Quite a Character: The Spectrum of Yang-Mills on S^3

We introduce a simple method to extract the representation content of the spectrum of a system with SU(2) symmetry from its partition function. The method is easily generalized to systems with SO(2,4) symmetry, such as conformal field theories in four dimensions. As a specific application we obtain an explicit generating function for the representation content of free planar Yang-Mills theory on S^3. The extension to N = 4 super Yang-Mills is also discussed.Comment: Based on a Brown University undergraduate thesis, 12 page

Four dimensional Lie symmetry algebras and fourth order ordinary differential equations

Realizations of four dimensional Lie algebras as vector fields in the plane are explicitly constructed. Fourth order ordinary differential equations which admit such Lie symmetry algebras are derived. The route to their integration is described.Comment: 12 page

Mineralisation of surfactants using ultrasound and the Advanced Fenton Process

The destruction of the surfactants, sodium dodecylbenzene sulfonate (DBS) and dodecyl pyridinium chloride (DPC), using an advanced oxidation process is described. The use of zero valent iron (ZVI) and hydrogen peroxide at pH = 2.5 (the advanced Fenton process), with and without, the application of 20 kHz ultrasound leads to extensive mineralisation of both materials as determined by total organic carbon (TOC)measurements. For DBS, merely stirring with ZVI and H2O2 at 20°C leads to a 51% decrease in TOC, but using 20 kHz ultrasound at 40°C, maintaining the pH at 2.5 throughout and adding extra amounts of ZVI and H2O2 during the degradation, then the extent of mineralisation of DBS is substantially increased to 93%. A similar result is seen for DPC where virtually no degradation occurs at 20°C, but if extra amounts of both ZVI and hydrogen peroxide are introduced during the reaction at 40°C and the pH is maintained at 2.5, then an 87% mineralisation of DPC is obtained. The slow latent remediation of both surfactants and the mechanism of degradation are also discussed

SL(2,Z) Multiplets in N=4 SYM Theory

We discuss the action of SL(2,Z) on local operators in D=4, N=4 SYM theory in the superconformal phase. The modular property of the operator's scaling dimension determines whether the operator transforms as a singlet, or covariantly, as part of a finite or infinite dimensional multiplet under the SL(2,Z) action. As an example, we argue that operators in the Konishi multiplet transform as part of a (p,q) PSL(2,Z) multiplet. We also comment on the non-perturbative local operators dual to the Konishi multiplet.Comment: 14 pages, harvmac; v2: published version with minor change

Conformal Partial Wave Expansions for N=4 Chiral Four Point Functions

The conformal partial wave analysis of four point functions of half BPS operators belonging to the SU(4) [0,p,0] representation is undertaken for p=2,3,4. Using the results of N=4 superconformal Ward identities the contributions from protected short and semi-short multiplets are identified in terms of the free field theory. In the large N limit contributions corresponding to long multiplets with twist up to 2p-2 are absent. The anomalous dimensions for twist two singlet multiplets are found to order g^4 and agree with other perturbative calculations. Results for twist four and six are also found.Comment: 53 pages, uses harvmac, includes 1 figure, version 2 some corrections and minor extensions, version 3 some further corrections, version 4 as to be publishe

Glueball Scattering Amplitudes from Holography

Using techniques developed in a previous paper three-point functions in field theories described by holographic renormalization group flows are computed. We consider a system of one active scalar and one inert scalar coupled to gravity. For the GPPZ flow, their dual operators create states that are interpreted as glueballs of the N=1 SYM theory, which lies at the infrared end of the renormalization group flow. The scattering amplitudes for three-glueball processes are calculated providing precise predictions for glueball decays in N=1 SYM theory. Numerical results for low-lying glueballs are included.Comment: 34 pages v2: comments on local terms and references added, v3: version published in JHE