Notes on Euclidean de Sitter space

We discuss issues relating to the topology of Euclidean de Sitter space. We show that in (2+1) dimensions, the Euclidean continuation of the`causal diamond', i.e the region of spacetime accessible to a timelike observer, is a three-hemisphere. However, when de Sitter entropy is computed in a `stretched horizon' picture, then we argue that the correct Euclidean topology is a solid torus. The solid torus shrinks and degenerates into a three-hemisphere as one goes from the `stretched horizon' to the horizon, giving the Euclidean continuation of the causal diamond. We finally comment on the generalisation of these results to higher dimensions.Comment: 10 pages, 2 figures, LaTeX, reference adde

Modelling quantum black holes

Física Teórica, Atómica y Óptic

Logarithmic Corrections to Black Hole Entropy and AdS/CFT Correspondence

We calculate the correction to the Bekenstein-Hawking entropy formula for five dimensional AdS-Schwarzschild black holes due to thermodynamic fluctuations. The result is then compared with the boundary gauge theory entropy corrections via AdS/CFT correspondence. We then further generalise our analysis for the rotating black hole in five dimensional AdS space.Comment: 7 pp. Accepted for publication in JHE

Non-commutative Duality: High Spin Fields and CP1CP^1 Model with Hopf Term

We show that the non-commutative $CP^1$ model coupled with Hopf term in 3 dimensions is equivalent to an interacting spin-$s$ theory where the spin $s$ of the dual theory is related to the coefficient of the Hopf term. We use the Seiberg-Witten map in studying this non-commutative duality equivalence, keeping terms to order $\theta$ and show that the spin of the dual theory do not get any $\theta$ dependant corrections. The map between current correlators show that topological index of the solitons in the non-commutative $CP^1$ model is unaffected by $\theta$ where as the Noether charge of the corresponding dual particle do get a $\theta$ dependence. We also show that this dual theory smoothly goes to the limit $\theta\to 0$ giving dual theory in the commutative plane.Comment: 13 pages, more references and a footnote are added. Version to appear in Phys. Lett.

On the Thermodynamic Geometry of BTZ Black Holes

We investigate the Ruppeiner geometry of the thermodynamic state space of a general class of BTZ black holes. It is shown that the thermodynamic geometry is flat for both the rotating BTZ and the BTZ Chern Simons black holes in the canonical ensemble. We further investigate the inclusion of thermal fluctuations to the canonical entropy of the BTZ Chern Simons black holes and show that the leading logartithmic correction due to Carlip is reproduced. We establish that the inclusion of thermal fluctuations induces a non zero scalar curvature to the thermodynamic geometry.Comment: 1+17 pages, LaTeX, 4 eps figure

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)$_k$ 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.Comment: 45 pages (without figures

Knot invariants from rational conformal field theories

A framework for studying knot and link invariants from any rational conformal field theory is developed. In particular, minimal models, superconformal models and $W_N$ 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.Comment: 18pages+6 figures (available on request through email

O(3) Sigma model with Hopf term on Fuzzy Sphere

We formulate the O(3) \s- model on fuzzy sphere and construct the Hopf term. We show that the field can be expanded in terms of the ladder operators of Holstein-Primakoff realisation of SU(2) algebra and the corresponding basis set can be classified into different topological sectors by the magnetic quantum numbers. We obtain topological charge $Q$ and show that $-2j\le Q \le2j$. We also construct BPS solitons. Using the covariantly conserved current, we construct the Hopf term and show that its value is $Q^2$ as in the commutative case. We also point out the interesting relation of physical space to deformed SU(2) algebra.Comment: 17 pages, Latex, typos corrected, added one reference, to appear in Nucl. Phys. B Reprt-no: IMSc/2002/11/3

Three-dimensional AdS gravity and extremal CFTs at c=8m

We note that Witten's proposed duality between extremal c=24k CFTs and three-dimensional anti-de Sitter gravity may possibly be extended to central charges that are multiples of 8, for which extremal self-dual CFTs are known to exist up to c=40. All CFTs of this type with central charge 24 or higher, provided that they exist, have the required mass gap and may serve as candidate duals to three-dimensional gravity at the corresponding values of the cosmological constant. Here, we compute the genus one partition function of these theories up to c=88, we give exact and approximate formulas for the degeneracies of states, and we determine the genus two partition functions of the theories up to c=40.Comment: 17 pages, harvmac; v2: references added, version accepted in JHE

Black Hole Entropy from a Highly Excited Elementary String

Suggested correspondence between a black hole and a highly excited elementary string is explored. Black hole entropy is calculated by computing the density of states for an open excited string. We identify the square root of oscillator number of the excited string with Rindler energy of black hole to obtain an entropy formula which, not only agrees at the leading order with the Bekenstein-Hawking entropy, but also reproduces the logarithmic correction obtained for black hole entropy in the quantum geometry framework. This provides an additional supporting evidence for correspondence between black holes and strings.Comment: revtex, 4 page