The Experts below are selected from a list of 17454 Experts worldwide ranked by ideXlab platform
Joerg Teschner - One of the best experts on this subject based on the ideXlab platform.
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line operators in theories of class mathcal s quantized moduli space of flat connections and toda field theory
Journal of High Energy Physics, 2015Co-Authors: Ioana Coman, Maxime Gabella, Joerg TeschnerAbstract:Non-perturbative aspects of $$ \mathcal{N}=2 $$ supersymmetric gauge theories of class $$ \mathcal{S} $$ are deeply encoded in the Algebra of functions on the moduli space $$ {\mathrm{\mathcal{M}}}_{\mathrm{flat}} $$ of flat SL(N )- connections on Riemann surfaces. Expectation values of Wilson and ’t Hooft line operators are related to holonomies of flat connections, and expectation values of line operators in the low-energy effective theory are related to Fock-Goncharov coordinates on $$ {\mathrm{\mathcal{M}}}_{\mathrm{flat}} $$ . Via the decomposition of UV line operators into IR line operators, we determine their Noncommutative Algebra from the quantization of Fock-Goncharov Laurent polynomials, and find that it coincides with the skein Algebra studied in the context of Chern-Simons theory. Another realization of the skein Algebra is generated by Verlinde network operators in Toda field theory. Comparing the spectra of these two realizations provides non-trivial support for their equivalence. Our results can be viewed as evidence for the generalization of the AGT correspondence to higher-rank class $$ \mathcal{S} $$ theories.
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line operators in theories of class mathcal s quantized moduli space of flat connections and toda field theory
arXiv: High Energy Physics - Theory, 2015Co-Authors: Ioana Coman, Maxime Gabella, Joerg TeschnerAbstract:Non-perturbative aspects of $\mathcal{N}=2$ supersymmetric gauge theories of class $\mathcal{S}$ are deeply encoded in the Algebra of functions on the moduli space $\mathcal{M}_\text{flat}$ of flat $SL(N)$-connections on Riemann surfaces. Expectation values of Wilson and 't Hooft line operators are related to holonomies of flat connections, and expectation values of line operators in the low-energy effective theory are related to Fock-Goncharov coordinates on $\mathcal{M}_\text{flat}$. Via the decomposition of UV line operators into IR line operators, we determine their Noncommutative Algebra from the quantization of Fock-Goncharov Laurent polynomials, and find that it coincides with the skein Algebra studied in the context of Chern-Simons theory. Another realization of the skein Algebra is generated by Verlinde network operators in Toda field theory. Comparing the spectra of these two realizations provides non-trivial support for their equivalence. Our results can be viewed as evidence for the generalization of the AGT correspondence to higher-rank class $\mathcal{S}$ theories.
Ioana Coman - One of the best experts on this subject based on the ideXlab platform.
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line operators in theories of class mathcal s quantized moduli space of flat connections and toda field theory
Journal of High Energy Physics, 2015Co-Authors: Ioana Coman, Maxime Gabella, Joerg TeschnerAbstract:Non-perturbative aspects of $$ \mathcal{N}=2 $$ supersymmetric gauge theories of class $$ \mathcal{S} $$ are deeply encoded in the Algebra of functions on the moduli space $$ {\mathrm{\mathcal{M}}}_{\mathrm{flat}} $$ of flat SL(N )- connections on Riemann surfaces. Expectation values of Wilson and ’t Hooft line operators are related to holonomies of flat connections, and expectation values of line operators in the low-energy effective theory are related to Fock-Goncharov coordinates on $$ {\mathrm{\mathcal{M}}}_{\mathrm{flat}} $$ . Via the decomposition of UV line operators into IR line operators, we determine their Noncommutative Algebra from the quantization of Fock-Goncharov Laurent polynomials, and find that it coincides with the skein Algebra studied in the context of Chern-Simons theory. Another realization of the skein Algebra is generated by Verlinde network operators in Toda field theory. Comparing the spectra of these two realizations provides non-trivial support for their equivalence. Our results can be viewed as evidence for the generalization of the AGT correspondence to higher-rank class $$ \mathcal{S} $$ theories.
