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The enhanced nonlinear optical response of a one-dimensional (1D) photonic crystal (PC) made from polymers and graphene composites is observed. The graphene PC was fabricated by spin-coating. It shows obvious bandgaps at two wavelengths in transmittance. Femtosecond Z-scan measurement at 515 nm and 1030 nm reveals a distinct enhancement in the effective nonlinear absorption coefficient Beff (and imaginary part of third-order dielectric susceptibility ImX(3)) for graphene nanoflakes embedded in the PC, when compared with the bulk graphene-polymer dispersion. The effect is studied in a wide range of laser intensities. The inclusion of graphene into a 1D-PC remarkably decreases the saturable absorption threshold and saturation intensity, providing a desired solution for an advanced all-optical laser mode-locking device., Comment: 10 pages, 2 figures, 1 table

We consider N=1 supersymmetric U(N), SO(N), and Sp(N) gauge theories, with two-index tensor matter and added tree-level superpotential, for general breaking patterns of the gauge group. By considering the string theory realization and geometric transitions, we clarify when glueball superfields should be included and extremized, or rather set to zero; this issue arises for unbroken group factors of low rank. The string theory results, which are equivalent to those of the matrix model, refer to a particular UV completion of the gauge theory, which could differ from conventional gauge theory results by residual instanton effects. Often, however, these effects exhibit miraculous cancellations, and the string theory or matrix model results end up agreeing with standard gauge theory. In particular, these string theory considerations explain and remove some apparent discrepancies between gauge theories and matrix models in the literature., Comment: 41 pages, 1 table, harvmac. v2: minor corrections and references added

In this dissertation we explore various aspects of the AdS/CFT correspondence. As string quantization on general backgrounds with fluxes is very difficult, one often uses the duality at the level of canonical fields of supergravity and the corresponding half-BPS operators in SYM, since they both belong to the shortest multiplets of the superconformal group SU(2,2|4). In addition to half-BPS operators, there are others with non-renormalization properties. One such class of operators is the quarter-BPS operators, which are dual to threshold bound states of elementary supergravity excitations. Their scaling dimension is also determined by their internal quantum numbers. Extended superspace methods make it simple to identify and remove descendant pieces from quarter-BPS candidates. We also compute three-point functions involving quarter-BPS operators, and explain how their non-renormalization translates into statements about the dual supergravity quantities. But we can go beyond discussing protected operators. The GS superstring on AdS(5) x S(5) can be quantized exactly in the limit where the AdS(5) radius R goes to infinity and the R-charge J scales like R^2. BMN states are then dual to single trace operators with certain phases inserted (BMN operators). BMN operators are another natural generalization of half-BPS operators. The perturbative expansion of scaling dimensions of BMN operators is in powers of gN/J^2. Moreover, one can do perturbation theory around the infinite R, J ~ R^2 limit. Both expansions have the same regime of validity in string theory and in SYM. We calculate the first 1/R^2 and 1/J corrections, and find complete agreement between the dual quantities., Comment: UCLA thesis, 169 pages, 11 figures, latex, UCLA thesis macro

We derive the Konishi anomaly equations for N=1 supersymmetric gauge theories based on the classical gauge groups with matter in two-index tensor and fundamental representations, thus extending the existing results for U(N). A general formula is obtained which expresses solutions to the Konishi anomaly equation in terms of solutions to the loop equations of the corresponding matrix model. This provides an alternative to the diagrammatic proof that the perturbative part of the glueball superpotential $W_{\rm eff}$ for these matter representations can be computed from matrix model integrals, and further shows that the two approaches always give the same result. The anomaly approach is found to be computationally more efficient in the cases we studied. Also, we show in the anomaly approach how theories with a traceless two-index tensor can be solved using an associated theory with a traceful tensor and appropriately chosen coupling constants., Comment: 27 pages, amstex, no figures. v2: references added. v3: minor corrections

We study the AdS/CFT correspondence for string states which flow into plane wave states in the Penrose limit. Leading finite radius corrections to the string spectrum are compared with scaling dimensions of finite R-charge BMN-like operators. We find agreement between string and gauge theory results., Comment: 35 pages, 13 eps figures v2: minor corrections, references added

We study some of the novel properties of conformal field theories with noncompact target spaces as applied to string theory. Standard CFT results get corrected by boundary terms in the target space in a way consistent with the expected spacetime physics. For instance, one-point functions of general operators on the sphere and boundary operators on the disk need not vanish; we show that they are instead equal to boundary terms in spacetime. By applying this result to vertex operators for spacetime gauge transformations with support at infinity, we derive formulas for conserved gauge charges in string theory. This approach provides a direct CFT definition of ADM energy-momentum in string theory., Comment: 29 pages, Harvmac

