arXiv subjects

Romesh K. Kaul

Publications and source records attributed to Romesh K. Kaul.

At least 19 recordsLinked to original sources

arXiv2019

Bi-partite vertex model and multi-colored link invariants

Construction of representations of braid group generators from $N$-state vertex models provide an elegant route to study knot and link invariants. Using such a braid group representation, an algebraic formula for the link invariants was put forth when the same spin $(N-1)/2$ are placed on all the component knots. In this paper, we generalise the procedure to deduce representations of braiding generators from bi-partite vertex models. Such a representation allows the study of multi-colored link invariants where the component knots carry different spins. We propose a multi-colored link invariant formula in terms of braiding generators derived from $R$ matrices of bi-partite vertex models.

hep-th↗

arXiv2018

Matter coupling to degenerate spacetimes in first order gravity

We develop a systematic study of the equations of motion in the first order gravity with matter fields for degenerate metrics. Like the Hilbert-Palatini action functional for pure gravity, the action functionals for matter fields used are first order. These are defined for both invertible and non- invertible metrics. Description for invertible metrics is equivalent to second order gravity theory with matter. For degenerate metrics the theory describes a different phase. The analysis for tetrads with one zero eigen value in theory with scalar, Abelian vector gauge and fermion matter fields is presented in detail.

gr-qc↗

arXiv2016

New solutions in pure gravity with degenerate tetrads

In first order formulation of pure gravity, we find a new class of solutions to the equations of motion represented by degenerate four-geometries. These configurations are described by non- invertible tetrads with two zero eigenvalues and admit non-vanishing torsion. The homogeneous ones among these infinitely many degenerate solutions admit a geometric classification provided by the three fundamental geometries that a closed two-surface can accomodate, namely, E^2 , S^2 and H^2.

gr-qc↗

arXiv2016

Degenerate spacetimes in first order gravity

We present a systematic framework to obtain the most general solutions of the equations of motion in first order gravity theory with degenerate tetrads. There are many possible solutions. Generically, these exhibit non-vanishing torsion even in the absence of any matter coupling. These solutions are shown to contain a special set of eight configurations which are associated with the homogeneous model three-geometries of Thurston.

gr-qc↗

arXiv2015

Torsional instanton effects in quantum gravity

We show that, in the first order gravity theory coupled to axions, the instanton number of the Giddings-Strominger wormhole can be interpreted as the Nieh-Yan topological index. The axion charge of the baby universes is quantized in terms of the Nieh-Yan integers. Tunneling between universes of different Nieh-Yan charges implies a nonperturbative vacuum state. The associated topological vacuum angle can be identified with the Barbero-Immirzi parameter.

gr-qc↗

arXiv2012

Entropy of Quantum Black Holes

In the Loop Quantum Gravity, black holes (or even more general Isolated Horizons) are described by a SU(2) Chern-Simons theory. There is an equivalent formulation of the horizon degrees of freedom in terms of a U(1) gauge theory which is just a gauged fixed version of the SU(2) theory. These developments will be surveyed here. Quantum theory based on either formulation can be used to count the horizon micro-states associated with quantum geometry fluctuations and from this the micro-canonical entropy can be obtained. We shall review the computation in SU(2) formulation. Leading term in the entropy is proportional to horizon area with a coefficient depending on the Barbero-Immirzi parameter which is fixed by matching this result with the Bekenstein-Hawking formula. Remarkably there are corrections beyond the area term, the leading one is logarithm of the horizon area with a definite coefficient -3/2, a result which is more than a decade old now. How the same results are obtained in the equivalent U(1) framework will also be indicated. Over years, this entropy formula has also been arrived at from a variety of other perspectives. In particular, entropy of BTZ black holes in three dimensional gravity exhibits the same logarithmic correction. Even in the String Theory, many black hole models are known to possess such properties. This suggests a possible universal nature of this logarithmic correction.

gr-qc↗

arXiv2011

Group velocity of neutrino waves

We follow up on the analysis of Mecozzi and Bellini (arXiv:1110:1253v1) where they showed, in principle, the possibility of superluminal propagation of neutrinos, as indicated by the recent OPERA result. We refine the analysis by introducing wave packets for the superposition of energy eigenstates and discuss the implications of their results with realistic values for the mixing and mass parameters in a full three neutrino mixing scenario. Our analysis shows the possibility of superluminal propagation of neutrino flavour in a very narrow range of neutrino parameter space. Simultaneously this reduces the number of observable events drastically. Therefore, the OPERA result cannot be explained in this frame-work.

hep-ph↗

arXiv2011

Topological parameters in gravity

We present the Hamiltonian analysis of the theory of gravity based on a Lagrangian density containing Hilbert-Palatini term along with three topological densities, Nieh-Yan, Pontryagin and Euler. The addition of these topological terms modifies the symplectic structure non-trivially. The resulting canonical theory develops a dependence on three parameters which are coefficients of these terms. In the time gauge, we obtain a real SU (2) gauge theoretic description with a set of seven first class constraints corresponding to three SU (2) rotations, three spatial diffeomorphism and one to evolution in a timelike direction. Inverse of the coefficient of Nieh-Yan term, identified as Barbero-Immirzi parameter, acts as the coupling constant of the gauge theory.

gr-qc↗

arXiv2010

Schwarzschild horizon dynamics and SU(2) Chern-Simons theory

We discuss the effect of different choices in partial gauge fixing of bulk local Lorentz invariance, on the description of the horizon degrees of freedom of a Schwarzschild black hole as an SU(2) Chern-Simons theory with specific sources. A classically equivalent description in terms of an ISO(2) Chern-Simons theory is also discussed. Further, we demonstrate that both these descriptions can be partially gauge fixed to a horizon theory with U(1) local gauge invariance, with the solder form sources being subject to extra constraints in directions orthogonal to an internal vector field left invariant by U(1) transformations. Seemingly disparate approaches on characterization of the horizon theory for the Schwarzschild black hole (as well as spherical Isolated Horizons in general) are thus shown to be equivalent physically.