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line operators in theories of class mathcal s quantized moduli space of flat connections and toda field theory
arXiv: High Energy Physics - Theory, 2015Co-Authors: Ioana Coman, Maxime Gabella, Joerg TeschnerAbstract:Non-perturbative aspects of $\mathcal{N}=2$ supersymmetric gauge theories of class $\mathcal{S}$ are deeply encoded in the Algebra of functions on the moduli space $\mathcal{M}_\text{flat}$ of flat $SL(N)$-connections on Riemann surfaces. Expectation values of Wilson and 't Hooft line operators are related to holonomies of flat connections, and expectation values of line operators in the low-energy effective theory are related to Fock-Goncharov coordinates on $\mathcal{M}_\text{flat}$. Via the decomposition of UV line operators into IR line operators, we determine their Noncommutative Algebra from the quantization of Fock-Goncharov Laurent polynomials, and find that it coincides with the skein Algebra studied in the context of Chern-Simons theory. Another realization of the skein Algebra is generated by Verlinde network operators in Toda field theory. Comparing the spectra of these two realizations provides non-trivial support for their equivalence. Our results can be viewed as evidence for the generalization of the AGT correspondence to higher-rank class $\mathcal{S}$ theories.
Carlos Castro - One of the best experts on this subject based on the ideXlab platform.
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on modified weyl heisenberg Algebras noncommutativity matrix valued planck constant and qm in clifford spaces
viXra, 2009Co-Authors: Carlos CastroAbstract:A novel Weyl-Heisenberg Algebra in Clifford-spaces is constructed that is based on a matrix-valued HAB extension of Planck's constant. As a result of this modifiedWeyl-Heisenberg Algebra one will no longer be able to measure, simultaneously, the pairs of variables (x, px); (x, py); (x, pz); (y, px), ... with absolute precision. New Klein-Gordon and Dirac wave equations and dispersion relations in Clifford-spaces are presented. The latter Dirac equation is a generalization of the Dirac-Lanczos-Barut-Hestenes equation. We display the explicit isomorphism between Yang's Noncommutative space-time Algebra and the area-coordinates Algebra associated with Clifford spaces. The former Yang's Algebra involves noncommuting coordinates and momenta with a minimum Planck scale λ (ultraviolet cutoff) and a minimum momentum p = ℏ/R (maximal length R, infrared cutoff ). The double-scaling limit of Yang's Algebra λ → 0, R → ∞, in conjunction with the large n → ∞ limit, leads naturally to the area quantization condition λR = L2 = nλ2 ( in Planck area units ) given in terms of the discrete angular-momentum eigenvalues n. It is shown how Modified Newtonian dynamics is also a consequence of Yang's Algebra resulting from the modified Poisson brackets. Finally, another Noncommutative Algebra ( which differs from the Yang's Algebra ) and related to the minimal length uncertainty relations is presented . We conclude with a discussion of the implications of Noncommutative QM and QFT's in Clifford-spaces.
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on modified weyl heisenberg Algebras noncommutativity matrix valued planck constant and qm in clifford spaces
Journal of Physics A, 2006Co-Authors: Carlos CastroAbstract:A novel Weyl–Heisenberg Algebra in Clifford spaces is constructed that is based on a matrix-valued extension of Planck's constant. As a result of this modified Weyl–Heisenberg Algebra one will no longer be able to measure, simultaneously, the pairs of variables (x, px), (x, py), (x, pz), (y, px), ... with absolute precision. New Klein–Gordon and Dirac wave equations and dispersion relations in Clifford spaces are presented. The latter Dirac equation is a generalization of the Dirac–Lanczos–Barut–Hestenes equation. We display the explicit isomorphism between Yang's Noncommutative spacetime Algebra and the area-coordinates Algebra associated with Clifford spaces. The former Yang's Algebra involves noncommuting coordinates and momenta with a minimum Planck scale λ (ultraviolet cutoff) and a minimum momentum p = /R (maximal length R, infrared cutoff). The double-scaling limit of Yang's Algebra λ → 0, R → ∞, in conjunction with the large n → ∞ limit, leads naturally to the area quantization condition λR = L2 = nλ2 (in Planck area units) given in terms of the discrete angular-momentum eigenvalues n. It is shown how modified Newtonian dynamics is also a consequence of Yang's Algebra resulting from the modified Poisson brackets. Finally, another Noncommutative Algebra which differs from Yang's Algebra and related to the minimal length uncertainty relations is presented. We conclude with a discussion of the implications of Noncommutative QM and QFT's in Clifford spaces.
