Effective SO Superpotential for N=1 Theory with N_f Fundamental Matter

Motivated by the duality conjecture of Dijkgraaf and Vafa between supersymmetric gauge theories and matrix models, we derive the effective superpotential of N=1 supersymmetric gauge theory with gauge group SO(N_c) and arbitrary tree level polynomial superpotential of one chiral superfield in the adjoint representation and N_f fundamental matter multiplets. For a special point in the classical vacuum where the gauge group is unbroken, we show that the effective superpotential matches with that obtained from the geometric engineering approach.Comment: LaTeX, 1+19 pages, To appear in Nucl.Phys.

U(N) Framed Links, Three-Manifold Invariants, and Topological Strings

Three-manifolds can be obtained through surgery of framed links in $S^3$. We study the meaning of surgery procedures in the context of topological strings. We obtain U(N) three-manifold invariants from U(N) framed link invariants in Chern-Simons theory on $S^3$. These three-manifold invariants are proportional to the trivial connection contribution to the Chern-Simons partition function on the respective three-manifolds. Using the topological string duality conjecture, we show that the large $N$ expansion of U(N) Chern-Simons free energies on three-manifolds, obtained from some class of framed links, have a closed string expansion. These expansions resemble the closed string $A$-model partition functions on Calabi-Yau manifolds with one Kahler parameter. We also determine Gopakumar-Vafa integer coefficients and Gromov-Witten rational coefficients corresponding to Chern-Simons free energies on some three-manifolds.Comment: Some clarifications added. Final version to appear in NP

Composite Representation Invariants and Unoriented Topological String Amplitudes

Sinha and Vafa \cite {sinha} had conjectured that the $SO$ Chern-Simons gauge theory on $S^3$ must be dual to the closed $A$-model topological string on the orientifold of a resolved conifold. Though the Chern-Simons free energy could be rewritten in terms of the topological string amplitudes providing evidence for the conjecture, we needed a novel idea in the context of Wilson loop observables to extract cross-cap $c=0,1,2$ topological amplitudes. Recent paper of Marino \cite{mar9} based on the work of Morton and Ryder\cite{mor} has clearly shown that the composite representation placed on the knots and links plays a crucial role to rewrite the topological string cross-cap $c=0$ amplitude. This enables extracting the unoriented cross-cap $c=2$ topological amplitude. In this paper, we have explicitly worked out the composite invariants for some framed knots and links carrying composite representations in $U(N)$ Chern-Simons theory. We have verified generalised Rudolph's theorem, which relates composite invariants to the invariants in $SO(N)$ Chern-Simons theory, and also verified Marino's conjectures on the integrality properties of the topological string amplitudes. For some framed knots and links, we have tabulated the BPS integer invariants for cross-cap $c=0$ and $c=2$ giving the open-string topological amplitude on the orientifold of the resolved conifold.Comment: 1+17 pages, condensed version of arXiv/1003.5282 to appear in Nucl. Phys.

MASS ATTENUATION COEFFICIENT AND ATOMIC CROSS SECTION OF GeO2 IN THE ENERGY RANGE 122-1330KeV

In the present investigation, we have determined here the mass attenuation coefficients (μm) of germanium oxide for energies of 122 -1330 keV. Photon energies are measured using the different radioactive sources Co57, Ba133, Cs137, Na22, Mn54 and Co60. In the current investigation to detect gamma rays NaI(Tl) scintillation detection system were used. The investigated attenuation coefficient values were then used to determine the important parameters i.e. total atomic cross sections (st) for germanium oxide. Graphically it is observed that the variations of μm and st with energy The values of μm, st, are higher at lower energies and they decrease sharply as energy increases. The XCOM data is used to calculate Theoretical values. We were observed that the Theoretical and experimental values are found to be in a good agreement (error < 3-4%)

String theory and the Kauffman polynomial

We propose a new, precise integrality conjecture for the colored Kauffman polynomial of knots and links inspired by large N dualities and the structure of topological string theory on orientifolds. According to this conjecture, the natural knot invariant in an unoriented theory involves both the colored Kauffman polynomial and the colored HOMFLY polynomial for composite representations, i.e. it involves the full HOMFLY skein of the annulus. The conjecture sheds new light on the relationship between the Kauffman and the HOMFLY polynomials, and it implies for example Rudolph's theorem. We provide various non-trivial tests of the conjecture and we sketch the string theory arguments that lead to it.Comment: 36 pages, many figures; references and examples added, typos corrected, final version to appear in CM

Genetic characterization of 2008 reassortant influenza A virus (H5N1), Thailand

In January and November 2008, outbreaks of avian influenza have been reported in 4 provinces of Thailand. Eight Influenza A H5N1 viruses were recovered from these 2008 AI outbreaks and comprehensively characterized and analyzed for nucleotide identity, genetic relatedness, virulence determinants, and possible sites of reassortment. The results show that the 2008 H5N1 viruses displayed genetic drift characteristics (less than 3% genetic differences), as commonly found in influenza A viruses. Based on phylogenetic analysis, clade 1 viruses in Thailand were divided into 3 distinct branches (subclades 1, 1.1 and 1.2). Six out of 8 H5N1 isolates have been identified as reassorted H5N1 viruses, while other isolates belong to an original H5N1 clade. These viruses have undergone inter-lineage reassortment between subclades 1.1 and 1.2 and thus represent new reassorted 2008 H5N1 viruses. The reassorted viruses have acquired gene segments from H5N1, subclade 1.1 (PA, HA, NP and M) and subclade 1.2 (PB2, PB1, NA and NS) in Thailand. Bootscan analysis of concatenated whole genome sequences of the 2008 H5N1 viruses supported the reassortment sites between subclade 1.1 and 1.2 viruses. Based on estimating of the time of the most recent common ancestors of the 2008 H5N1 viruses, the potential point of genetic reassortment of the viruses could be traced back to 2006. Genetic analysis of the 2008 H5N1 viruses has shown that most virulence determinants in all 8 genes of the viruses have remained unchanged. In summary, two predominant H5N1 lineages were circulating in 2008. The original CUK2-like lineage mainly circulated in central Thailand and the reassorted lineage (subclades 1.1 and 1.2) predominantly circulated in lower-north Thailand. To prevent new reassortment, emphasis should be put on prevention of H5N1 viruses circulating in high risk areas. In addition, surveillance and whole genome sequencing of H5N1 viruses should be routinely performed for monitoring the genetic drift of the virus and new reassorted strains, especially in light of potential reassortment between avian and mammalian H5N1 viruses

SO(N) Reformulated Link Invariants from Topological Strings

Large N duality conjecture between U(N) Chern-Simons gauge theory on S3 and A-model topological string theory on the resolved conifold was verified at the level of partition function and Wilson loop observables. As a consequence, the conjectured form for the expectation value of the topological operators in A-model string theory led to a reformulation of link invariants in U(N) Chern-Simons theory giving new polynomial invariants whose integer coefficients could be given a topological meaning. We show that the A-model topological operator involving SO(N) holonomy leads to a reformulation of link invariants in SO(N) Chern-Simons theory. Surprisingly, the SO(N) reformulated invariants also has a similar form with integer coefficients. The topological meaning of the integer coefficients needs to be explored from the duality conjecture relating SO(N) Chern-Simons theory to A-model closed string theory on orientifold of the resolved conifold background