Matrix Models for Supersymmetric Chern-Simons Theories with an ADE Classification

We consider N=3 supersymmetric Chern-Simons (CS) theories that contain product U(N) gauge groups and bifundamental matter fields. Using the matrix model of Kapustin, Willett and Yaakov, we examine the Euclidean partition function of these theories on an S^3 in the large N limit. We show that the only such CS theories for which the long range forces between the eigenvalues cancel have quivers which are in one-to-one correspondence with the simply laced affine Dynkin diagrams. As the A_n series was studied in detail before, in this paper we compute the partition function for the D_4 quiver. The D_4 example gives further evidence for a conjecture that the saddle point eigenvalue distribution is determined by the distribution of gauge invariant chiral operators. We also see that the partition function is invariant under a generalized Seiberg duality for CS theories.Comment: 20 pages, 3 figures; v2 refs added; v3 conventions in figure 3 altered, version to appear in JHE

Supersymmetry Breaking in Chern-Simons-matter Theories

Some of supersymmetric Chern-Simons theories are known to exhibit supersymmetry breaking when the Chern-Simons level is less than a certain number. The mechanism of the supersymmetry breaking is, however, not clear from the field theory viewpoint. In this paper, we discuss vacuum states of ${\cal N}=2$ pure Chern-Simons theory and ${\cal N}=2$ Chern-Simons-matter theories of quiver type using related theories in which Chern-Simons terms are replaced with (anti-)fundamental chiral multiplets. In the latter theories, supersymmetry breaking can be shown to occur by examining that the vacuum energy is non-zero.Comment: 17 pages, 3 figures, v2) references adde

Page charge of D-branes and its behavior in topologically nontrivial B-fields

The RR Page charges for the D(2p+1)-branes with B-field in type IIB supergravity are constructed consistently from brane source currents. The resulting Page charges are B-independent in the nontrivial and intricate way. It is found that in topologically trivial B-field the Page charge is conserved, but in the topologically nontrivial B-field it is no longer to be conserved, instead there is a jump between two Page charges defined in each patch, and we interpret this jump as Hanany-Witten effect.Comment: 25 pages, 4 figures, typos corrected and reference adde

Hepatocelluar nodules in liver cirrhosis: hemodynamic evaluation (angiography-assisted CT) with special reference to multi-step hepatocarcinogenesis

To understand the hemodynamics of hepatocellular carcinoma (HCC) is important for the precise imaging diagnosis and treatment, because there is an intense correlation between their hemodynamics and pathophysiology. Angiogenesis such as sinusoidal capillarization and unpaired arteries shows gradual increase during multi-step hepatocarcinogenesis from high-grade dysplastic nodule to classic hypervascular HCC. In accordance with this angiogenesis, the intranodular portal supply is decreased, whereas the intranodular arterial supply is first decreased during the early stage of hepatocarcinogenesis and then increased in parallel with increasing grade of malignancy of the nodules. On the other hand, the main drainage vessels of hepatocellular nodules change from hepatic veins to hepatic sinusoids and then to portal veins during multi-step hepatocarcinogenesis, mainly due to disappearance of the hepatic veins from the nodules. Therefore, in early HCC, no perinodular corona enhancement is seen on portal to equilibrium phase CT, but it is definite in hypervascular classical HCC. Corona enhancement is thicker in encapsulated HCC and thin in HCC without pseudocapsule. To understand these hemodynamic changes during multi-step hepatocarcinogenesis is important, especially for early diagnosis and treatment of HCCs

The ABCDEF's of Matrix Models for Supersymmetric Chern-Simons Theories

We consider N = 3 supersymmetric Chern-Simons gauge theories with product unitary and orthosymplectic groups and bifundamental and fundamental fields. We study the partition functions on an S^3 by using the Kapustin-Willett-Yaakov matrix model. The saddlepoint equations in a large N limit lead to a constraint that the long range forces between the eigenvalues must cancel; the resulting quiver theories are of affine Dynkin type. We introduce a folding/unfolding trick which lets us, at the level of the large N matrix model, (i) map quivers with orthosymplectic groups to those with unitary groups, and (ii) obtain non-simply laced quivers from the corresponding simply laced quivers using a Z_2 outer automorphism. The brane configurations of the quivers are described in string theory and the folding/unfolding is interpreted as the addition/subtraction of orientifold and orbifold planes. We also relate the U(N) quiver theories to the affine ADE quiver matrix models with a Stieltjes-Wigert type potential, and derive the generalized Seiberg duality in 2 + 1 dimensions from Seiberg duality in 3 + 1 dimensions.Comment: 30 pages, 5 figure

