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SUMMARY:Witten index for weak supersymmetric systems: invariance under def
ormations
DTSTART;VALUE=DATE-TIME:20221007T090000Z
DTEND;VALUE=DATE-TIME:20221007T110000Z
DTSTAMP;VALUE=DATE-TIME:20221209T093714Z
UID:indico-event-1192227@indico.cern.ch
DESCRIPTION:When a $4D$ supersymmetric theory is placed on $S^3 \\times \\
mathbb{R}$\, the supersymmetric algebra is necessarily modified to $su(2|1
)$ (its central extension) and we are dealing with a {\\it weak} supersy
mmetric system. For such systems\, the excited states of the Hamiltonian a
re not all paired. As a result\, the Witten index Tr$\\{(-1)^F e^{-\\beta
H}\\}$ is no longer an integer number\, but a $\\beta$-dependent function.
This index is often called ``superconformal index"\, because it is useful
for studying dualities in superconformal gauge theories\, but conformal s
ymmetry plays no role in its definition. Similarly to the ordinary Witt
en index\, this index stays invariant under deformations of the theory tha
t keep the supersymmetry algebra intact. Based on the Hilbert space analys
is\, we give a simple general proof of this fact. We then show how this in
variance works for two simplest weak supersymmetric quantum mechanical sys
tems involving a real or a complex bosonic degree of freedom. There exist
also weak supersymmetric quantum mechanical systems based on the central
extension of the algebra $su(N|1)$ with arbitrary $N$.We present a coupl
e of examples of such systems and discuss their dynamics.\n\nhttps://indic
o.cern.ch/event/1192227/
LOCATION:CERN 4/3-006 - TH Conference Room
URL:https://indico.cern.ch/event/1192227/
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