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Matrix Theory
In the recent past we have described an Oscillating D-String
Configuration in the framework of the IIB Matrix Theories
(IKKT models). These preserve one quarter of the N=2 supersymmetry
and are BPS configurations. This automaticaly entails the realization
of a chiraly supersymmetric ( 8,0) U(1) gauge theory on the two
dimensional world volume of the Oscillating D-string. We further
established the quantum mechanical equivalence with the (8,8) gauge
theory of the static D-string through certain Bogoliubov
transformations. This shows that the Oscillating D-String is a
collective excitation of the static case.
Duality Symmetries
We have used the continuous version of the SL(2,R) S-duality as a
Solution Generating Transformation for Superstring backgrounds. In
this connection we obtained type IIB plane wave superstring backgrounds
with non trivial Ramond-Ramond gauge fields. Using a geometrical
analysis based on the tensorial form of the perturbative higher order
contributions to the equations of motion for the low energy effective
theory we showed that these backgrounds were perturbatively exact. This
was later extended to the type IIB anlogs of the Brinkmann metric using
a non-symmetric connection framework and it could be shown that these
too were perturbatively exact under certain restrictions.
Coset Conformal Field Theories, WZW models and Black Holes in String Theory
Classical string backgrounds have been constructed which posess an exact
description as Coset Conformal Field Theories obtained from
Chiral Gauged Wess-Zumino-Witten ( WZW) Models. In this context
we obtained one of the first examples of a string background with a
geometry of a four dimensional black membrane with torsion from an
SL(2,R) x R WZW model and various T dual versions. We also explored
the tagrget space structure of an asymmetricaly chiral gauged SL(2,R)
WZW model by gauging a compact and a non-compact subgroup from the
holomorphic and the antiholomorphic sectors. The resultant space time
geometry could be related to a three dimensional Black String
metric.
Conformal Field Theory and Topological Field Theory (Ph.D. Thesis)
My thesis work was concerned with the construction of a Global Operator Formalism
for Conformal Field Theories on a Compact Riemann Surfaceof arbitrary
genus using the Krichever-Novikov (KN) formalism. Utilizing the global
Fourier-Laurent bases for complex tensor fields on the compact Riemann surface
the BRST quantization of a closed superstring in a
curved background could
be established. This was subsequently extended to obtain the classical
constraint algebra of a Heterotic string in an arbitrary massless background.
The operator formalism obtained was applied to construct a Topological
Conformal Field Theory on a compact Riemann surface leading to the
discovery of a topological version of the KN algebra. This was later
extended to construct topological sueprconformal field Theories on
compact Riemann surfaces and led to a realization of the topological
super KN algebra.
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Research Interests |
Current Research
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