Average Structures of a Single Knotted Ring Polymer

Two types of average structures of a single knotted ring polymer are studied by Brownian dynamics simulations. For a ring polymer with N segments, its structure is represented by a 3N -dimensional conformation vector consisting of the Cartesian coordinates of the segment positions relative to the center of mass of the ring polymer. The average structure is given by the average conformation vector, which is self-consistently defined as the average of the conformation vectors obtained from a simulation each of which is rotated to minimize its distance from the average conformation vector. From each conformation vector sampled in a simulation, 2N conformation vectors are generated by changing the numbering of the segments. Among the 2N conformation vectors, the one closest to the average conformation vector is used for one type of the average structure. The other type of the averages structure uses all the conformation vectors generated from those sampled in a simulation. In thecase of the former average structure, the knotted part of the average structure is delocalized for small N and becomes localized as N is increased. In the case of the latter average structure, the average structure changes from a double loop structure for small N to a single loop structure for large N, which indicates the localization-delocalization transition of the knotted part.Comment: 15 pages, 19 figures, uses jpsj2.cl

D-brane Charges in Gravitational Duals of 2+1 Dimensional Gauge Theories and Duality Cascades

We perform a systematic analysis of the D-brane charges associated with string theory realizations of d=3 gauge theories, focusing on the examples of the N=4 supersymmetric U(N)xU(N+M) Yang-Mills theory and the N=3 supersymmetric U(N)xU(N+M) Yang-Mills-Chern-Simons theory. We use both the brane construction of these theories and their dual string theory backgrounds in the supergravity approximation. In the N=4 case we generalize the previously known gravitational duals to arbitrary values of the gauge couplings, and present a precise mapping between the gravity and field theory parameters. In the N=3 case, which (for some values of N and M) flows to an N=6 supersymmetric Chern-Simons-matter theory in the IR, we argue that the careful analysis of the charges leads to a shift in the value of the B-field in the IR solution by 1/2, in units where its periodicity is one, compared to previous claims. We also suggest that the N=3 theories may exhibit, for some values of N and M, duality cascades similar to those of the Klebanov-Strassler theory.Comment: 47 pages, 9 figures; minor changes, references adde

Branes and fluxes in special holonomy manifolds and cascading field theories

We conduct a study of holographic RG flows whose UV is a theory in 2+1 dimensions decoupled from gravity, and the IR is the N=6,8 superconformal fixed point of ABJM. The solutions we consider are constructed by warping the M-theory background whose eight spatial dimensions are manifolds of special holonomies sp(1) times sp(1) and spin(7). Our main example for the spin(7) holonomy manifold is the A8 geometry originally constructed by Cvetic, Gibbons, Lu, and Pope. On the gravity side, our constructions generalize the earlier construction of RG flow where the UV was N=3 Yang-Mills-Chern-Simons matter system and are simpler in a number of ways. Through careful consideration of Page, Maxwell, and brane charges, we identify the discrete and continuous parameters characterizing each system. We then determine the range of the discrete data, corresponding to the flux/rank for which the supersymmetry is unbroken, and estimate the dynamical supersymmetry breaking scale as a function of these data. We then point out the similarity between the physics of supersymmetry breaking between our system and the system considered by Maldacena and Nastase. We also describe the condition for unbroken supersymmetry on class of construction based on a different class of spin(7) manifolds known as B8 spaces whose IR is different from that of ABJM and exhibit some interesting features.Comment: 51 pages, 12 figures. Update in quantization of G4 on B8 in equations (5.12) and (5.13

Notes on adding D6 branes wrapping RP3 in AdS4 x CP3

We deform the N=6 Chern Simons theory by adding extra matter hypermultiplets in a fundamental representation of one or both gauge groups. We compute the quantum corrected moduli space. We verify that the holographic dual of the modified theory consists of the usual AdS4 x CP3 background in presence of AdS4 filling D6 branes which wrap RP3 in CP3. We extend the correspondence to a similar modification of more general known N=3 dual pairsComment: 16 pages. v2: a reference, the name of a manifold, minor typos correcte