An Unpublished Slovak Manuscript

Abstract

Through the gracious courtesy of the Hungarian authorities I have been permitted to seek for Slavonic material in the Royal Hungarian National Museum. I was gratified to find that owing to a millennium of close contacts between the Magyar and the Slav, Budapest contains much interesting material. During this search I was fortunate enough to come upon the unpublished manuscript which is here reproduced. It was found by itself and was not a part of any collection. For purposes of identification I suggest calling it Slovak Manuscript M.M.C.

Quantum field theory of non-abelian strings and vortices

“…2.2, it is an inevitable consequence of the non-abelian Aharonov-Bohm phenomenon that a loop of string (or a pair of vortices) can carry charge, and can exchange charge with other charged objects [5,12,13]. Let us see how this property is reflected in the behavior of the correlation functions of our string operators [30].…”

“…Thus we see that charge is transferred to the vortex pair, via the non-abelian Aharonov-Bohm effect, when a charged particle winds around the vortex [5,12,131; an initially uncharged vortex pair becomes a non-trivial superposition of charge eigenstates. This is "Cheshire charge."…”

“…Aside from their topological charges, vortices can also carry ordinary H quantum numbers [5,12,13]. These are easiest to discuss if we consider a vortex-antivortex pair, with trivial total topological charge.…”

“…Thus, even when .~and C are far apart, (A~C~, x0 C)) is not a purely topological quantity that depends only on the linking number of~and C. Of course, in higher orders in the strong coupling expansion, the behavior of~becomes still more complicated. Similarly, if a loop C links with two different surfaces .~,and~2' the operator A~'~,,2(.Z1, .12, x0 C) acquires a factor (1/n)~~(a,) each time the electric flux tube crosses .1~and a factor (1/n~)~°~(a2) each time it crosses 12 (in the leading order of the strong-coupling expansion). Because of confinement, the string world-sheets combine as trivial charge eigenstates rather than group eigenstates, even though both are defined with respect to a common basepoint.…”

“…In that case, we say that the string is "non-abelian" [10]. The physical properties of a non-abelian string are qualitatively different from the properties of an abelian string [5,6,[11][12][13].In particular, a ioop of non-abelian string (or a pair of non-abelian vortices, in 2 + 1 dimensions) can carry a non-trivial gauge charge, so that the loop has an Aharonov-Bohm interaction with other strings. Moreover, non-abelian Aharonov-Bohm interactions involve transfer of charge between string ioops and charged particles.…”