arXiv subjects

P. Ramadevi

Publications and source records attributed to P. Ramadevi.

At least 37 records · Page 2Linked to original sources

arXiv2018

Checks of integrality properties in topological strings

Tests of the integrality properties of a scalar operator in topological strings on a resolved conifold background or orientifold of conifold backgrounds have been performed for arborescent knots and some non-arborescent knots. The recent results on polynomials for those knots colored by SU(N) and SO(N) adjoint representations are useful to verify Marino's integrality conjecture up to two boxes in the Young diagram. In this paper, we review the salient aspects of the integrality properties and tabulate explicitly for an arborescent knot and a link. In our knotebook website, we have put these results for over 100 prime knots available in Rolfsen table and some links. The first application of the obtained results, an observation of the Gaussian distribution of the LMOV invariants is also reported.

hep-th↗

arXiv2017

Colored HOMFLY polynomials that distinguish mutant knots

We illustrate from the viewpoint of braiding operations on WZNW conformal blocks how colored HOMFLY polynomials with multiplicity structure can detect mutations. As an example, we explicitly evaluate the (2,1)-colored HOMFLY polynomials that distinguish a famous mutant pair, Kinoshita-Terasaka and Conway knot.

math.GT↗

arXiv2016

Knot Invariants and M-Theory I: Hitchin Equations, Chern-Simons Actions, and the Surface Operators

Recently Witten introduced a type IIB brane construction with certain boundary conditions to study knot invariants and Khovanov homology. The essential ingredients used in his work are the topologically twisted N = 4 Yang-Mills theory, localization equations and surface operators. In this paper we extend his construction in two possible ways. On one hand we show that a slight modification of Witten's brane construction could lead, using certain well defined duality transformations, to the model used by Ooguri-Vafa to study knot invariants using gravity duals. On the other hand, we argue that both these constructions, of Witten and of Ooguri-Vafa, lead to two different seven-dimensional manifolds in M-theory from where the topological theories may appear from certain twisting of the G-flux action. The non-abelian nature of the topological action may also be studied if we take the wrapped M2-brane states in the theory. We discuss explicit constructions of the seven-dimensional manifolds in M-theory, and show that both the localization equations and surface operators appear naturally from the Hamiltonian formalism of the theories. Knots and link invariants are then constructed using M2-brane states in both the models.

hep-th↗

arXiv2016

Time-dependence of the holographic spectral function: Diverse routes to thermalisation

We develop a new method for computing the holographic retarded propagator in generic (non-)equilibrium states using the state/geometry map. We check that our method reproduces the thermal spectral function given by the Son-Starinets prescription. The time-dependence of the spectral function of a relevant scalar operator is studied in a class of non-equilibrium states. The latter are represented by AdS-Vaidya geometries with an arbitrary parameter characterising the timescale for the dual state to transit from an initial thermal equilibrium to another due to a homogeneous quench. For long quench duration, the spectral function indeed follows the thermal form at the instantaneous effective temperature adiabatically, although with a slight initial time delay and a bit premature thermalisation. At shorter quench durations, several new non-adiabatic features appear: (i) time-dependence of the spectral function is seen much before than that in the effective temperature (advanced time-dependence), (ii) a big transfer of spectral weight to frequencies greater than the initial temperature occurs at an intermediate time (kink formation) and (iii) new peaks with decreasing amplitudes but in greater numbers appear even after the effective temperature has stabilised (persistent oscillations). We find four broad routes to thermalisation for lower values of spatial momenta. At higher values of spatial momenta, kink formations and persistent oscillations are suppressed, and thermalisation time decreases. The general thermalisation pattern is globally top-down, but a closer look reveals complexities.

hep-th↗

arXiv2016

Analytic corrections to AdS by scalar matter and curvature squared term

We revisit the background solution for scalar matter coupled higher derivative gravity originally reported in arXiv: 1409.8019[hep-th]. In this letter, we choose a convenient ansatz for metric which determines the first order perturbative corrections to scalar as well as geometry.

hep-th↗

arXiv2016

Tabulating knot polynomials for arborescent knots

Arborescent knots are the ones which can be represented in terms of double fat graphs or equivalently as tree Feynman diagrams. This is the class of knots for which the present knowledge is enough for lifting topological description to the level of effective analytical formulas. The paper describes the origin and structure of the new tables of colored knot polynomials, which will be posted at the dedicated site. Even if formal expressions are known in terms of modular transformation matrices, the computation in finite time requires additional ideas. We use the "family" approach, and apply it to arborescent knots in the Rolfsen table by developing a Feynman diagram technique associated with an auxiliary matrix model field theory. Gauge invariance in this theory helps to provide meaning to Racah matrices in the case of non-trivial multiplicities and explains the need for peculiar sign prescriptions in the calculation of [21]-colored HOMFLY polynomials.

