Romesh K. Kaul

Logarithmic correction to the Bekenstein-Hawking entropy

The exact formula derived by us earlier for the entropy of a four dimensional nonrotating black hole within the quantum geometry formulation of the event horizon in terms of boundary states of a three dimensional Chern-Simons theory is reexamined for large horizon areas. In addition to the semiclassical Bekenstein-Hawking contribution proportional to the area obtained earlier, we find a contribution proportional to the logarithm of the area together with subleading corrections that constitute a series in inverse powers of the area.

Cancellation of quadratically divergent mass corrections in globally supersymmetric spontaneously broken gauge theories

The one-loop quadratically divergent mass corrections in globally supersymmetric gauge theories with spontaneously broken abelian and non-abelian gauge symmetry are studied. Quadratically divergent mass corrections are found to persist in an abelian model with an ABJ anomaly. However, additional supermultiplets necessary to cancel the ABJ anomaly, turn out to be sufficient to eliminate the quadratic divergences as well, rendering the theory natural. Quadratic divergences are shown to vanish also in the case of an anomaly free model with spontaneously broken non-abelian gauge symmetry.

Three-dimensional Chern-Simons theory as a theory of knots and links

Three dimensional SU(2) Chern-Simons theory has been studied as a topological field theory to provide a field theoretic description of knots and links in three dimensions. A systematic method has been developed to obtain the link-invariants within this field theoretic framework. The monodromy properties of the correlators of the associated Wess-Zumino SU(2)

Gauge Hierarchy in a Supersymmetric Model

_k

Quantum black hole entropy

conformal field theory on a two-dimensional sphere prove to be useful tools. The method is simple enough to yield a whole variety of new knot invariants of which the Jones polynomials are the simplest example.

Knot invariants from rational conformal field theories

In a globally supersymmetric gauge theory with two distinct mass scales, the possible limitation on the gauge hierarchy due to the structure of the loop-corrected Higgs potential is shown to be absent. Also it has been demonstrated that the supersymmetry forces the large corrections to the two-point Greens functions of the light fields from the quadratic divergences and the logarithmic divergences with large coefficients to be zeroseparately. This would, therefore, allow a gauge hierarchy as large as desired.

A New holographic entropy bound from quantum geometry

We derive an exact formula for the dimensionality of the Hilbert space of the boundary states of SU(2) Chern-Simons theory, which, according to the recent work of Ashtekar et al., leads to the Bekenstein-Hawking entropy of a four dimensional Schwarzschild black hole. Our result stems from the relation between the (boundary) Hilbert space of the Chern-Simons theory with the space of conformal blocks of the Wess-Zumino model on the boundary 2-sphere.

Three-dimensional Chern-Simons theory as a theory of knots and links: (II). Multicoloured links

Abstract A framework for studying knot and link invariants from any rational conformal field theory is developed. In particular, minimal models, superconformal models and WN models are studied. The invariants are related to the invariants obtained from the Wess-Zumino models associated with the coset representations of these models. Possible Chern-Simons representation of these models is also indicated. This generalises the earlier work on knot and link invariants from Chern-Simons theories.

Representations of composite braids and invariants for mutant knots and links in Chern-Simons field theories

A new entropy bound, tighter than the standard holographic bound due to Bekenstein, is derived for space-times with nonrotating isolated horizons from the quantum geometry approach, in which the horizon is described by the boundary degrees of freedom of a three dimensional Chern-Simons theory.

Chern-Simons Theory, Coloured-Oriented Braids and Link Invariants

A method for obtaining invariants associated with multi-coloured links as the expectation values of Wilson link operators with different representations on the component knots in a three-dimensional SU(2) Chern-Simons gauge theory is developed. Some explicit calculations of these link invariants have been presented. This generalises the earlier work where the same representation of SU(2) was placed on all the component knots of a link.