In a recent paper hep-th/0109064, quarter-BPS chiral primaries were constructed in the fully interacting four dimensional N=4 Super-Yang-Mills theory with gauge group SU(N). These operators are annihilated by four supercharges, and at order g^2 have protected scaling dimension and normalization. Here, we compute three-point functions involving these quarter-BPS operators along with half-BPS operators. The combinatorics of the problem is rather involved, and we consider the following special cases: (1) correlators < half half BPS > of two half-BPS primaries with an arbitrary chiral primary; (2) certain classes of < half quarter quarter > and < quarter quarter quarter > three-point functions; (3) three-point functions involving the Delta < 8 operators found in hep-th/0109064; (4) < half quarter quarter> correlators with the special quarter-BPS operator made of single and double trace operators only. The analysis in cases (1)-(3) is valid for general N, while (4) is a large N approximation. Order g^2 corrections to all three-point functions considered in this paper are found to vanish. In the AdS/CFT correspondence, quarter-BPS chiral primaries are dual to threshold bound states of elementary supergravity excitations. We present a supergravity discussion of two- and three-point correlators involving these bound states., Comment: 44 pages, Latex, eps figures, uses epsfig.sty; references added

Chiral primary operators annihilated by a quarter of the supercharges are constructed in the four dimensional N=4 Super-Yang-Mills theory with gauge group SU(N). These quarter-BPS operators share many non-renormalization properties with the previously studied half-BPS operators. However, they are much more involved, which renders their construction nontrivial in the fully interacting theory. In this paper we calculate order g^2 two-point functions of local, polynomial, scalar composite operators within a given representation of the SU(4) R-symmetry group. By studying these two-point functions, we identify the eigenstates of the dilatation operator, which turn out to be complicated mixtures of single and multiple trace operators. Given the elaborate combinatorics of this problem, we concentrate on two special cases. First, we present explicit computations for quarter-BPS operators with scaling dimension Delta < 8. In this case, the discussion applies to arbitrary N of the gauge group. Second, we carry out a leading plus subleading large N analysis for the particular class of operators built out of double and single trace operators only. The large N construction addresses quarter-BPS operators of general dimension., Comment: 38 pages, Latex, eps figures, uses epsfig.sty; references added

For quantum theories with a classical limit (which includes the large N limits of typical field theories), we derive a hierarchy of evolution equations for equal time correlators which systematically incorporate corrections to the limiting classical evolution. Explicit expressions are given for next-to-leading order, and next-to-next-to-leading order time evolution. The large N limit of N-component vector models, and the usual semiclassical limit of point particle quantum mechanics are used as concrete examples. Our formulation directly exploits the appropriate group structure which underlies the construction of suitable coherent states and generates the classical phase space. We discuss the growth of truncation error with time, and argue that truncations of the large-N evolution equations are generically expected to be useful only for times short compared to a ``decoherence'' time which scales like N^{1/2}., Comment: 36 pages, 2 eps figures, latex, uses revtex, epsfig, floats

A subset of 150 globular clusters in M87 has been selected on the basis of S/N ratio for abundance and age determinations from the sample of Paper I. Indices measuring the strength of the strongest spectral features were determined for the M87 GCs and from new data for twelve galactic GCs. Combining the new and existing data for the galactic GCs and comparing the $(U-R)$ colors and the line indices gives qualitative indications for the ages and abundances of the GCs. Quantitative results are obtained by applying the Worthey (1994) models for the integrated light of stellar systems of a single age, calibrated by observations of galactic GCs, to deduce abundances and ages for the objects in our sample. We find that the M87 GCs span a wide range in metallicity, from very metal poor to somewhat above solar metallicity. The mean [Fe/H] of -0.95 dex is higher than that of the galactic GC system, and there is a metal rich tail that reaches to higher [Fe/H] than one finds among the galactic GCs. The mean metallicity of the M87 GC system is about a factor of four lower than that of the M87 stellar halo at a fixed projected radius $R$. The metallicity inferred from the X-ray studies is similar to that of the M87 stellar halo, not to that of GCs. We infer the relative abundances of Na, Mg, and Fe in the M87 GCs from the strength of their spectral features. The behavior of these elements between the metal rich and metal poor M87 GCs is similar to that shown by the galactic GCs and by halo stars in the Galaxy. The pattern of chemical evolution in these disparate old stellar systems is indistinguishable. We obtain a median age for the M87 GC system of 13 Gyr, similar to that of the galactic GCs, with a small dispersion about this value., Comment: 56 pages with included postscript figures; added derived M87 GC metallicities to Table 2, a statistical analysis of possible bimodality, an appendix on the metallicity calibration of U-R and the Washington system, and other smaller changes. Accepted for publication in ApJ. (See paper for complete version of the Abstract.)

We present the results from a study of the dynamics of the system of globular clusters around M87. After eliminating foreground galactic stars and background galaxies, we end up with a sample of 205 bona fide M87 globular clusters for which we have radial velocities determined from multi-slit spectra taken with the LRIS on the Keck Telescope. We find that the mean radial velocity of the M87 globular clusters agrees well with that of M87 itself, and that the velocity histogram is well represented by a Gaussian distribution. We find evidence for rotation in the globular cluster system. We find that the observed velocity dispersion of the M87 globular cluster system increases with radius from 270 \kms~ at $r$ = 9 kpc to $\approx$400 \kms~ at $r$ = 40 kpc. The inferred mass-to-light ratio in solar units increases from 5 at $r$ = 9 kpc to $\approx$30 at $r$ = 40 kpc with $M(r) \sim r^{1.7}$. The long slit optical spectroscopy near the center of M87 and the recent analysis of the ROSAT X-ray data are in good agreement with this analysis near the nucleus and in the outer parts of M87 respectively., Comment: 29 pages, TeX, with 6 Figures. Accepted for publication in the ApJ