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F. Vian – One of the best experts on this subject based on the ideXlab platform.

  • wilson loops in the Adjoint Representation and multiple vacua in two dimensional yang mills theory
    Annals of Physics, 2000
    Co-Authors: A. Bassetto, Luca Griguolo, F. Vian
    Abstract:

    Abstract QCD 2 with fermions in the Adjoint Representation is invariant under SU ( N )/ Z N and thereby is endowed with a nontrivial vacuum structure ( k -sectors). The static potential between Adjoint charges, in the limit of infinite mass, can be therefore obtained by computing Wilson loops in the pure Yang–Mills theory with the same nontrivial structure. When the (Euclidean) space-time is compacted on a sphere S 2 , Wilson loops can be exactly expressed in terms of an infinite series of topological excitations (instantons). The presence of k -sectors modifies the energy spectrum of the theory and its instanton content. For the exact solution, in the limit in which the sphere is decompacted, a k -sector can be mimicked by the presence of k -fundamental charges at ∞, according to Witten’s suggestion. However, this property does not hold before decompaction or for the genuine perturbative solution which corresponds to the zero-instanton contribution on S 2 .

  • Wilson loops in the Adjoint Representation and multiple vacua in two-dimensional Yang-Mills theory
    Annals of Physics, 2000
    Co-Authors: A. Bassetto, Luca Griguolo, F. Vian
    Abstract:

    $QCD_2$ with fermions in the Adjoint Representation is invariant under $SU(N)/Z_N$ and thereby is endowed with a non-trivial vacuum structure (k-sectors). The static potential between Adjoint charges, in the limit of infinite mass, can be therefore obtained by computing Wilson loops in the pure Yang-Mills theory with the same non-trivial structure. When the (Euclidean) space-time is compactified on a sphere $S^2$, Wilson loops can be exactly expressed in terms of an infinite series of topological excitations (instantons). The presence of k-sectors modifies the energy spectrum of the theory and its instanton content. For the exact solution, in the limit in which the sphere is decompactified, a k-sector can be mimicked by the presence of k-fundamental charges at $\infty$, according to a Witten’s suggestion. However this property neither holds before decompactification nor for the genuine perturbative solution which corresponds to the zero-instanton contribution on $S^2$.

Kimmo Tuominen – One of the best experts on this subject based on the ideXlab platform.

A. Bassetto – One of the best experts on this subject based on the ideXlab platform.

  • wilson loops in the Adjoint Representation and multiple vacua in two dimensional yang mills theory
    Annals of Physics, 2000
    Co-Authors: A. Bassetto, Luca Griguolo, F. Vian
    Abstract:

    Abstract QCD 2 with fermions in the Adjoint Representation is invariant under SU ( N )/ Z N and thereby is endowed with a nontrivial vacuum structure ( k -sectors). The static potential between Adjoint charges, in the limit of infinite mass, can be therefore obtained by computing Wilson loops in the pure Yang–Mills theory with the same nontrivial structure. When the (Euclidean) space-time is compacted on a sphere S 2 , Wilson loops can be exactly expressed in terms of an infinite series of topological excitations (instantons). The presence of k -sectors modifies the energy spectrum of the theory and its instanton content. For the exact solution, in the limit in which the sphere is decompacted, a k -sector can be mimicked by the presence of k -fundamental charges at ∞, according to Witten’s suggestion. However, this property does not hold before decompaction or for the genuine perturbative solution which corresponds to the zero-instanton contribution on S 2 .

  • Wilson loops in the Adjoint Representation and multiple vacua in two-dimensional Yang-Mills theory
    Annals of Physics, 2000
    Co-Authors: A. Bassetto, Luca Griguolo, F. Vian
    Abstract:

    $QCD_2$ with fermions in the Adjoint Representation is invariant under $SU(N)/Z_N$ and thereby is endowed with a non-trivial vacuum structure (k-sectors). The static potential between Adjoint charges, in the limit of infinite mass, can be therefore obtained by computing Wilson loops in the pure Yang-Mills theory with the same non-trivial structure. When the (Euclidean) space-time is compactified on a sphere $S^2$, Wilson loops can be exactly expressed in terms of an infinite series of topological excitations (instantons). The presence of k-sectors modifies the energy spectrum of the theory and its instanton content. For the exact solution, in the limit in which the sphere is decompactified, a k-sector can be mimicked by the presence of k-fundamental charges at $\infty$, according to a Witten’s suggestion. However this property neither holds before decompactification nor for the genuine perturbative solution which corresponds to the zero-instanton contribution on $S^2$.

Mojtaba Nouraddini – One of the best experts on this subject based on the ideXlab platform.

  • right suq 2 and left suq 1 2 invariances of the q hilbert schmidt scalar products for an Adjoint Representation of the quantum algebra uq su2
    Journal of Geometry and Physics, 2016
    Co-Authors: H. Fakhri, Mojtaba Nouraddini
    Abstract:

    Abstract The Jordan–Schwinger realization is used to construct tensor operators as the even and odd dimensional irreducible submodules of an Adjoint Representation of the quantum algebra U q ( s u 2 ) . All U q ( s u 2 ) -submodules are equipped with the so-called left and right q -Hilbert–Schmidt scalar products by using the Wigner–Eckart theorem. The bases of all irreducible submodules of the Adjoint Representation are orthonormal with respect to the left q -Hilbert–Schmidt scalar product, and are orthogonal, but not normalized, with respect to the right one. Consequently, only with respect to the left q -Hilbert–Schmidt scalar product, the Adjoint Representation of the quantum algebra U q ( s u 2 ) on the tensor operators is a ∗ –Representation. We show that both left and right q -Hilbert–Schmidt scalar products are right S U q ( 2 ) -invariant and left S U q − 1 ( 2 ) -invariant. Moreover, every irreducible submodule of the Adjoint Representation of the quantum algebra U q ( s u 2 ) as an associative algebra with unit, is a left quantum space for O ( S U q − 1 ( 2 ) ) and a right quantum space for O ( S U q ( 2 ) ) . Finally, it is shown that there is a natural compatibility between the coproducts and the Haar measures of the quantum groups O ( S U q − 1 ( 2 ) ) and O ( S U q ( 2 ) ) and the definitions of the left and right q -Hilbert–Schmidt scalar products on the tensor operators of the Hopf algebra U q ( s u 2 ) .

