The fully packed loop model as a non-rational<i>W</i><sub>3</sub>conformal field theory

Dupic, Thomas; Estienne, Benoît; Ikhlef, Yacine

doi:10.1088/1751-8113/49/50/505202

Cited by 11 publications

(17 citation statements)

References 35 publications

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“…So for fixed rank of the affine algebra, one can construct arbitrarily large adjacency graphs labelled by k. These can also be converted to CSOS-type models by suitably tuning the w 0 parameter to make the weights periodic [89]. We refer to the original literature, as well as to [90,91] for the details of the construction.…”

Section: Jhep08(2021)127mentioning

confidence: 99%

“…) See [90,101] for recent discussions of the dilute loop models based on the tiles above and more details on their relations to the RSOS and vertex models.…”

Section: Jhep08(2021)127mentioning

confidence: 99%

“…Our actual set of tiles/weights makes our model more like the 15-vertex model, which is related to the adjacency diagram of the A (1) 2 algebra. For details of this model we refer to [90,91,101]. These references, however, are mostly concerned with the trigonometric case.…”

Section: Jhep08(2021)127mentioning

confidence: 99%

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Dynamical spin chains in 4D $$ \mathcal{N} $$ = 2 SCFTs

Pomoni¹,

Rabe

Zoubos

2021

J. High Energ. Phys.

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This is the first in a series of papers devoted to the study of spin chains capturing the spectral problem of 4d $$ \mathcal{N} $$ N = 2 SCFTs in the planar limit. At one loop and in the quantum plane limit, we discover a quasi-Hopf symmetry algebra, defined by the R-matrix read off from the superpotential. This implies that when orbifolding the $$ \mathcal{N} $$ N = 4 symmetry algebra down to the $$ \mathcal{N} $$ N = 2 one and then marginaly deforming, the broken generators are not lost, but get upgraded to quantum generators. Importantly, we demonstrate that these chains are dynamical, in the sense that their Hamiltonian depends on a parameter which is dynamically determined along the chain. At one loop we map the holomorphic SU(3) scalar sector to a dynamical 15-vertex model, which corresponds to an RSOS model, whose adjacency graph can be read off from the gauge theory quiver/brane tiling. One scalar SU(2) sub-sector is described by an alternating nearest-neighbour Hamiltonian, while another choice of SU(2) sub-sector leads to a dynamical dilute Temperley-Lieb model. These sectors have a common vacuum state, around which the magnon dispersion relations are naturally uniformised by elliptic functions. Concretely, for the ℤ2 quiver theory we study these dynamical chains by solving the one- and two-magnon problems with the coordinate Bethe ansatz approach. We confirm our analytic results by numerical comparison with the explicit diagonalisation of the Hamiltonian for short closed chains.

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Section: Jhep08(2021)127mentioning

confidence: 99%

“…) See [90,101] for recent discussions of the dilute loop models based on the tiles above and more details on their relations to the RSOS and vertex models.…”

Section: Jhep08(2021)127mentioning

confidence: 99%

See 1 more Smart Citation

Dynamical spin chains in 4D $$ \mathcal{N} $$ = 2 SCFTs

Pomoni¹,

Rabe

Zoubos

2021

J. High Energ. Phys.

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show abstract

“…So for fixed rank of the affine algebra, one can construct arbitrarily large adjacency graphs labelled by k. These can also be converted to CSOS-type models by suitably tuning the w 0 parameter to make the weights periodic [84]. We refer to the original literature, as well as to [85,86] for the details of the construction.…”

Section: The Dynamical R-matrixmentioning

confidence: 99%

Dynamical Spin Chains in 4D $\mathcal{N}=2$ SCFTs

Pomoni,

Rabe,

Zoubos

2021

Preprint

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This is the first in a series of papers devoted to the study of spin chains capturing the spectral problem of 4d N = 2 SCFTs in the planar limit. At one loop and in the quantum plane limit, we discover a quasi-Hopf symmetry algebra, defined by the R-matrix read off from the superpotential. This implies that when orbifolding the N = 4 symmetry algebra down to the N = 2 one and then marginaly deforming, the broken generators are not lost, but get upgraded to quantum generators. Importantly, we demonstrate that these chains are dynamical, in the sense that their Hamiltonian depends on a parameter which is dynamically determined along the chain. At one loop we map the holomorphic SU(3) scalar sector to a dynamical 15-vertex model, which corresponds to an RSOS model, whose adjacency graph can be read off from the gauge theory quiver/brane tiling. One scalar SU(2) sub-sector is described by an alternating nearest-neighbour Hamiltonian, while another choice of SU(2) sub-sector leads to a dynamical dilute Temperley-Lieb model. These sectors have a common vacuum state, around which the magnon dispersion relations are naturally uniformised by elliptic functions. Concretely, for the Z 2 quiver theory we study these dynamical chains by solving the one-and two-magnon problems with the coordinate Bethe ansatz approach. We confirm our analytic results by numerical comparison with the explicit diagonalisation of the Hamiltonian for short closed chains.

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“…The exponents ν 1 + ν 2 + ν 3 + ν 4 + σ 1 + 1, ν 1 + ν 2 + ν 3 + ν 4 + σ 1 + 2 at x = ∞ are realized by linear combinations of the cycles 15) where two linear relations among these four cycles hold by Cauchy's theorem on t 1 -plane. The exponents ν 1 + ν 2 + σ 1 − σ 2 , ν 1 + ν 2 + σ 1 − σ 2 + 1 at x = ∞ are realized by linear combinations of the cycles…”

Section: Cycles Corresponding To Local Fundamental Systems Of Solutionsmentioning

confidence: 99%

Rigid Fuchsian Systems in 2-Dimensional Conformal Field Theories

Belavin

Haraoka

Santachiara

2018

Commun. Math. Phys.

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We investigate Fuchsian equations arising in the context of 2-dimensional conformal field theory (CFT) and we apply the Katz theory of Fucshian rigid systems to solve some of these equations. We show that the Katz theory provides a precise mathematical framework to answer the question whether the fusion rules of degenerate primary fields are enough for determining the differential equations satisfied by their correlation functions. We focus on the case of W 3 Toda CFT: we argue that the differential equations arising for four-point conformal blocks with one nth level semi-degenerate field and a fully-degenerate one in the fundamental sl 3 representation are associated to Fuchsian rigid systems. We show how to apply Katz theory to determine the explicit form of the differential equations, the integral expression of solutions and the monodromy group representation. The theory of twisted homology is also used in the analysis of the integral expression. This approach allows to construct the corresponding fusion matrices and to perform the whole bootstrap program: new explicit factorization of W 3 correlation functions as well shift relations between structure constants are also provided.

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The fully packed loop model as a non-rationalW₃conformal field theory

Cited by 11 publications

References 35 publications

Dynamical spin chains in 4D $$ \mathcal{N} $$ = 2 SCFTs

Dynamical spin chains in 4D $$ \mathcal{N} $$ = 2 SCFTs

Dynamical Spin Chains in 4D $\mathcal{N}=2$ SCFTs

Rigid Fuchsian Systems in 2-Dimensional Conformal Field Theories

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The fully packed loop model as a non-rationalW3conformal field theory

Cited by 11 publications

References 35 publications

Dynamical spin chains in 4D $$ \mathcal{N} $$ = 2 SCFTs

Dynamical spin chains in 4D $$ \mathcal{N} $$ = 2 SCFTs

Dynamical Spin Chains in 4D $\mathcal{N}=2$ SCFTs

Rigid Fuchsian Systems in 2-Dimensional Conformal Field Theories

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The fully packed loop model as a non-rationalW₃conformal field theory