P. Ramadevi - Academia.edu (original) (raw)

Papers by P. Ramadevi

Journal of physics, Dec 31, 2013

N = 1 quiver gauge theories on coincident D3 branes placed at a tip of a Calabi-Yau singularity C... more N = 1 quiver gauge theories on coincident D3 branes placed at a tip of a Calabi-Yau singularity C are dual to string theories on AdS5 × X5 where X5 are Sasaki-Einstein spaces. We present a neat combinatorial approach called dimer model to understand interrelations between toric quiver gauge theories and toric data representing the Calabi-Yau singularities.

Group Theory for Physicists, 2007

Series on Knots and Everything, Sep 1, 2011

In this brief presentation, we would like to present our attempts of detecting chirality and muta... more In this brief presentation, we would like to present our attempts of detecting chirality and mutations from Chern-Simons gauge theory. The results show that the generalised knot invariants, obtained from Chern-Simons gauge theory, are more powerful than Jones, HOMFLYPT and Kauffman polynomials. However the classification problem of knots and links is still an open challenging problem.

Annales Henri Poincaré, 2019

Obtaining colored HOMFLY-PT polynomials for knots from 3-strand braid carrying arbitrary SU (N) r... more Obtaining colored HOMFLY-PT polynomials for knots from 3-strand braid carrying arbitrary SU (N) representation is still tedious. For a class of rank r symmetric representations, [r]-colored HOMFLY-PT H [r] evaluation becomes simpler. Recently [1], it was shown that H [r] , for such knots from 3-strand braid, can be constructed using the quantum Racah coefficients (6j-symbols) of Uq(sl2). In this paper, we generalise it to links whose components carry different symmetric representations. We illustrate the technique by evaluating multi-colored link polynomials H [r 1 ],[r 2 ] for the two-component link L7a3 whose components carry [r1] and [r2] colors.

Letters in Mathematical Physics

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

Resonance, 2003

During the last few decades, theoretical physicists have introducedsymmetries (which may or may n... more During the last few decades, theoretical physicists have introducedsymmetries (which may or may not have any geometrical interpretation) with the aim of solving difficult problems. In this article, we shall first present the salient features of one such symmetry calledsupersymmetry. Then, we shall show the power of supersymmetry in tackling quantum mechanical systems described by non-trivial potentials.

arXiv: High Energy Physics - Theory, 2018

Construction of representations of braid group generators from NNN-state vertex models provide an... more Construction of representations of braid group generators from NNN-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(N-1)/2(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 RRR matrices of bi-partite vertex models.

Contemporary Mathematics, 2016

We conjecture a closed form expression for the simplest class of multiplicity-free quantum 6 j-sy... more We conjecture a closed form expression for the simplest class of multiplicity-free quantum 6 j-symbols for Uq (slN ). The expression is a natural generalization of the quan- tum 6 j-symbols for Uq (sl2) obtained by Kirillov and Reshetikhin. Our conjectured form enables computation of colored HOMFLY polynomials for various knots and links carry- ing arbitrary symmetric representations.

Journal of High Energy Physics

The entanglement entropy of many quantum systems is difficult to compute in general. They are obt... more The entanglement entropy of many quantum systems is difficult to compute in general. They are obtained as a limiting case of the Rényi entropy of index m, which captures the higher moments of the reduced density matrix. In this work, we study pure bipartite states associated with S3 complements of a two-component link which is a connected sum of a knot mathcalK\mathcal{K}mathcalK K and the Hopf link. For this class of links, the Chern-Simons theory provides the necessary setting to visualise the m-moment of the reduced density matrix as a three-manifold invariant Z(MmathcalKm{M}_{{\mathcal{K}}_m}MmathcalKm M K m ), which is the partition function of MmathcalKm{M}_{{\mathcal{K}}_m}MmathcalKm M K m . Here MmathcalKm{M}_{{\mathcal{K}}_m}MmathcalKm M K m is a closed 3-manifold associated with the knot mathcalK\mathcal{K}mathcalK K m, where mathcalK\mathcal{K}mathcalK K m is a connected sum of m-copies of mathcalK\mathcal{K}mathcalK K (i.e., mathcalK\mathcal{K}mathcalK K #mathcalK\mathcal{K}mathcalK K . . . #mathcalK\mathcal{K}mathcalK K ) which mimics the well-known replica method. We analayse th...