Maxime Gabella - One of the best experts on this subject based on the ideXlab platform.
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line operators in theories of class mathcal s quantized moduli space of flat connections and toda field theory
Journal of High Energy Physics, 2015Co-Authors: Ioana Coman, Maxime Gabella, Joerg TeschnerAbstract:Non-perturbative aspects of $$ \mathcal{N}=2 $$ supersymmetric gauge theories of class $$ \mathcal{S} $$ are deeply encoded in the Algebra of functions on the moduli space $$ {\mathrm{\mathcal{M}}}_{\mathrm{flat}} $$ of flat SL(N )- connections on Riemann surfaces. Expectation values of Wilson and ’t Hooft line operators are related to holonomies of flat connections, and expectation values of line operators in the low-energy effective theory are related to Fock-Goncharov coordinates on $$ {\mathrm{\mathcal{M}}}_{\mathrm{flat}} $$ . Via the decomposition of UV line operators into IR line operators, we determine their Noncommutative Algebra from the quantization of Fock-Goncharov Laurent polynomials, and find that it coincides with the skein Algebra studied in the context of Chern-Simons theory. Another realization of the skein Algebra is generated by Verlinde network operators in Toda field theory. Comparing the spectra of these two realizations provides non-trivial support for their equivalence. Our results can be viewed as evidence for the generalization of the AGT correspondence to higher-rank class $$ \mathcal{S} $$ theories.
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line operators in theories of class mathcal s quantized moduli space of flat connections and toda field theory
arXiv: High Energy Physics - Theory, 2015Co-Authors: Ioana Coman, Maxime Gabella, Joerg TeschnerAbstract:Non-perturbative aspects of $\mathcal{N}=2$ supersymmetric gauge theories of class $\mathcal{S}$ are deeply encoded in the Algebra of functions on the moduli space $\mathcal{M}_\text{flat}$ of flat $SL(N)$-connections on Riemann surfaces. Expectation values of Wilson and 't Hooft line operators are related to holonomies of flat connections, and expectation values of line operators in the low-energy effective theory are related to Fock-Goncharov coordinates on $\mathcal{M}_\text{flat}$. Via the decomposition of UV line operators into IR line operators, we determine their Noncommutative Algebra from the quantization of Fock-Goncharov Laurent polynomials, and find that it coincides with the skein Algebra studied in the context of Chern-Simons theory. Another realization of the skein Algebra is generated by Verlinde network operators in Toda field theory. Comparing the spectra of these two realizations provides non-trivial support for their equivalence. Our results can be viewed as evidence for the generalization of the AGT correspondence to higher-rank class $\mathcal{S}$ theories.
José M. Pérez-izquierdo - One of the best experts on this subject based on the ideXlab platform.
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The loop of formal power series with Noncommutative coefficients under substitution
São Paulo Journal of Mathematical Sciences, 2019Co-Authors: José M. Pérez-izquierdoAbstract:The set of formal power series with coefficients in an associative but Noncommutative Algebra becomes a loop with the substitution product. We study this loop by describing certain Lie and Sabinin Algebras related to it. Some examples of Lie Algebras satisfying the standard identities of degrees 5 and 6 appear naturally.
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The loop of formal power series with Noncommutative coefficients under substitution
arXiv: Group Theory, 2018Co-Authors: José M. Pérez-izquierdoAbstract:The set of formal power series with coefficients in an associative but Noncommutative Algebra becomes a loop with the substitution product. We initiate the study of this loop by describing certain Lie and Sabinin Algebras related to it. Some examples of Lie Algebras satisfying the standard identities of degrees $5$ and $6$ appear naturally.