CHIRALITY OF KNOTS 9<sub>42</sub> AND 10<sub>71</sub> AND CHERN-SIMONS THEORY

Ramadevi, P.; Govindarajan, T. R.; Kaul, Romesh K.

doi:10.1142/s0217732394003026

Cited by 56 publications

(70 citation statements)

References 10 publications

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“…These three cases are 3-strand (and thus already known) According to [42] and [43], seven thick knots from [11] can be realized just as triple-finger starfish diagrams: …”

Section: A32 4-parallel Pretzel Finger Casesmentioning

confidence: 92%

“…• The second is the conjectured expression [42][43][44][45][46][47] for knots in S 3 obtained from gluing three-manifolds with one or more four-punctured S 2 boundaries. We call such diagrams as double fat tree diagrams (see definitions below) .…”

Section: Jhep07(2015)109mentioning

confidence: 99%

“…There is lot of evidence for the eq. (1.2) from the conformal block method [42][43][44][45][46][47] and its advanced versions like the evolution [70], cabling [40] and differential expansion [39] methods for symmetric representations. In this paper, we will do similar verification for R = [21].…”

Section: Jhep07(2015)109mentioning

confidence: 99%

“…Ten intersection chiral knot 10 71 has a neat presentation as a three-finger with each finger being non-pretzel type [42]. Using the states for such non-pretzel fingers, the HOMFLY polynomial for this knot is:…”

Section: Non-pretzel Fingersmentioning

confidence: 99%

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Colored HOMFLY polynomials of knots presented as double fat diagrams

Миронов

Морозов

Ramadevi

et al. 2015

J. High Energ. Phys.

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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.

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“…These three cases are 3-strand (and thus already known) According to [42] and [43], seven thick knots from [11] can be realized just as triple-finger starfish diagrams: …”

Section: A32 4-parallel Pretzel Finger Casesmentioning

confidence: 92%

Section: Jhep07(2015)109mentioning

confidence: 99%

Section: Jhep07(2015)109mentioning

confidence: 99%

Section: Non-pretzel Fingersmentioning

confidence: 99%

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Colored HOMFLY polynomials of knots presented as double fat diagrams

Миронов

Морозов

Ramadevi

et al. 2015

J. High Energ. Phys.

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“…Then, the cabling method can be applied to extract the colored HOMFLY polynomials [80]. This method turns out to be rather powerful and calculations involving 12-strands determine [21]-colored HOMFLY polynomials for some 4-strand knots, and [31]-or [22]-colored HOMFLY polynomials for the 3-strand braids.…”

Section: Sum Over Paths For Fundamental Representations and Cablingmentioning

confidence: 99%

Checks of integrality properties in topological strings

Mironov¹,

Морозов²,

Морозов³

et al. 2017

J. High Energ. Phys.

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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 [1] 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.

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Communication Protocols and QECC From the Perspective of TQFT, Part II: QECCs as Spacetimes

Fields,

Glazebrook,

Marcianò

2024

Fortschritte der Physik

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Topological quantum field theories (TQFTs) provide a general, minimal‐assumption language for describing quantum‐state preparation and measurement. They therefore provide a general language in which to express multi‐agent communication protocols, e.g., local operations, classical communication (LOCC) protocols. In the accompanying Part I, we construct LOCC protocols using TQFT, and show that LOCC protocols induce quantum error‐correcting codes (QECCs) on the agent‐environment boundary. Such QECCs can be regarded as implementing or inducing the emergence of spacetimes on such boundaries. Here connection between inter‐agent communication and spacetime is investigated, by exploiting different realizations of TQFT. The authors delved into TQFTs that support on their boundaries spin‐networks as computational systems: these are known as topological quantum neural networks (TQNNs). TQNNs, which have a natural representation as tensor networks, implement QECC. The HaPPY code is recognized to be a paradigmatic example. How generic QECCs, as bulk‐boundary codes, induce effective spacetimes is then shown. The effective spatial and temporal separations that take place in QECC enables LOCC protocols between spatially separated observers. The implementation of QECCs in BF and Chern‐Simons theories are then considered, and QECC‐induced spacetimes are shown to provide the classical redundancy required for LOCC. Finally, the topological M‐theory is considered as an implementation of QECC in higher spacetime dimensions.

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CHIRALITY OF KNOTS 9₄₂ AND 10₇₁ AND CHERN-SIMONS THEORY

Cited by 56 publications

References 10 publications

Colored HOMFLY polynomials of knots presented as double fat diagrams

Colored HOMFLY polynomials of knots presented as double fat diagrams

Checks of integrality properties in topological strings

Communication Protocols and QECC From the Perspective of TQFT, Part II: QECCs as Spacetimes

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CHIRALITY OF KNOTS 942 AND 1071 AND CHERN-SIMONS THEORY

Cited by 56 publications

References 10 publications

Colored HOMFLY polynomials of knots presented as double fat diagrams

Colored HOMFLY polynomials of knots presented as double fat diagrams

Checks of integrality properties in topological strings

Communication Protocols and QECC From the Perspective of TQFT, Part II: QECCs as Spacetimes

Contact Info

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CHIRALITY OF KNOTS 9₄₂ AND 10₇₁ AND CHERN-SIMONS THEORY