Lata Kh Joshi,1, 2, ∗ Ayan Mukhopadhyay,3, 4, † Florian Preis,3, ‡ and Pichai Ramadevi1, § Depart... more Lata Kh Joshi,1, 2, ∗ Ayan Mukhopadhyay,3, 4, † Florian Preis,3, ‡ and Pichai Ramadevi1, § Department of Physics, Indian Institute of Technology Bombay, Mumbai 400 076, India School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom Institut für Theoretische Physik, Technische Universität Wien, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria CERN, Theoretical Physics Department, 1211 Geneva 23, Switzerland

Letters in Mathematical Physics, 2014

The generalized volume conjecture and the AJ conjecture (a.k.a. the quantum volume conjecture) ar... more The generalized volume conjecture and the AJ conjecture (a.k.a. the quantum volume conjecture) are extended to U q (sl 2) colored quantum invariants of the theta and tetrahedron graph. The SL(2, C) 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.

Journal of Geometry and Physics

Proceedings of The European Physical Society Conference on High Energy Physics — PoS(EPS-HEP2015)

ABSTRACT

Journal of High Energy Physics

Topological entanglement structure amongst disjoint torus boundaries of three manifolds have alre... more Topological entanglement structure amongst disjoint torus boundaries of three manifolds have already been studied within the context of Chern-Simons theory. In this work, we study the topological entanglement due to interaction between the quasiparticles inside three-manifolds with one or more disjoint S 2 boundaries in SU(N) Chern-Simons theory. We focus on the world-lines of quasiparticles (Wilson lines), carrying SU(N) representations, creating four punctures on every S 2. We compute the entanglement entropy by partial tracing some of the boundaries. In fact, the entanglement entropy depends on the SU(N) representations on these four-punctured S 2 boundaries. Further, we observe interesting features on the GHZ-like and W-like entanglement structures. Such a distinction crucially depends on the multiplicity of the irreducible representations in the tensor product of SU(N) representations.

Journal of Knot Theory and Its Ramifications

We illustrate from the viewpoint of braiding operations on WZNW conformal blocks how colored HOMF... more We illustrate from the viewpoint of braiding operations on WZNW conformal blocks how colored HOMFLY-PT polynomials with multiplicity structure can detect mutations. As an example, we explicitly evaluate the [Formula: see text]-colored HOMFLY-PT polynomials that distinguish a famous mutant pair, Kinoshita–Terasaka and Conway knot.

Encyclopedia of Mathematical Physics, 2006

Modern Physics Letters A, 2015

AdS-hydrodynamics has proven to be a useful tool for obtaining transport coefficients observed in... more 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.

Journal of physics, Dec 31, 2013

N = 1 quiver gauge theories on coincident D3 branes placed at a tip of a Calabi-Yau singularity C... more N = 1 quiver gauge theories on coincident D3 branes placed at a tip of a Calabi-Yau singularity C are dual to string theories on AdS5 × X5 where X5 are Sasaki-Einstein spaces. We present a neat combinatorial approach called dimer model to understand interrelations between toric quiver gauge theories and toric data representing the Calabi-Yau singularities.

Group Theory for Physicists, 2007

Series on Knots and Everything, Sep 1, 2011

In this brief presentation, we would like to present our attempts of detecting chirality and muta... more In this brief presentation, we would like to present our attempts of detecting chirality and mutations from Chern-Simons gauge theory. The results show that the generalised knot invariants, obtained from Chern-Simons gauge theory, are more powerful than Jones, HOMFLYPT and Kauffman polynomials. However the classification problem of knots and links is still an open challenging problem.

Annales Henri Poincaré, 2019

Obtaining colored HOMFLY-PT polynomials for knots from 3-strand braid carrying arbitrary SU (N) r... more Obtaining colored HOMFLY-PT polynomials for knots from 3-strand braid carrying arbitrary SU (N) representation is still tedious. For a class of rank r symmetric representations, [r]-colored HOMFLY-PT H [r] evaluation becomes simpler. Recently [1], it was shown that H [r] , for such knots from 3-strand braid, can be constructed using the quantum Racah coefficients (6j-symbols) of Uq(sl2). In this paper, we generalise it to links whose components carry different symmetric representations. We illustrate the technique by evaluating multi-colored link polynomials H [r 1 ],[r 2 ] for the two-component link L7a3 whose components carry [r1] and [r2] colors.

Letters in Mathematical Physics

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

Resonance, 2003

During the last few decades, theoretical physicists have introducedsymmetries (which may or may n... more During the last few decades, theoretical physicists have introducedsymmetries (which may or may not have any geometrical interpretation) with the aim of solving difficult problems. In this article, we shall first present the salient features of one such symmetry calledsupersymmetry. Then, we shall show the power of supersymmetry in tackling quantum mechanical systems described by non-trivial potentials.

arXiv: High Energy Physics - Theory, 2018

Construction of representations of braid group generators from NNN-state vertex models provide an... more Construction of representations of braid group generators from NNN-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(N-1)/2(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 RRR matrices of bi-partite vertex models.

