22,754 research outputs found
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
Dynamics of compact homogeneous universes
A complete description of dynamics of compact locally homogeneous universes
is given, which, in particular, includes explicit calculations of Teichm\"uller
deformations and careful counting of dynamical degrees of freedom. We regard
each of the universes as a simply connected four dimensional spacetime with
identifications by the action of a discrete subgroup of the isometry group. We
then reduce the identifications defined by the spacetime isometries to ones in
a homogeneous section, and find a condition that such spatial identifications
must satisfy. This is essential for explicit construction of compact
homogenoeus universes. Some examples are demonstrated for Bianchi II, VI,
VII, and I universal covers.Comment: 32 pages with 2 figures (LaTeX with epsf macro package
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
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