On D0-branes in Gepner models

We show why and when D0-branes at the Gepner point of Calabi-Yau manifolds given as Fermat hypersurfaces exist.Comment: 22 pages, substantial improvements in sections 2 and 3, references added, version to be publishe

Drinfeld-Manin Instanton and Its Noncommutative Generalization

The Drinfeld-Manin construction of U(N) instanton is reformulated in the ADHM formulism, which gives explicit general solutions of the ADHM constraints for U(N) (N>=2k-1) k-instantons. For the N<2k-1 case, implicit results are given systematically as further constraints, which can be used to the collective coordinate integral. We find that this formulism can be easily generalized to the noncommutative case, where the explicit solutions are as well obtained.Comment: 17 pages, LaTeX, references added, mailing address added, clarifications adde

Stability and BPS branes

We define the concept of Pi-stability, a generalization of mu-stability of vector bundles, and argue that it characterizes N=1 supersymmetric brane configurations and BPS states in very general string theory compactifications with N=2 supersymmetry in four dimensions.Comment: harvmac, 18 p

Quantum many-body models with cold atoms coupled to photonic crystals

Using cold atoms to simulate strongly interacting quantum systems represents an exciting frontier of physics. However, as atoms are nominally neutral point particles, this limits the types of interactions that can be produced. We propose to use the powerful new platform of cold atoms trapped near nanophotonic systems to extend these limits, enabling a novel quantum material in which atomic spin degrees of freedom, motion, and photons strongly couple over long distances. In this system, an atom trapped near a photonic crystal seeds a localized, tunable cavity mode around the atomic position. We find that this effective cavity facilitates interactions with other atoms within the cavity length, in a way that can be made robust against realistic imperfections. Finally, we show that such phenomena should be accessible using one-dimensional photonic crystal waveguides in which coupling to atoms has already been experimentally demonstrated

A Point's Point of View of Stringy Geometry

The notion of a "point" is essential to describe the topology of spacetime. Despite this, a point probably does not play a particularly distinguished role in any intrinsic formulation of string theory. We discuss one way to try to determine the notion of a point from a worldsheet point of view. The derived category description of D-branes is the key tool. The case of a flop is analyzed and Pi-stability in this context is tied in to some ideas of Bridgeland. Monodromy associated to the flop is also computed via Pi-stability and shown to be consistent with previous conjectures.Comment: 15 pages, 3 figures, ref 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

World-sheet Instantons via the Myers Effect and N=1^* Quiver Superpotentials

In this note we explore the stringy interpretation of non-perturbative effects in N=1^* deformations of the A_{k-1} quiver models. For certain types of deformations we argue that the massive vacua are described by Nk fractional D3-branes at the orbifold polarizing into k concentric 5-brane spheres each carrying fractional brane charge. The polarization of the D3-branes induces a polarization of D-instantons into string world-sheets wrapped on the Myers spheres. We show that the superpotentials in these models are indeed generated by these world-sheet instantons. We point out that for certain parameter values the condensates yield the exact superpotential for a relevant deformation of the Klebanov-Witten conifold theory.Comment: 24 pages, JHEP, some small errors and typos correcte

Holomorphic potentials for graded D-branes

We discuss gauge-fixing, propagators and effective potentials for topological A-brane composites in Calabi-Yau compactifications. This allows for the construction of a holomorphic potential describing the low-energy dynamics of such systems, which generalizes the superpotentials known from the ungraded case. Upon using results of homotopy algebra, we show that the string field and low energy descriptions of the moduli space agree, and that the deformations of such backgrounds are described by a certain extended version of `off-shell Massey products' associated with flat graded superbundles. As examples, we consider a class of graded D-brane pairs of unit relative grade. Upon computing the holomorphic potential, we study their moduli space of composites. In particular, we give a general proof that such pairs can form acyclic condensates, and, for a particular case, show that another branch of their moduli space describes condensation of a two-form.Comment: 47 pages, 7 figure

String Spectrum of 1+1-Dimensional Large N QCD with Adjoint Matter

We propose gauging matrix models of string theory to eliminate unwanted non-singlet states. To this end we perform a discretised light-cone quantisation of large N gauge theory in 1+1 dimensions, with scalar or fermionic matter fields transforming in the adjoint representation of SU(N). The entire spectrum consists of bosonic and fermionic closed-string excitations, which are free as N tends to infinity. We analyze the general features of such bound states as a function of the cut-off and the gauge coupling, obtaining good convergence for the case of adjoint fermions. We discuss possible extensions of the model and the search for new non-critical string theories.Comment: 20 pages (7 figures available from authors as postscipt files), PUPT-134