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Current Research |
Past Research
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Introduction to String Theory:
My principal research interests deal with the various modern aspects
of Quantum Field Theories, specifically String Theories and their
application to Quantum Gravity. String Theory is
a developing mathematical framework with the potential of unifying all the known fundamental forces in a
single theoretical structure. Construction of a consistent quantum theory of gravity has been a
major impediment to unification of the four basic forces into a single theoretical structure. Although the other fundamental forces admit of a quantum description, the gravitational force described by Einstein's General Theory of Relativity has
resisted all attempts at quantization forcing unification to remain an elusive dream. String Theory which describes the universe in terms of ultramicroscopic fundamental vibrating strings is a paradigm shift from the usual description of fundamental physics in terms of pointlike elementary particles arising as quantized excitations of relativistic quantum fields.
In String Theory the usual exprimentaly observed pointlike elementary particles and their associated quantum field theories arise as low energy effective descriptions of quantized transverse excitations of fundamental strings. A quantum framework for gravity arises naturaly in string theory as the spectrum of closed string excitations involve a spin two particle which is a typical gravitational field quanta called a graviton. Strings are conjectured to be of two types
open strings with endpoints and closed strings which are loops.
Whereas the open string excitation spectrum naturaly embodies a framework for describing the other forces and particles closed strings typicaly describes the gravitational field. A quantum description of gravity is appropriate only at ultramicroscopic length scales and consequently ultrahigh energies comparable to the big bang energies operable during the creation of the universe. This energy scale is called the Planck scale and the corresponding length scale is termed the Planck Length. Fundamental ultramicrscopic strings correspond to the Planck length.
Higher Dimensional Universe and Compactification:
Quantum string theories are however only consistent in higher dimensional space times with extra spatial dimensions over above the usual three. At low energies the extra dimensions are conjectured to be curled up into a compact space of ultrashort radius. Thus providing an effective four dimensional description of the universe at low energies. Thus in this scenario every point in the low energy four dimensional space-time involves a higher dimensional
compact space of ultrashort length scale. The size and shape of the compact internal space crucialy determines characteristics of the four dimensional low energy description. This naturaly entails a plethora of such low energy descriptions associated with such infinitude of admissible internal compact spaces. Moreover five apparently inequivalent consistent quantum String Theories seem to abound in the perturbative regime for low string interaction strengths.
Duality Symmetries and Dirichlet (D) Branes:
Post modern String Theory has seen the focus move to a non perturbative description valid for
strongly interacting strings. This was enabled through the discovery of the remarkable Duality Symmetries of String Theory in 1994 which showed that the five disparate string theories were
actualy interrelated. A striking consequence of these symmetries was that fundamental and collective excitations of string theories were just distinct perspectives of the same physical
theory and also different string theories could be related for different interaction strengths. These ideas received a considerable corroboration with the discovery of stringy collective excitations termed Dirichlet brane ( D-branes). These D-branes were objects extended in several directions and supported a supersymmetric gauge theory on their world volume and were sources for higher rank exotic gauge ( electric and magnetic like) fields which arise as excitations of fundamental strings. Following this line of study a conjectured fundamental theory in eleven dimensions could be envisaged such that the five consistent perturbative string theories and eleven dimensional supergravity ( gravity with suspersymmetry) arose in some limit. The full space of the M-theory ( Master Theory) as it was termed seemed to be much larger although
the exact degrees of freedom of M-theory are still to be clearly elucidated. It was only possible
to explore a restricted perspective of the degrees of freedom of this theory in some infinite momentum frame. In this framework M-theory reduced to the large N limit of a (0 + 1) dimensional supersymmetric SU(N) Matrix Quantum Mechanics. These Matrix Field Theories provided a remarkable
short distance non commutative description of space time geometries.
Black Hole Entropy and Space Time Holography:
Duality and D-branes led to one of the most exciting developments in post modern String Theory
which was a correct microscopic explanation of the Bekenstein-Hawking entropy of singular
gravitational field configurations which were called Black Holes. These objects were known to be
thermodynamic systems with a temperature and entropy. However a microscopic statistical basis
underlying this entropy seemed elusive.
This was an outstanding theoretical issue for two decades. String Theory described a class of stable Black Holes with zero temperature but a non-zero entropy as
suitable bound states of D-branes. The conformal field theory of these D-brane bound states
provided a clear resolution of the Black Hole entropy in terms of degeneracy of states. This led
to intense focus and excitement in studying Black Holes using String Theory. These ideas coupled
with the fact that the entropy of black holes was proportional to the area of their event horzion
inspired the idea of space-time holography. This idea like its optical counterpart proposed that
the dynamics of a theory of quantum gravity in a bulk space may be completely encoded into the
boundary of this region. The idea of holography was provided a concrete realization by the Maldacena conjecture which stated that StringTheory/M-Theory in a bulk space-time of constant
negative curvature with a Cosmological Constant ( Anti deSitter space-time) may be completely
encoded in a supersymmetric non abelian gauge field theory of point particles on the boundary of the AdS space-time in a certain limit. This was the first insight into the elusive relation between quantum gravity and quantum gauge theories and although much remains to be learnt the
gauge-gravity or the AdS-CFT correspondence has been one of the remarkable insights into the
future of fundamental physics.
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