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SUMMARY:On generalized Melvin solutions for Lie algebras of rank $3$
DTSTART;VALUE=DATE-TIME:20181025T141000Z
DTEND;VALUE=DATE-TIME:20181025T143000Z
DTSTAMP;VALUE=DATE-TIME:20200530T065352Z
UID:indico-contribution-1073@cern.ch
DESCRIPTION:Speakers: Vladimir Ivashchuk ()\nGeneralized Melvin solutions
for rank-$3$ Lie algebras $A_3$\, $B_3$ and $C_3$\n are considered. Any
solution contains metric\, three Abelian 2-forms and\n three scalar fields
. It is governed by three moduli functions $H_1(z)\,H_2(z)\,H_3(z)$\n ($z
= \\rho^2$ and $\\rho$ is a radial variable)\, obeying\n three different
ial equations with certain boundary conditions\n imposed. These functions
are polynomials with powers $(n_1\,n_2\, n_3) = (3\,4\,3)\, (6\,10\,6)\, (
5\,8\,9)$ for\n Lie algebras $A_3$\, $B_3$\, $C_3$\, respectively. \n The
solutions depend upon integration constants $q_1\, q_2\, q_3 \\neq 0$.\n
The power-law asymptotic relations for polynomials at large $z$ \n are
governed by integer-valued $3 \\times 3$ matrix $\\nu$\, which coincides
\n with twice the inverse Cartan matrix $2 A^{-1}$ for Lie algebras $
B_3$ and $C_3$\, while in the $A_3$ case $\\nu = A^{-1} (I + P)$\, wh
ere $I$ is the identity matrix and $P$ is a permutation matrix\, cor
responding to a generator of the $\\mathbb{Z}_2$-group of symmetry of
the Dynkin diagram. The duality identities for polynomials and asymp
totic relations for solutions at large distances are obtained. 2-form fl
ux integrals over a $2$-dimensional disc of radius $R$ and correspond
ing Wilson loop factors over a circle of radius $R$ are presented.\n\nhttp
s://indico.particle.mephi.ru/event/22/contributions/1073/
LOCATION:Hotel Intourist Kolomenskoye 4* Moskvorechye 1 hall
URL:https://indico.particle.mephi.ru/event/22/contributions/1073/
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