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P. Ramadevi

Publications and source records attributed to P. Ramadevi.

At least 55 records · Page 3Linked to original sources
arXiv2011

Inverse algorithm and M2-brane theories

Recent paper arXiv:1103.0553 studied the quiver gauge theories on coincident $M2$ branes on a singular toric Calabi-Yau 4-folds which are complex cone over toric Fano 3-folds. There are 18 toric Fano manifolds but only 14 toric Fano were obtained from the forward algorithm. We attempt to systematize the inverse algorithm which helps in obtaining quiver gauge theories on $M2$-branes from the toric data of the Calabi-Yau 4-folds. In particular, we obtain quiver gauge theories on coincident $M2$-branes corresponding to the remaining 4 toric Fano 3-folds. We observe that these quiver gauge theories cannot be given a dimer tiling presentation.

hep-th↗
arXiv2010

Composite Representation Invariants and Unoriented Topological String Amplitudes

Sinha and Vafa \cite {sinha} had conjectured that the $SO$ Chern-Simons gauge theory on $S^3$ must be dual to the closed $A$-model topological string on the orientifold of a resolved conifold. Though the Chern-Simons free energy could be rewritten in terms of the topological string amplitudes providing evidence for the conjecture, we needed a novel idea in the context of Wilson loop observables to extract cross-cap $c=0,1,2$ topological amplitudes. Recent paper of Marino \cite{mar9} based on the work of Morton and Ryder\cite{mor} has clearly shown that the composite representation placed on the knots and links plays a crucial role to rewrite the topological string cross-cap $c=0$ amplitude. This enables extracting the unoriented cross-cap $c=2$ topological amplitude. In this paper, we have explicitly worked out the composite invariants for some framed knots and links carrying composite representations in $U(N)$ Chern-Simons theory. We have verified generalised Rudolph's theorem, which relates composite invariants to the invariants in $SO(N)$ Chern-Simons theory, and also verified Marino's conjectures on the integrality properties of the topological string amplitudes. For some framed knots and links, we have tabulated the BPS integer invariants for cross-cap $c=0$ and $c=2$ giving the open-string topological amplitude on the orientifold of the resolved conifold.

hep-th↗
arXiv2010

Composite Invariants and Unoriented Topological String Amplitudes

Sinha and Vafa had conjectured that the $SO$ Chern-Simons gauge theory on $S^3$ must be dual to the closed $A$-model topological string on the orientifold of a resolved conifold. Though the Chern-Simons free energy could be rewritten in terms of the topological string amplitudes providing evidence for the conjecture, we needed a novel idea in the context of Wilson loop observables to extract cross-cap $c=0,1,2$ topological amplitudes. Recent paper of Marino based on the work of Morton and Ryder has clearly shown that the composite representation placed on the knots and links plays a crucial role to rewrite the topological string cross-cap $c=0$ amplitude. This enables extracting the unoriented cross-cap $c=2$ topological amplitude. In this paper, we have explicitly worked out the composite invariants for some framed knots and links carrying composite representations in U(N) Chern-Simons theory. We have verified generalised Rudolph's theorem, which relates composite invariants to the invariants in SO(N) Chern-Simons theory, and also verified Marino's conjectures on the integrality properties of the topological string amplitudes. For some framed knots and links, we have tabulated the BPS integer invariants for cross-cap $c=0$, $c=1$ and $c=2$ giving the open-string topological amplitude on the orientifold of the resolved conifold.

hep-th↗
arXiv2008

A Note on Dimer Models and D-brane Gauge Theories

The connection between quiver gauge theories and dimer models has been well studied. It is known that the matter fields of the quiver gauge theories can be represented using the perfect matchings of the corresponding dimer model.We conjecture that a subset of perfect matchings associated with an internal point in the toric diagram is sufficient to give information about the charge matrix of the quiver gauge theory. Further, we perform explicit computations on some aspects of partial resolutions of toric singularities using dimer models. We analyse these with graph theory techniques, using the perfect matchings of orbifolds of the form $\BC^3/Γ$, where the orbifolding group $Γ$ may be noncyclic. Using these, we study the construction of the superpotential of gauge theories living on D-branes which probe these singularities, including the case where one or more adjoint fields are present upon partial resolution. Applying a combination of open and closed string techniques to dimer models, we also study some aspects of their symmetries.

