Groundstate finite-size corrections and dilogarithm identities for the twisted $A_1^{(1)}$, $A_2^{(1)}$ and $A_2^{(2)}$ models

Morin-Duchesne, Alexi; Klümper, Andreas; Pearce, Paul A.

doi:10.48550/arxiv.2006.08233

Cited by 2 publications

(6 citation statements)

References 61 publications

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“…RSOS description of this 15-vertex model, which is expected to be similar to the elliptic (off-critical) models described in [91,101]. 41 The symmetries and the periodicity of the problem allowed us to determine the adjacency graph of the dilute RSOS model associated to the Z 2 quiver theory depicted in figure 7.…”

Section: Jhep08(2021)127mentioning

confidence: 84%

“…) 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: 84%

“…) 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.

View full text Add to dashboard Cite

show abstract

“….15) See [85,96] 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: Dilute Rsos Modelsmentioning

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 [85,86,96]. These references, however, are mostly concerned with the trigonometric case.…”

Section: The Su(3) Sector As a Dynamical 15-vertex Modelmentioning

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.

show abstract

Groundstate finite-size corrections and dilogarithm identities for the twisted $A_1^{(1)}$, $A_2^{(1)}$ and $A_2^{(2)}$ models

Cited by 2 publications

References 61 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

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