Contemporary Mathematics, 2016

We conjecture a closed form expression for the simplest class of multiplicity-free quantum 6 j-sy... more We conjecture a closed form expression for the simplest class of multiplicity-free quantum 6 j-symbols for Uq (slN ). The expression is a natural generalization of the quan- tum 6 j-symbols for Uq (sl2) obtained by Kirillov and Reshetikhin. Our conjectured form enables computation of colored HOMFLY polynomials for various knots and links carry- ing arbitrary symmetric representations.

Journal of High Energy Physics

The entanglement entropy of many quantum systems is difficult to compute in general. They are obt... more The entanglement entropy of many quantum systems is difficult to compute in general. They are obtained as a limiting case of the Rényi entropy of index m, which captures the higher moments of the reduced density matrix. In this work, we study pure bipartite states associated with S3 complements of a two-component link which is a connected sum of a knot mathcalK\mathcal{K}mathcalK K and the Hopf link. For this class of links, the Chern-Simons theory provides the necessary setting to visualise the m-moment of the reduced density matrix as a three-manifold invariant Z(MmathcalKm{M}_{{\mathcal{K}}_m}MmathcalKm M K m ), which is the partition function of MmathcalKm{M}_{{\mathcal{K}}_m}MmathcalKm M K m . Here MmathcalKm{M}_{{\mathcal{K}}_m}MmathcalKm M K m is a closed 3-manifold associated with the knot mathcalK\mathcal{K}mathcalK K m, where mathcalK\mathcal{K}mathcalK K m is a connected sum of m-copies of mathcalK\mathcal{K}mathcalK K (i.e., mathcalK\mathcal{K}mathcalK K #mathcalK\mathcal{K}mathcalK K . . . #mathcalK\mathcal{K}mathcalK K ) which mimics the well-known replica method. We analayse th...

Lata Kh Joshi,1, 2, ∗ Ayan Mukhopadhyay,3, 4, † Florian Preis,3, ‡ and Pichai Ramadevi1, § Depart... more Lata Kh Joshi,1, 2, ∗ Ayan Mukhopadhyay,3, 4, † Florian Preis,3, ‡ and Pichai Ramadevi1, § Department of Physics, Indian Institute of Technology Bombay, Mumbai 400 076, India School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom Institut für Theoretische Physik, Technische Universität Wien, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria CERN, Theoretical Physics Department, 1211 Geneva 23, Switzerland

Letters in Mathematical Physics, 2014

The generalized volume conjecture and the AJ conjecture (a.k.a. the quantum volume conjecture) ar... more The generalized volume conjecture and the AJ conjecture (a.k.a. the quantum volume conjecture) are extended to U q (sl 2) colored quantum invariants of the theta and tetrahedron graph. The SL(2, C) 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.

Journal of Geometry and Physics

Proceedings of The European Physical Society Conference on High Energy Physics — PoS(EPS-HEP2015)

ABSTRACT

Journal of High Energy Physics

Topological entanglement structure amongst disjoint torus boundaries of three manifolds have alre... more Topological entanglement structure amongst disjoint torus boundaries of three manifolds have already been studied within the context of Chern-Simons theory. In this work, we study the topological entanglement due to interaction between the quasiparticles inside three-manifolds with one or more disjoint S 2 boundaries in SU(N) Chern-Simons theory. We focus on the world-lines of quasiparticles (Wilson lines), carrying SU(N) representations, creating four punctures on every S 2. We compute the entanglement entropy by partial tracing some of the boundaries. In fact, the entanglement entropy depends on the SU(N) representations on these four-punctured S 2 boundaries. Further, we observe interesting features on the GHZ-like and W-like entanglement structures. Such a distinction crucially depends on the multiplicity of the irreducible representations in the tensor product of SU(N) representations.

Journal of Knot Theory and Its Ramifications

We illustrate from the viewpoint of braiding operations on WZNW conformal blocks how colored HOMF... more We illustrate from the viewpoint of braiding operations on WZNW conformal blocks how colored HOMFLY-PT polynomials with multiplicity structure can detect mutations. As an example, we explicitly evaluate the [Formula: see text]-colored HOMFLY-PT polynomials that distinguish a famous mutant pair, Kinoshita–Terasaka and Conway knot.

Encyclopedia of Mathematical Physics, 2006

Modern Physics Letters A, 2015

AdS-hydrodynamics has proven to be a useful tool for obtaining transport coefficients observed in... more 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.