hep-th↗
arXiv2007

Effective SO Superpotential for N=1 Theory with N_f Fundamental Matter

Motivated by the duality conjecture of Dijkgraaf and Vafa between supersymmetric gauge theories and matrix models, we derive the effective superpotential of N=1 supersymmetric gauge theory with gauge group SO(N_c) and arbitrary tree level polynomial superpotential of one chiral superfield in the adjoint representation and N_f fundamental matter multiplets. For a special point in the classical vacuum where the gauge group is unbroken, we show that the effective superpotential matches with that obtained from the geometric engineering approach.

hep-th↗
arXiv2006

Quantum Computation of Jones' Polynomials

It is a challenging problem to construct an efficient quantum algorithm which can compute the Jones' polynomial for any knot or link obtained from platting or capping of a $2n$-strand braid. We recapitulate the construction of braid-group representations from vertex models. We present the eigenbases and eigenvalues for the braiding generators and its usefulness in direct evaluation of Jones' polynomial. The calculation suggests that it is possible to associate a series of unitary operators for any braid word. Hence we propose a quantum algorithm using these unitary operators as quantum gates acting on a $2n$ qubit state. We show that the quantum computation gives Jones' polynomial for achiral knots and links.

quant-ph↗
arXiv2006

Exact Effective Superpotential for SO(N_c) Gauge Theory with $N_f$ Flavors

Motivated by the duality conjecture of Dijkgraaf and Vafa between supersymmetric gauge theories and matrix models, we derive the effective superpotential of N=1 supersymmetric gauge theory with gauge group SO(N_c) and arbitrary tree-level polynomial superpotential of one chiral superfield in the adjoint representation and $N_f$ fundamental matter multiplets.

hep-th↗
arXiv2005

Schwarz Type Topological Quantum Field Theories

Topological quantum field theories can be used to probe topological properties of low dimensional manifolds. A class of these theories known as Schwarz type theories, comprise of Chern-Simons theories and BF theories. In three dimensions both capture the properties of knots and links leading to invariants characterising them. These can also be used to construct three-manifold invariants. Three dimensional gravity is described by these field theories. BF theories exist also in higher dimensions. In four dimensions, these describe two-dimensional generalization of knots as well as Donaldson invariants.

hep-th↗
arXiv2005

SO(N) Reformulated Link Invariants from Topological Strings

Large N duality conjecture between U(N) Chern-Simons gauge theory on $S^3$ and A-model topological string theory on the resolved conifold was verified at the level of partition function and Wilson loop observables. As a consequence, the conjectured form for the expectation value of the topological operators in A-model string theory led to a reformulation of link invariants in U(N) Chern-Simons theory giving new polynomial invariants whose integer coefficients could be given a topological meaning. We show that the A-model topological operator involving SO(N) holonomy leads to a reformulation of link invariants in SO(N) Chern-Simons theory. Surprisingly, the SO(N) reformulated invariants also has a similar form with integer coefficients. The topological meaning of the integer coefficients needs to be explored from the duality conjecture relating SO(N) Chern-Simons theory to A-model closed string theory on orientifold of the resolved conifold background.

hep-th↗
arXiv2005

Spectrum of rotating black holes and its implications for Hawking radiation

The reduced phase space formalism for quantising black holes has recently been extended to find the area and angular momentum spectra of four dimensional Kerr black holes. We extend this further to rotating black holes in all spacetime dimensions and show that although as in four dimensions the spectrum is discrete, it is not equispaced in general. As a result, Hawking radiation spectra from these black holes are continuous, as opposed to the discrete spectrum predicted for four dimensional black holes.