hep-th↗

arXiv2015

Colored HOMFLY polynomials of knots presented as double fat diagrams

Many knots and links in S^3 can be drawn as gluing of three manifolds with one or more four-punctured S^2 boundaries. We call these knot diagrams as double fat graphs whose invariants involve only the knowledge of the fusion and the braiding matrices of four-strand braids. Incorporating the properties of four-point conformal blocks in WZNW models, we conjecture colored HOMFLY polynomials for these double fat graphs where the color can be rectangular or non-rectangular representation. With the recent work of Gu-Jockers, the fusion matrices for the non-rectangular [21] representation, the first which involves multiplicity is known. We verify our conjecture by comparing with the [21] colored HOMFLY of many knots, obtained as closure of three braids. The conjectured form is computationally very effective leading to writing [21]-colored HOMFLY polynomials for many pretzel type knots and non-pretzel type knots. In particular, we find class of pretzel mutants which are distinguished and another class of mutants which cannot be distinguished by [21] representation. The difference between the [21]-colored HOMFLY of two mutants seems to have a general form, with A-dependence completely defined by the old conjecture due to Morton and Cromwell. In particular, we check it for an entire multi-parametric family of mutant knots evaluated using evolution method.

hep-th↗

arXiv2015

Non-Zero $θ_{13}$ and $δ_{CP}$ in a Neutrino Mass Model with $A_4$ Symmetry

In this paper, we consider a neutrino mass model based on $A_4$ symmetry. The spontaneous symmetry breaking in this model is chosen to obtain tribimaximal mixing in the neutrino sector. We introduce $Z_2 \times Z_2$ invariant perturbations in this model which can give rise to acceptable values of $θ_{13}$ and $δ_{CP}$. Perturbation in the charged lepton sector alone can lead to viable values of $θ_{13}$, but cannot generate $δ_{CP}$. Perturbation in the neutrino sector alone can lead to acceptable $θ_{13}$ and maximal CP violation. By adjusting the magnitudes of perturbations in both sectors, it is possible to obtain any value of $δ_{CP}$.

hep-ph↗

arXiv2014

Backreaction effects due to matter coupled higher derivative gravity

AdS-hydrodynamics has proven to be a useful tool for obtaining transport coefficients observed in the collective flow of strongly coupled fluids like quark gluon plasma (QGP). Particularly, the ratio of shear viscosity to entropy density ${η/ s}$ obtained from elliptic flow measurements can be matched with the computation done in the dual gravity theory. The experimentally observed temperature dependence of ${η/ s}$ requires the study of scalar matter coupled AdS gravity including higher derivative curvature corrections. We obtain the backreaction to the metric for such a matter coupled AdS gravity in $D$-dimensional spacetime due to the higher derivative curvature corrections. Then, we present the backreaction corrections to shear-viscosity $η$ and entropy density $s$.

hep-th↗

arXiv2014

Is toric duality a Seiberg-like duality in (2+1)-d ?

We show that not all $(2+1)$ dimensional toric phases are Seiberg-like duals. Particularly, we work out superconformal indices for the toric phases of Fanos ${\cal{C}}_3$, ${\cal{C}}_5$ and ${\cal{B}}_2$. We find that the indices for the two toric phases of Fano ${\cal{B}}_2$ do not match, which implies that they are not Seiberg-like duals. We also take the route of acting Seiberg-like duality transformation on toric quiver Chern-Simons theories to obtain dual quivers. We study two examples and show that Seiberg-like dual quivers are not always toric quivers.

hep-th↗

arXiv2014

Trivalent graphs, volume conjectures and character varieties

The generalized volume conjecture and the AJ conjecture (a.k.a. the quantum volume conjecture) are extended to $U_q(\fraksl_2)$ colored quantum invariants of the theta and tetrahedron graph. The $\SL(2,\bC)$ character variety of the fundamental group of the complement of a trivalent graph with $E$ edges in $S^3$ is a Lagrangian subvariety of the Hitchin moduli space over the Riemann surface of genus $g=E/3+1$. For the theta and tetrahedron graph, we conjecture that the configuration of the character variety is locally determined by large color asymptotics of the quantum invariants of the trivalent graph in terms of complex Fenchel-Nielsen coordinates. Moreover, the $q$-holonomic difference equation of the quantum invariants provides the quantization of the character variety.

