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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:20260422T090629Z
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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