hep-th↗
arXiv2004

Working Group Report: Neutrino and Astroparticle Physics

This is the report of neutrino and astroparticle physics working group at WHEPP-8. We present the discussions carried out during the workshop on selected topics in the above fields and also indicate progress made subsequently. The neutrino physics subgroup studied the possibilites of constraining neutrino masses, mixing and CPT violation in lepton sector from future experiments. Neutrino mass models in the context of abelian horizontal symmetries, warped extra dimensions and in presence of triplet Higgs were studied. Effect of threshold corrections on radiative magnification of mixing angles was investigated. The astroparticle physics subgroup focused on how various particle physics inputs affect the CMBR fluctuation spectrum, and on brane cosmology. This report also contains an introduction on how to use the publicly available code CMBFAST to calculate the CMBR fluctuations.

hep-ph↗
arXiv2003

U(N) Framed Links, Three-Manifold Invariants, and Topological Strings

Three-manifolds can be obtained through surgery of framed links in $S^3$. We study the meaning of surgery procedures in the context of topological strings. We obtain U(N) three-manifold invariants from U(N) framed link invariants in Chern-Simons theory on $S^3$. These three-manifold invariants are proportional to the trivial connection contribution to the Chern-Simons partition function on the respective three-manifolds. Using the topological string duality conjecture, we show that the large $N$ expansion of U(N) Chern-Simons free energies on three-manifolds, obtained from some class of framed links, have a closed string expansion. These expansions resemble the closed string $A$-model partition functions on Calabi-Yau manifolds with one Kahler parameter. We also determine Gopakumar-Vafa integer coefficients and Gromov-Witten rational coefficients corresponding to Chern-Simons free energies on some three-manifolds.

hep-th↗
arXiv2002

Quantum Mechanical Spectra of Charged Black Holes

It has been argued by several authors, using different formalisms, that the quantum mechanical spectrum of black hole horizon area is discrete and uniformly spaced. Recently it was shown that two such approaches, namely the one involving quantisation on a reduced phase space, and the algebraic approach of Bekenstein and Gour are equivalent for spherically symmetric, neutral black holes (hep-th/0202076). The observables of one can be mapped to those of the other. Here we extend that analysis to include charged black holes. Once again, we find that the ground state of the black hole is a Planck size remnant.

hep-th↗
arXiv2002

Black hole area quantization

It has been argued by several authors that the quantum mechanical spectrum of black hole horizon area must be discrete. This has been confirmed in different formalisms, using different approaches. Here we concentrate on two approaches, the one involving quantization on a reduced phase space of collective coordinates of a Black Hole and the algebraic approach of Bekenstein. We show that for non-rotating, neutral black holes in any spacetime dimension, the approaches are equivalent. We introduce a primary set of operators sufficient for expressing the dynamical variables of both, thus mapping the observables in the two formalisms onto each other. The mapping predicts a Planck size remnant for the black hole.

hep-th↗
arXiv2000

On Link Invariants and Topological String Amplitudes

We explicitly show that the new polynomial invariants for knots, upto nine crossings, agree with the Ooguri-Vafa conjecture relating Chern-Simons gauge theory to topological string theory on the resolution of the conifold.

hep-th↗
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↗
arXiv1999

Computation of Lickorish's Three Manifold Invariants using Chern-Simons Theory

It is well known that any three-manifold can be obtained by surgery on a framed link in $S^3$. Lickorish gave an elementary proof for the existence of the three-manifold invariants of Witten using a framed link description of the manifold and the formalisation of the bracket polynomial as the Temperley-Lieb Algebra. Kaul determined three-manifold invariants from link polynomials in SU(2) Chern-Simons theory. Lickorish's formula for the invariant involves computation of bracket polynomials of several cables of the link. We describe an easier way of obtaining the bracket polynomial of a cable using representation theory of composite braiding in SU(2) Chern-Simons theory. We prove that the cabling corresponds to taking tensor products of fundamental representations of SU(2). This enables us to verify that the two apparently distinct three-manifold invariants are equivalent for a specific relation of the polynomial variables.

hep-th↗