*Cemsinan Deliduman, a fifth year USC Physics Ph.D. student, submitted the following
article describing his research with Professor Itzhak Bars. Bars and Deliduman spent a
year at CERN during the 1996-97 academic year. Deliduman plans to finish his Ph.D.
this summer, 1999.*

During my Ph.D. studies, I concentrated mainly in finding physical models which are defined

in higher dimensions containing multiple time-like coordinates and become the ordinary string

or particle theories upon fixing the extra gauge degrees of freedom. I was also interested in

WZW models on non-compact group manifolds, in particular on SL(2, R) manifold which is

AdS3.

Spacetimes with multiple time-like coordinates begin to be taken seriously after Vafa's

F-theory and Bars's S-theory proposals. In S-theory, even though one has multiple time-like

coordinates, there is actually only one "evolution parameter" (i.e. time). In the first two of my

published works, we described models that have Bars-Kounnas type supersymmetry algebra

and defined in spacetimes with multiple time-like coordinates. We obtained ordinary

superstring (IIA, IIB and heterotic) and superparticle actions from certain effective

descriptions of the models. In the later works, we showed that the formalism is actually more

powerful: In this formalism one has the freedom to choose the evolution parameter as any

linear or non-linear function of time- or space-like coordinates. The choice of the evolution

parameter is done as follows: One begins in (d, 2) dimensional theory and turns the Sp(2, R)

global symmetry of the phase space into a local symmetry of the theory. Sp(2, R) has three

local transformation parameters including t-reparametrizations. The choice of the evolution

parameter is actually a gauge choice in this Sp(2, R) gauge theory. After various gauge

choices one finds different physical systems that are "dual" to each other. These systems were

found to have amazing variety: Massless and massive relativistic particle, Hydrogen atom,

harmonic oscillator, particle in AdS spacetimes, spinning particles in various potentials, etc.

We also showed that the theory defined in (d, 2) dimensions is covariant. Therefore all the

mentioned systems above have SO(d, 2) conformal symmetry from the point of view of

(d -1, 1) dimensional physics.

I am continuing to work in this exciting area of research. Recently we supersymmetrized this

model and currently we are trying to find a formulation of the string theory in (d,2)

dimensions. This theory could have far reaching consequences: It could help us to construct a

covariant formulation of M(atrix) theory, to get better understanding of AdS/CFT

correspondence and the idea of holography.

I am also interested in the recently conjectured AdS/CFT correspondence. We constructed

a vertex operator in WZW model on SL(2, R) manifold (AdS3) and showed that it has the

correct flat limit when one sends the level of the WZW model (or the radius of the AdS3) to

infinity. This vertex operator can help us to better understand the relation between AdS3 and

2-dimensional CFT on the boundary of AdS3. It can also simplify the calculation of the

correlation functions. The paper is currently under preparation.

I find the unified theories in higher dimensions and the dualities between them very interesting

and believe that they will help us to find non-perturbative answers to the questions we long

have had in high energy physics.

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