gr-qc↗

arXiv2009

Canonical supergravity with Barbero-Immirzi parameter

A canonical formulation of the N=1 supergravity theory containing the topological Nieh-Yan term in its Lagrangian density is developed. The constraints are analysed without choosing any gauge. In the time gauge, the theory is shown to be described in terms of real SU(2) variables.

hep-th↗

arXiv2009

Entropy of Isolated Horizons revisited

The decade-old formulation of the isolated horizon classically and within loop quantum gravity, and the extraction of the microcanonical entropy of such a horizon from this formulation, is reviewed, in view of recent renewed interest. There are two main approaches to this problem: one employs an SU(2) Chern-Simons theory describing the isolated horizon degrees of freedom, while the other uses a reduced U(1) Chern-Simons theory obtained from the SU(2) theory, with appropriate constraints imposed on the spectrum of boundary states `living' on the horizon. It is shown that both these ways lead to the same infinite series asymptotic in horizon area for the microcanonical entropy of an isolated horizon. The leading area term is followed by an unambiguous correction term logarithmic in area with a coefficient $-\frac32$, with subleading corrections dropping off as inverse powers of the area.

gr-qc↗

arXiv2008

Topological Interpretation of Barbero-Immirzi Parameter

We set up a canonical Hamiltonian formulation for a theory of gravity based on a Lagrangian density made up of the Hilbert-Palatini term and, instead of the Holst term, the Nieh-Yan topological density. The resulting set of constraints in the time gauge are shown to lead to a theory in terms of a real SU(2) connection which is exactly the same as that of Barbero and Immirzi with the coefficient of the Nieh-Yan term identified as the inverse of Barbero-Immirzi parameter. This provides a topological interpretation for this parameter. Matter coupling can then be introduced in the usual manner, {\em without} changing the universal topological Nieh-Yan term.

gr-qc↗

arXiv2008

Naturalness and Electro-weak Symmetry Breaking

The Principle of Naturalness of small parameters of a theory is reviewed. While quantum field theories constructed from gauge fields and fermions only are natural, those containing elementary scalar fields are not. In particular the Higgs boson mass in the Standard Model of electro-weak forces is not stable against radiative corrections. Two old canonical solutions of this problem are: (i) where the Higgs boson is a fermion-antifermion composite (technicolour solution) or otherwise (ii) we need supersymmetry to protect the mass of elementary Higgs boson from possible large radiative corrections. In recent years some other mechanisms for electroweak symmetry breaking have been under intense investigation. These include the little Higgs models and the gauge-Higgs unification models where the Higgs boson is the zero mode of the extra-dimensional component of a higher dimensional gauge field. Naturalness issues of such models are also briefly reviewed.

hep-ph↗

arXiv2007

Holst Actions for Supergravity Theories

Holst action containing Immirzi parameter for pure gravity is generalised to the supergravity theories. Supergravity equations of motion are not modified by such generalisations, thus preserving supersymmetry. Dependence on the Immirzi parameter does not emerge in the classical equations of motion. This is in contrast with the recent observation of Perez and Rovelli for gravity action containing original Holst term and a minimally coupled Dirac fermion where the classical equations of motion do develop a dependence on Immirzi parameter.

gr-qc↗

arXiv2006

Gauge Theory of Gravity and Supergravity

We present a formulation of gravity in terms of a theory based on complex SU(2) gauge fields with a general coordinate invariant action functional quadratic in the field strength. Self-duality or anti-self-duality of the field strength emerges as a constraint from the equations of motion of this theory. This in turn leads to Einstein gravity equations for a dilaton and an axion conformally coupled to gravity for the self-dual constraint. The analysis has also been extended to N=1 and 2 super Yang-Mills theory of complex SU(2) gauge fields. This leads, besides other equations of motion, to self-duality/anti-self-duality of generalized supercovariant field-strengths. The self-dual case is then shown to yield as its solutions $N = 1, 2$ supergravity equations respectively.

gr-qc↗

arXiv2003

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.

hep-th↗

arXiv2003

Black Hole Entropy from Spin One Punctures

Recent suggestion, that the emission of a quantum of energy corresponding to the asymptotic value of quasinormal modes of a Schwarzschild black hole should be associated with the loss of spin one punctures from the black hole horizon, fixes the Immirzi parameter to a definite value. We show that saturating the horizon with spin one punctures reproduces the earlier formula for the black hole entropy, including the $ln (area)$ correction with definite coefficient (- 3/2) for large area.

gr-qc↗

arXiv2000

Three-Manifold Invariants from Chern-Simons Field Theory with Arbitrary Semi-Simple Gauge Groups

Invariants for framed links in $S^3$ obtained from Chern-Simons gauge field theory based on an arbitrary gauge group (semi-simple) have been used to construct a three-manifold invariant. This is a generalization of a similar construction developed earlier for SU(2) Chern-Simons theory. The procedure exploits a theorem of Lickorish and Wallace and also those of Kirby, Fenn and Rourke which relate three-manifolds to surgeries on framed unoriented links. The invariant is an appropriate linear combination of framed link invariants which does not change under Kirby calculus. This combination does not see the relative orientation of the component knots. The invariant is related to the partition function of Chern-Simons theory. This thus provides an efficient method of evaluating the partition function for these field theories. As some examples, explicit computations of these manifold invariants for a few three-manifolds have been done.

hep-th↗