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SUMMARY:On generalized Melvin solutions for Lie algebras of rank 4
DTSTART;VALUE=DATE-TIME:20201006T080000Z
DTEND;VALUE=DATE-TIME:20201006T082000Z
DTSTAMP;VALUE=DATE-TIME:20260515T132832Z
UID:indico-contribution-2109@cern.ch
DESCRIPTION:Speakers: Sergei Bolokhov ()\nWe consider generalized Melvin-l
 ike solutions associated with Lie algebras of rank $4$ (namely\, $A_4$\, $
 B_4$\, $C_4$\, $D_4$\, and the exceptional algebra $F_4$} corresponding to
  certain internal symmetries of the solutions. The system under considerat
 ion is a static cylindrically-symmetric gravitational configuration in $D$
  dimensions in presence of four Abelian 2-forms and four scalar fields. Th
 e solution is governed by four moduli functions $H_s(z)$ ($s = 1\,...\,4$)
  of squared radial coordinate $z=\\rho^2$ obeying four differential equati
 ons of the Toda chain type. These functions turn out to be polynomials of 
 powers $(n_1\,n_2\, n_3\, n_4) = (4\,6\,6\,4)\, (8\,14\,18\,10)\, (7\,12\,
 15\,16)\, (6\,10\,6\,6)\, (22\,42\,30\,16)$ for Lie algebras $A_4$\, $B_4$
 \, $C_4$\, $D_4$\, $F_4$\, respectively. The asymptotic behaviour for the 
 polynomials at large distances is governed by some integer-valued $4 \\tim
 es 4$ matrix $\\nu$ connected in a certain way with the inverse Cartan mat
 rix of the Lie algebra and (in $A_4$ case) the matrix representing a gener
 ator of the $Z_2$-group of symmetry of the Dynkin diagram. The symmetry pr
 operties and duality identities for polynomials are obtained\, as well as 
 asymptotic relations for solutions at large distances. We also calculate 2
 -form flux integrals over  $2$-dimensional discs and corresponding Wilson 
 loop factors over their boundaries.\n\nhttps://indico.particle.mephi.ru/ev
 ent/35/contributions/2109/
LOCATION:Zoom
URL:https://indico.particle.mephi.ru/event/35/contributions/2109/
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