The Bethe ansatz for superconformal Chern-Simons

We study the anomalous dimensions for scalar operators for a three-dimensional Chern-Simons theory recently proposed in arXiv:0806.1218. We show that the mixing matrix at two-loop order is that for an integrable Hamiltonian of an SU(4) spin chain with sites alternating between the fundamental and the anti-fundamental representations. We find a set of Bethe equations from which the anomalous dimensions can be determined and give a proposal for the Bethe equations to the full superconformal group of OSp(2,2|6).Comment: 22 pages, 9 figures; v2 Overall normalization of the Hamiltonian corrected and missing diagram contributing to two-site interactions included. Typos fixed; v3 Figure 8 corrected; v4 Misprints corrected; v5 Correct figures recovered. Published version; v6: misprints in (3.15), (3.16), (3.17) correcte

Seiberg-Witten Curve for the E-String Theory

We construct the Seiberg-Witten curve for the E-string theory in six-dimensions. The curve is expressed in terms of affine E_8 characters up to level 6 and is determined by using the mirror-type transformation so that it reproduces the number of holomorphic curves in the Calabi-Yau manifold and the amplitudes of N=4 U(n) Yang-Mills theory on 1/2 K3. We also show that our curve flows to known five- and four-dimensional Seiberg-Witten curves in suitable limits.Comment: 18 pages, 1 figure; appendix C adde

Seiberg-Witten prepotential for E-string theory and random partitions

We find a Nekrasov-type expression for the Seiberg-Witten prepotential for the six-dimensional non-critical E_8 string theory toroidally compactified down to four dimensions. The prepotential represents the BPS partition function of the E_8 strings wound around one of the circles of the toroidal compactification with general winding numbers and momenta. We show that our expression exhibits expected modular properties. In particular, we prove that it obeys the modular anomaly equation known to be satisfied by the prepotential.Comment: 14 page

Exceptional String: Instanton Expansions and Seiberg-Witten Curve

We investigate instanton expansions of partition functions of several toric E-string models using local mirror symmetry and elliptic modular forms. We also develop a method to obtain the Seiberg--Witten curve of E-string with arbitrary Wilson lines with the help of elliptic functions.Comment: 71 pages, three Wilson line

Seiberg-Witten prepotential for E-string theory and global symmetries

We obtain Nekrasov-type expressions for the Seiberg-Witten prepotential for the six-dimensional (1,0) supersymmetric E-string theory compactified on T^2 with nontrivial Wilson lines. We consider compactification with four general Wilson line parameters, which partially break the E_8 global symmetry. In particular, we investigate in detail the cases where the Lie algebra of the unbroken global symmetry is E_n + A_{8-n} with n=8,7,6,5 or D_8. All our Nekrasov-type expressions can be viewed as special cases of the elliptic analogue of the Nekrasov partition function for the SU(N) gauge theory with N_f=2N flavors. We also present a new expression for the Seiberg-Witten curve for the E-string theory with four Wilson line parameters, clarifying the connection between the E-string theory and the SU(2) Seiberg-Witten theory with N_f=4 flavors.Comment: 22 pages. v2: comments and a reference added, version to appear in JHE

Characterization of solar-grade silicon produced by the SiF4-Na process

A process was developed for producing low cost solar grade silicon by the reaction between SiF4 gas and sodium metal. The results of the characterization of the silicon are presented. These results include impurity levels, electronic properties of the silicon after crystal growth, and the performance of solar photovoltaic cells fabricated from wafers of the single crystals. The efficiency of the solar cells fabricated from semiconductor silicon and SiF4-Na silicon was the same

Dynamics with Infinitely Many Time Derivatives and Rolling Tachyons

Both in string field theory and in p-adic string theory the equations of motion involve infinite number of time derivatives. We argue that the initial value problem is qualitatively different from that obtained in the limit of many time derivatives in that the space of initial conditions becomes strongly constrained. We calculate the energy-momentum tensor and study in detail time dependent solutions representing tachyons rolling on the p-adic string theory potentials. For even potentials we find surprising small oscillations at the tachyon vacuum. These are not conventional physical states but rather anharmonic oscillations with a nontrivial frequency--amplitude relation. When the potentials are not even, small oscillatory solutions around the bottom must grow in amplitude without a bound. Open string field theory resembles this latter case, the tachyon rolls to the bottom and ever growing oscillations ensue. We discuss the significance of these results for the issues of emerging closed strings and tachyon matter.Comment: 46 pages, 14 figures, LaTeX. Replaced version: Minor typos corrected, some figures edited for clarit

Realization of Brane Descent Relations in Effective Theories

We examine Sen's descent relations among (non-)BPS D-branes by using low energy effective field theories of DpDpbar system. We find that the fluctuation around the kink solution reproduces the low energy matter content on a non-BPS D(p-1)-brane. The effective action for these fluctuation modes turns out to be a generalization of Minahan-Zwiebach model. In addition, it is shown that the fluctuations around the vortex solution consist of massless fields on a BPS D(p-2)-brane and they are subject to Dirac-Born-Infeld action. We find the universality that the above results do not refer to particular forms of the effective action.Comment: 24 pages, LaTeX, 1 eps figure; v2:minor correction

Antiferromagnetic Operators in N=4 Supersymmetric Yang-Mills Theory

The spectrum of operators in the su(2) sector of N=4 SYM is bounded because the number of operators is finite. According to the AdS/CFT correspondence, the string spectrum in this sector should be also bounded. In this paper the upper bound on the scaling dimension is calculated in the limit of the large R-charge using Bethe ansatz.Comment: 12 page