On Goldman bracket for G 2 gauge group

Chowdhury, S. Hasibul Hassan

doi:10.1007/jhep02(2016)001

Cited by 3 publications

(3 citation statements)

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“…rerouted loops) at the intersection points. For a derivation of (3.128) using CS theories as well but in a different context, see [50]. Our construction easily generalizes to the case where the disc is replaced by a genus g Riemann surface Σ g with boundaries (recall [46]), which is a more natural scenario to be considered due to the novel connection of (3.127) with the Goldman bracket.…”

Section: W (γ Smentioning

confidence: 98%

“…The curve (γ 1 • γ −1 2 )(ŝ) simply means that at the point y i (ŝ) the second loop is traveled in the reverse direction. See fig 1. in [50] for further reference. This is how the intersection point is resolved in terms of the product of (rerouted) loops.…”

Section: The Spectral Parametermentioning

confidence: 99%

“…Following [50], we now write the tensor Casimir for several classical Lie groups using a n-dimensional matrix representation based on the generalized Gell-Mann matrices.…”

Section: W (γ Smentioning

confidence: 99%

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Lambda models from Chern-Simons theories

Schmidtt¹

2018

J. High Energ. Phys.

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In this paper we refine and extend the results of [1], where a connection between the AdS 5 × S 5 superstring lambda model on S 1 = ∂D and a double Chern-Simons (CS) theory on D based on the Lie superalgebra psu(2, 2|4) was suggested, after introduction of the spectral parameter z. The relation between both theories mimics the well-known CS/WZW symplectic reduction equivalence but is non-chiral in nature. All the statements are now valid in the strong sense, i.e. valid on the whole phase space, making the connection between both theories precise. By constructing a z-dependent gauge field in the 2+1 Hamiltonian CS theory it is shown that: i) by performing a symplectic reduction of the CS theory the Maillet algebra satisfied by the extended Lax connection of the lambda model emerges as a boundary current algebra and ii) the Poisson algebra of the supertraces of z-dependent Wilson loops in the CS theory obey some sort of spectral parameter generalization of the Goldman bracket. The latter algebra is interpreted as the precursor of the (ambiguous) lambda model monodromy matrix Poisson algebra prior to the symplectic reduction. As a consequence, the problematic non-ultralocality of lambda models is avoided (for any value of the deformation parameter λ ⊂ [0, 1]), showing how the lambda model classical integrable structure can be understood as a byproduct of the symplectic reduction process of the z-dependent CS theory.

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Section: W (γ Smentioning

confidence: 98%

Section: The Spectral Parametermentioning

confidence: 99%

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Lambda models from Chern-Simons theories

Schmidtt¹

2018

J. High Energ. Phys.

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Sign problem in a Z3 -symmetric effective Polyakov-line model

et al. 2017

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As an effective model corresponding to Z3-symmetric QCD (Z3-QCD), we construct a Z3-symmetric effective Polyakov-line model (Z3-EPLM) by using the logarithmic fermion effective action. Since Z3-QCD tends to QCD in the zero-temperature limit, Z3-EPLM also agrees with the ordinary effective Polyakov-line model (EPLM) there; note that (ordinary) EPLM does not possess Z3 symmetry. Our main purpose is to discuss a sign problem appearing in Z3-EPLM. The action of Z3-EPLM is real, when the Polyakov line is not only real but also its Z3 images. This suggests that the sign problem becomes milder in Z3-EPLM than in EPLM. In order to confirm this suggestion, we do lattice simulations for both EPLM and Z3-EPLM by using the reweighting method with the phase quenched approximation. In the low-temperature region, the sign problem is milder in Z3-EPLM than in EPLM. We also propose a new reweighting method. This makes the sign problem very weak in Z3-EPLM.

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