The boundary length and point spectrum enumeration of partial chord diagrams using cut and join recursion

We introduce the boundary length and point spectrum, as a joint generalization of the boundary length spectrum and boundary point spectrum in arXiv:1307.0967. We establish by cut-and-join methods that the number of partial chord diagrams filtered by the boundary length and point spectrum satisfies a recursion relation, which combined with an initial condition determines these numbers uniquely. This recursion relation is equivalent to a second order, non-linear, algebraic partial differential equation for the generating function of the numbers of partial chord diagrams filtered by the boundary length and point spectrum.Comment: 16 pages, 6 figure

Partial chord diagrams and matrix models

In this article, the enumeration of partial chord diagrams is discussed via matrix model techniques. In addition to the basic data such as the number of backbones and chords, we also consider the Euler characteristic, the backbone spectrum, the boundary point spectrum, and the boundary length spectrum. Furthermore, we consider the boundary length and point spectrum that unifies the last two types of spectra. We introduce matrix models that encode generating functions of partial chord diagrams filtered by each of these spectra. Using these matrix models, we derive partial differential equations - obtained independently by cut-and-join arguments in an earlier work - for the corresponding generating functions.Comment: 42 pages, 14 figure

Paper Session II-A - Space Station On-Orbit Solar Array Loads During Assembly

This paper is concerned with the closed-loop dynamic analysis of on-orbit maneuvers when the Space Shuttle is fully mated to the Space Station Freedom. A flexible model of the Space Station in the form of component modes is attached to a rigid orbiter and on-orbit maneuvers are performed using the Shuttle Primary Reaction Control System jets. The traditional approach for this type of problems is to perform an open-loop analysis to determine the attitude control system jet profiles based on rigid vehicles and apply the resulting profile to a flexible Space Station. In this study a closed-loop Structure/Control model was developed in the Dynamic Analysis and Design System (DADS) program and the solar array loads were determined for single axis maneuvers with various delay times between jet firings. It is shown that the Digital Auto Pilot jet selection is affected by Space Station flexibility. It is also shown that for obtaining solar array loads the effect of high frequency modes cannot be ignored

More on N=1 Matrix Model Curve for Arbitrary N

Using both the matrix model prescription and the strong-coupling approach, we describe the intersections of n=0 and n=1 non-degenerated branches for quartic (polynomial of adjoint matter) tree-level superpotential in N=1 supersymmetric SO(N)/USp(2N) gauge theories with massless flavors. We also apply the method to the degenerated branch. The general matrix model curve on the two cases we obtain is valid for arbitrary N and extends the previous work from strong-coupling approach. For SO(N) gauge theory with equal massive flavors, we also obtain the matrix model curve on the degenerated branch for arbitrary N. Finally we discuss on the intersections of n=0 and n=1 non-degenerated branches for equal massive flavors.Comment: 36pp; to appear in JHE

New nonlinear coherent states and some of their nonclassical properties

We construct a displacement operator type nonlinear coherent state and examine some of its properties. In particular it is shown that this nonlinear coherent state exhibits nonclassical properties like squeezing and sub-Poissonian behaviour.Comment: 3 eps figures. to appear in J.Opt

Note on Matrix Model with Massless Flavors

In this note, following the work of Seiberg in hep-th/0211234 for the conjecture between the field theory and matrix model in the case with massive fundamental flavors, we generalize it to the case with massless fundamental flavors. We show that with a little modifications, the analysis given by Seiberg can be used directly to the case of massless flavors. Furthermore, this new method explains the insertion of delta functions in the matrix model given by Demasure and Janik in hep-th/0211082.Comment: 10 pages. Type fixed. Remarks adde

Phases of N=1 USp(2N_c) Gauge Theories with Flavors

We studied the phase structures of N=1 supersymmetric USp(2N_c) gauge theory with N_f flavors in the fundamental representation as we deformed the N=2 supersymmetric QCD by adding the superpotential for adjoint chiral scalar field. We determined the most general factorization curves for various breaking patterns, for example, the two different breaking patterns of quartic superpotential. We observed all kinds of smooth transitions for quartic superpotential. Finally we discuss the intriguing role of USp(0) in the phase structure and the possible connection with observations made recently in hep-th/0304271 (Aganagic, Intriligator, Vafa and Warner) and in hep-th/0307063 (Cachazo).Comment: 61pp; Improved the presentation, references are added and to appear in PR

Adding flavor to Dijkgraaf-Vafa

We study matrix models related via the correspondence of Dijkgraaf and Vafa to supersymmetric gauge theories with matter in the fundamental. As in flavorless examples, measure factors of the matrix integral reproduce information about R-symmetry violation in the field theory. The models, studied previously as models of open strings, exhibit a large-M phase transition as the number of flavors is varied. This is the matrix model's manifestation of the end of asymptotic freedom. Using the relation to a quiver gauge theory, we extract the effective glueball superpotential and Seiberg-Witten curve from the matrix model.Comment: 15 pages, harvmac; improved analysis of the healing of cuts, added calculation of superpotential, improved referencing and notatio

Effective superpotential for U(N) with antisymmetric matter

We consider an N=1 U(N) gauge theory with matter in the antisymmetric representation and its conjugate, with a tree level superpotential containing at least quartic interactions for these fields. We obtain the effective glueball superpotential in the classically unbroken case, and show that it has a non-trivial N-dependence which does not factorize. We also recover additional contributions starting at order S^N from the dynamics of Sp(0) factors. This can also be understood by a precise map of this theory to an Sp(2N-2) gauge theory with antisymmetric matter.Comment: 22 pages. v2: comment (and a reference) added at the end of section 2 on low rank cases; minor typos corrected. v3: 2 footnotes added with additional clarifications; version to appear in journa

Exact Superpotentials for Theories with Flavors via a Matrix Integral

We extend and test the method of Dijkgraaf and Vafa for computing the superpotential of N=1 theories to include flavors in the fundamental representation of the gauge group. This amounts to computing the contribution to the superpotential from surfaces with one boundary in the matrix integral. We compute exactly the effective superpotential for the case of gauge group U(N_c), N_f massive flavor chiral multiplets in the fundamental and one massive chiral multiplet in the adjoint, together with a Yukawa coupling. We compare up to sixth-order with the result obtained by standard field theory techniques in the already non trivial case of N_c=2 and N_f=1. The agreement is perfect.Comment: 7 pages, v2: typos involving signs fixed; v3: version to appear in Phys.Rev.