math.GT↗

arXiv2014

Colored Kauffman Homology and Super-A-polynomials

We study the structural properties of colored Kauffman homologies of knots. Quadruple-gradings play an essential role in revealing the differential structure of colored Kauffman homology. Using the differential structure, the Kauffman homologies carrying the symmetric tensor products of the vector representation for the trefoil and the figure-eight are determined. In addition, making use of relations from representation theory, we also obtain the HOMFLY homologies colored by rectangular Young tableaux with two rows for these knots. Furthermore, the notion of super-A-polynomials is extended in order to encompass two-parameter deformations of PSL(2,C) character varieties.

hep-th↗

arXiv2013

Partial resolution of complex cones over Fano ${\cal{B}}$

In our recent paper arXiv:1108.2387, we systematized inverse algorithm to obtain quiver gauge theory living on the M2-branes probing the singularities of special kind of Calabi-Yau four-folds which were complex cones over toric Fano $\mathbb{P}^3$, ${\cal{B}}_1$, ${\cal{B}}_2$, ${\cal{B}}_3$. These quiver gauge theories cannot be given a dimer tiling presentation. We use the method of partial resolution to show that the toric data of $\mathbb{C}^4$ and Fano $\mathbb{P}^3$ can be embedded inside the toric data of Fano ${\cal{B}}$ theories. This method indirectly justfies that the two node quiver Chern-Simons theories corresponding to $\mathbb{C}^4$, Fano $\mathbb{P}^3$ and their orbifolds can be obtained by higgsing matter fields of the three node parent quiver corresponding to Fano ${\cal{B}}_1$, ${\cal{B}}_2$, ${\cal{B}}_3$, ${\cal{B}}_4$ three-folds.

hep-th↗

arXiv2013

Multiplicity-free quantum 6j-symbols for U_q(sl_N)

We conjecture a closed form expression for the simplest class of multiplicity-free quantum 6j-symbols for U_q(sl_N). The expression is a natural generalization of the quantum 6j-symbols for U_q(sl_2) obtained by Kirillov and Reshetikhin. Our conjectured form enables computation of colored HOMFLY polynomials for various knots and links carrying arbitrary symmetric representations.

hep-th↗

arXiv2013

Colored HOMFLY polynomials from Chern-Simons theory

We elaborate the Chern-Simons field theoretic method to obtain colored HOMFLY invariants of knots and links. Using multiplicity-free quantum 6j-symbols for U_q(sl_N), we present explicit evaluations of the HOMFLY invariants colored by symmetric representations for a variety of knots, two-component links and three-component links.

hep-th↗

arXiv2013

Super-A-polynomials for Twist Knots

We conjecture formulae of the colored superpolynomials for a class of twist knots $K_p$ where p denotes the number of full twists. The validity of the formulae is checked by applying differentials and taking special limits. Using the formulae, we compute both the classical and quantum super-A-polynomial for the twist knots with small values of p. The results support the categorified versions of the generalized volume conjecture and the quantum volume conjecture. Furthermore, we obtain the evidence that the Q-deformed A-polynomials can be identified with the augmentation polynomials of knot contact homology in the case of the twist knots.

hep-th↗

arXiv2013

SU(N) quantum Racah coefficients & non-torus links

It is well-known that the SU(2) quantum Racah coefficients or the Wigner $6j$ symbols have a closed form expression which enables the evaluation of any knot or link polynomials in SU(2) Chern-Simons field theory. Using isotopy equivalence of SU(N) Chern-Simons functional integrals over three balls with one or more $S^2$ boundaries with punctures, we obtain identities to be satisfied by the SU(N) quantum Racah coefficients. This enables evaluation of the coefficients for a class of SU(N) representations. Using these coefficients, we can compute the polynomials for some non-torus knots and two-component links. These results are useful for verifying conjectures in topological string theory.

hep-th↗

arXiv2012

Reformulated invariants for non-torus knots and links

Using the Racah coefficients in our earlier paper arXiv:1107.3918, we explicitly write the Chern-Simons field theory invariants for many non-torus knot and links. Further, we have tabulated the reformulated invariants which agrees with the Ooguri-Vafa conjecture for knots and Labastida-Marino-Vafa conjecture for links.

hep-th↗