On the 29nd of November 2018, at 10:15 a.m.
Rafał Suszek (KMMF)
will give a talk on
"Contractible $\kappa$-symmetric supergerbes on homogeneous spaces of Lie supergroups"
Abstract
Rafał Suszek (KMMF)
will give a talk on
"Contractible $\kappa$-symmetric supergerbes on homogeneous spaces of Lie supergroups"
Abstract
The geometrodynamics of
topologically charged extended objects, in
particular that of loops and paths, in the
homogeneous space ${\rm AdS}_5\times\mathbb{S}^5$ of
the supersymmetry Lie supergroup ${\rm SU}(2,2|4)$
has long been known to play an important role in
modern attempts, based on the so-called AdS/CFT
correspondence, at understanding the
non-perturbative quantum mechanics of realistic
strongly coupled systems with gauge symmetry, such
as, e.g., the quark gluon plasma. An important
feature of the dynamics is an asymptotic transtiion
into its fairly well-understood counterpart on the
super-Monikowski space under the Inonu-Wigner
contraction
$\mathfrak{su}(2,2|4)/\mathfrak{so}(4,1)\times\mathfrak{so}(5))\to
\mathfrak{siso}(9,1|32)/so(9,1)$. A rigorous
treatment of the gauge field coupling to the
topological charge carried by these objects, leading
through a supersymmetry-equivariant Dirac-type
geometrisation of the corresponding class in the
Cartan-Eilenberg cohomology of ${\rm SU}(2,2|4)$,
paves the way to a geometric quantisation of the
dynamics and a systematic construction of
supersymmetric defects central to the AdS/CFT
correspondence, and so offers hope for an in-depth
elucidation of the higher geometry behind the
holographic principle.
In my talk, I shall recapitulate the construction of the so-called super $\sigma$-model on a homogeneous space of a supersymmetry Lie supergroup $\,G\,$ associated with a distinguished super-cocycle $\,\chi\,$ that employs integrable supercentral extensions of the Lie superalgebra of $\,G\,$ induced by the super-cocycle through the standard correspondence between the Cartan-Eilenberg cohomolgy of the Lie (super)group and the Chevalley-Eilenberg cohomoogy of its Lie (super)algebra. An intrincate topological interpretation of the ensuing supersymmetry extension in terms of the Kostelecky--Rabin winding charge shall be given, and due emphasis shall be laid upon the issues of (weak) $\kappa$-equivariance of the geometrisation and its compatibility with the Inonu--Wigner contraction on the base supermanifold. The general construction shall be illustrate with the examples of the super 1-gerbe associated with the super 3-cocycle of Metsaev and Tseytlin, and the super-0-gerbe associated with Zhou's super 2-cocyle.
In my talk, I shall recapitulate the construction of the so-called super $\sigma$-model on a homogeneous space of a supersymmetry Lie supergroup $\,G\,$ associated with a distinguished super-cocycle $\,\chi\,$ that employs integrable supercentral extensions of the Lie superalgebra of $\,G\,$ induced by the super-cocycle through the standard correspondence between the Cartan-Eilenberg cohomolgy of the Lie (super)group and the Chevalley-Eilenberg cohomoogy of its Lie (super)algebra. An intrincate topological interpretation of the ensuing supersymmetry extension in terms of the Kostelecky--Rabin winding charge shall be given, and due emphasis shall be laid upon the issues of (weak) $\kappa$-equivariance of the geometrisation and its compatibility with the Inonu--Wigner contraction on the base supermanifold. The general construction shall be illustrate with the examples of the super 1-gerbe associated with the super 3-cocycle of Metsaev and Tseytlin, and the super-0-gerbe associated with Zhou's super 2-cocyle.
The seminar takes place on Thursdays from 10:15 a.m. to
12:00 in the room 2.23 of the main building of the
Faculty of Physics (the 2nd floor), Pasteur Str. 5,
Warszawa.
Additional information can be found on the webpage http://oldwww.fuw.edu.pl/KMMF/sem.czw.przedp.html.
Additional information can be found on the webpage http://oldwww.fuw.edu.pl/KMMF/sem.czw.przedp.html.