  • From the Wigner-Eckart theorem to the Hilbert-Schmidt scalar product for an Adjoint Representation of the quantum algebra Up,q(su2)
    International Journal of Geometric Methods in Modern Physics, 2016
    Co-Authors: H. Fakhri, Mojtaba Nouraddini
    Abstract:

    Irreducible tensor operators as the irreducible submodules of an Adjoint Representation of the two-parametric quantum ∗-algebra Up,q(su2) are constructed by using its Jordan–Schwinger formulation on two independent (p,q)-oscillator ∗-algebras. All Up,q(su2)-submodules are equipped with an appropriate Hilbert–Schmidt scalar product with the help of the Wigner–Eckart theorem. We show that with respect to this scalar product, not only the bases of all irreducible submodules of the Adjoint Representation are orthonormal, but also the Adjoint Representation is a ∗-Representation.

  • Right SUq(2) – and left SUq−1(2) -invariances of the q -Hilbert–Schmidt Scalar products for an Adjoint Representation of the quantum algebra Ŭq(su2)
    Journal of Geometry and Physics, 2016
    Co-Authors: H. Fakhri, Mojtaba Nouraddini
    Abstract:

    Abstract The Jordan–Schwinger realization is used to construct tensor operators as the even and odd dimensional irreducible submodules of an Adjoint Representation of the quantum algebra U q ( s u 2 ) . All U q ( s u 2 ) -submodules are equipped with the so-called left and right q -Hilbert–Schmidt scalar products by using the Wigner–Eckart theorem. The bases of all irreducible submodules of the Adjoint Representation are orthonormal with respect to the left q -Hilbert–Schmidt scalar product, and are orthogonal, but not normalized, with respect to the right one. Consequently, only with respect to the left q -Hilbert–Schmidt scalar product, the Adjoint Representation of the quantum algebra U q ( s u 2 ) on the tensor operators is a ∗ –Representation. We show that both left and right q -Hilbert–Schmidt scalar products are right S U q ( 2 ) -invariant and left S U q − 1 ( 2 ) -invariant. Moreover, every irreducible submodule of the Adjoint Representation of the quantum algebra U q ( s u 2 ) as an associative algebra with unit, is a left quantum space for O ( S U q − 1 ( 2 ) ) and a right quantum space for O ( S U q ( 2 ) ) . Finally, it is shown that there is a natural compatibility between the coproducts and the Haar measures of the quantum groups O ( S U q − 1 ( 2 ) ) and O ( S U q ( 2 ) ) and the definitions of the left and right q -Hilbert–Schmidt scalar products on the tensor operators of the Hopf algebra U q ( s u 2 ) .

Kari Rummukainen – One of the best experts on this subject based on the ideXlab platform.

  • Perturbative improvement of SU(2) gauge theory with two Wilson fermions in the Adjoint Representation
    arXiv: High Energy Physics – Lattice, 2010
    Co-Authors: Tuomas Karavirta, Anne-mari Mykkanen, Jarno Rantaharju, Kari Rummukainen, Kimmo Tuominen
    Abstract:

    We present a perturbative calculation of the improvement coefficients of SU(2) gauge theory with Adjoint Representation Wilson-clover fermions and using Schrodinger functional boundary conditions. The computation of the boundary improvement terms is necessary for the full O(a) improvement. With two flavours of Adjoint Representation fermions this theory is called Minimal Walking Technicolor model.

  • non perturbatively improved clover action for su 2 gauge fundamental and Adjoint Representation fermions
    arXiv: High Energy Physics – Lattice, 2010
    Co-Authors: Tuomas Karavirta, Kimmo Tuominen, Anne-mari Mykkanen, Jarno Rantaharju, Kari Rummukainen
    Abstract:

    The research of strongly coupled beyond-the-standard-model theories has generated significant interest in non-abelian gauge field theories with different number of fermions in different Representations. Motivated by the increased interest to various technicolor scenarios, we study the non-perturbative improvement of the Wilson-clover action with SU(2) gauge fields and 2 flavors of fermions in the fundamental and Adjoint Representations. The Sheikholeslami-Wohlert coefficients are fixed using Schroedinger functional boundary conditions. The Adjoint Representation theory is a candidate for a “minimal technicolor” theory, already studied on the lattice using unimproved Wilson fermions.

  • Non-perturbatively improved clover action for SU(2) gauge + fundamental and Adjoint Representation fermions
    arXiv: High Energy Physics – Lattice, 2010
    Co-Authors: Anne-mari Mykkanen, Tuomas Karavirta, Jarno Rantaharju, Kari Rummukainen, Kimmo Tuominen
    Abstract:

    The research of strongly coupled beyond-the-standard-model theories has generated significant interest in non-abelian gauge field theories with different number of fermions in different Representations. Motivated by the increased interest to various technicolor scenarios, we study the non-perturbative improvement of the Wilson-clover action with SU(2) gauge fields and 2 flavors of fermions in the fundamental and Adjoint Representations. The Sheikholeslami-Wohlert coefficients are fixed using Schroedinger functional boundary conditions. The Adjoint Representation theory is a candidate for a “minimal technicolor” theory, already studied on the lattice using unimproved Wilson fermions.