set of sheaves satisfying special mapping properties, gives a convenient basis of D-branes. We find such collections and analyze the gauge theories for weighted projective spaces, and many of the Y^{p,q} and L^{p,q,r} spaces. In particular, we prove the strong exceptionality for all p in the Y^{p,p-1} case, and similarly for the Y^{p,p-2r} case.Comment: 49 pages, 6 figures; v2 refs added; v3 published versio

String Tensions and Three Dimensional Confining Gauge Theories

In the context of gauge/gravity duality, we try to understand better the proposed duality between the fractional D2-brane supergravity solutions of (Nucl. Phys. B 606 (2001) 18, hep-th/0101096) and a confining 2+1 dimensional gauge theory. Based on the similarities between this fractional D2-brane solution and D3-brane supergravity solutions with more firmly established gauge theory duals, we conjecture that a confining q-string in the 2+1 dimensional gauge theory is dual to a wrapped D4-brane. In particular, the D4-brane looks like a string in the gauge theory directions but wraps a S**3 in S**4 in the transverse geometry. For one of the supergravity solutions, we find a near quadratic scaling law for the tension: $T \sim q (N-q)$. Based on the tension, we conjecture that the gauge theory dual is SU(N) far in the infrared. We also conjecture that a quadratic or near quadratic scaling is a generic feature of confining 2+1 dimensional SU(N) gauge theories.Comment: 23 pages, 2 figure

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