Reverse geometric engineering of singularities

One can geometrically engineer supersymmetric field theories theories by placing D-branes at or near singularities. The opposite process is described, where one can reconstruct the singularities from quiver theories. The description is in terms of a noncommutative quiver algebra which is constructed from the quiver diagram and the superpotential. The center of this noncommutative algebra is a commutative algebra, which is the ring of holomorphic functions on a variety V. If certain algebraic conditions are met, then the reverse geometric engineering produces V as the geometry that D-branes probe. It is also argued that the identification of V is invariant under Seiberg dualities.Comment: 17 pages, Latex. v2: updates reference

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

D3-branes on partial resolutions of abelian quotient singularities of Calabi-Yau threefolds

We investigate field theories on the worldvolume of a D3-brane transverse to partial resolutions of a $\Z_3\times\Z_3$ Calabi-Yau threefold quotient singularity. We deduce the field content and lagrangian of such theories and present a systematic method for mapping the moment map levels characterizing the partial resolutions of the singularity to the Fayet-Iliopoulos parameters of the D-brane worldvolume theory. As opposed to the simpler cases studied before, we find a complex web of partial resolutions and associated field-theoretic Fayet-Iliopoulos deformations. The analysis is performed by toric methods, leading to a structure which can be efficiently described in the language of convex geometry. For the worldvolume theory, the analysis of the moduli space has an elegant description in terms of quivers. As a by-product, we present a systematic way of extracting the birational geometry of the classical moduli spaces, thus generalizing previous work on resolution of singularities by D-branes.Comment: 52 pages, 9 figure

The Runaway Quiver

We point out that some recently proposed string theory realizations of dynamical supersymmetry breaking actually do not break supersymmetry in the usual desired sense. Instead, there is a runaway potential, which slides down to a supersymmetric vacuum at infinite expectation values for some fields. The runaway direction is not on a separated branch; rather, it shows up as a"tadpole" everywhere on the moduli space of field expectation values.Comment: 12 pages, no figures. v2: reference chang

Duality cascades and duality walls

We recast the phenomenon of duality cascades in terms of the Cartan matrix associated to the quiver gauge theories appearing in the cascade. In this language, Seiberg dualities for the different gauge factors correspond to Weyl reflections. We argue that the UV behavior of different duality cascades depends markedly on whether the Cartan matrix is affine ADE or not. In particular, we find examples of duality cascades that can't be continued after a finite energy scale, reaching a "duality wall", in terminology due to M. Strassler. For these duality cascades, we suggest the existence of a UV completion in terms of a little string theory.Comment: harvmac, 24 pages, 4 figures. v2: references added. v3: reference adde

Quiver theories, soliton spectra and Picard-Lefschetz transformations

Quiver theories arising on D3-branes at orbifold and del Pezzo singularities are studied using mirror symmetry. We show that the quivers for the orbifold theories are given by the soliton spectrum of massive 2d N=2 theory with weighted projective spaces as target. For the theories obtained from the del Pezzo singularities we show that the geometry of the mirror manifold gives quiver theories related to each other by Picard-Lefschetz transformations, a subset of which are simple Seiberg duals. We also address how one indeed derives Seiberg duality on the matter content from such geometrical transitions and how one could go beyond and obtain certain ``fractional Seiberg duals.'' Moreover, from the mirror geometry for the del Pezzos arise certain Diophantine equations which classify all quivers related by Picard-Lefschetz. Some of these Diophantine equations can also be obtained from the classification results of Cecotti-Vafa for the 2d N=2 theories.Comment: 34 pages, 11 figure

The Generalized Green-Schwarz Mechanism for Type IIB Orientifolds with D3- and D7-Branes

In this paper, we work out in detail the tadpole cancellation conditions as well as the generalized Green-Schwarz mechanism for type IIB orientifold compactifications with D3- and D7-branes. We find that not only the well-known D3- and D7-tadpole conditions have to be satisfied, but in general also the vanishing of the induced D5-brane charges leads to a non-trivial constraint. In fact, for the case $h^{1,1}_{-} \neq 0$ the latter condition is important for the cancellation of chiral anomalies. We also extend our analysis by including D9- as well as D5-branes and determine the rules for computing the chiral spectrum of the combined system.Comment: 33+7 pages; 2 figures; v2: references added; v3: published versio

Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2d qYM theory

We study the WZW, Chern-Simons, and 2d qYM theories with gauge group U(N). The U(N) WZW model is only well-defined for odd level K, and this model is shown to exhibit level-rank duality in a much simpler form than that for SU(N). The U(N) Chern-Simons theory on Seifert manifolds exhibits a similar duality, distinct from the level-rank duality of SU(N) Chern-Simons theory on S^3. When q = e^{2 pi i/(N+K)}, the observables of the 2d U(N) qYM theory can be expressed as a sum over a finite subset of U(N) representations. When N and K are odd, the qYM theory exhibits N K duality, provided q = e^{2 pi i/(N+K)} and theta = 0 mod 2 pi /(N+K).Comment: 19 pages; v2: minor typo corrected, 1 paragraph added, published versio

D-brane Instantons on the T^6/Z_3 orientifold

We give a detailed microscopic derivation of gauge and stringy instanton generated superpotentials for gauge theories living on D3-branes at Z_3-orientifold singularities. Gauge instantons are generated by D(-1)-branes and lead to Affleck, Dine and Seiberg (ADS) like superpotentials in the effective N=1 gauge theories with three generations of bifundamental and anti/symmetric matter. Stringy instanton effects are generated by Euclidean ED3-branes wrapping four-cycles on T^6/\Z_3. They give rise to Majorana masses in one case and non-renormalizable superpotentials for the other cases. Finally we determine the conditions under which ADS like superpotentials are generated in N=1 gauge theories with adjoints, fundamentals, symmetric and antisymmetric chiral matter.Comment: 31 pages, no figure

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