810 research outputs found
FQHE and tt * geometry
Cumrun Vafa [1] has proposed a microscopic description of the Fractional Quantum Hall Effect (FQHE) in terms of a many-body Hamiltonian H invariant under four supersymmetries. The non-Abelian statistics of the defects (quasi-holes and quasi-particles) is then determined by the monodromy representation of the associated tt* geometry. In this paper we study the monodromy representation of the Vafa 4-susy model. Modulo some plausible assumption, we find that the monodromy representation factors through a Temperley-Lieb/Hecke algebra with q = \ub1 exp (\u3c0i/\u3bd) as predicted in [1]. The emerging picture agrees with the other predictions of [1] as well. The bulk of the paper is dedicated to the development of new concepts, ideas, and techniques in tt* geometry which are of independent interest. We present several examples of these geometric structures in various contexts
Chemistry of Chern-Simons Supergravity: reduction to a BPS kink, oxidation to M-theory and thermodynamical aspects
We construct a supersymmetric extension of the two dimensional
Kaluza-Klein-reduced gravitational Chern-Simons term, and globally study its
solutions, labelled by mass and U(1) charge c. The kink solution is BPS, and in
an appropriate conformal frame all solutions asymptotically approach AdS. The
thermodynamics of the Hawking effect yields interesting behavior for the
specific heat and hints at a Hawking-Page-like transition at T_{critical} \sim
c^{3/2}. We address implications for higher dimensions ("oxidation"), in
particular D=3,4 and 11, and comment briefly on AdS/CFT aspects of the kink.Comment: 39 pages, 2 figures. v2: reference added, minor changes, typo
Mosaic of submerged habitats in the Venice lagoon shows signs of marinization
The relationships between habitat patterns and ecosystem functioning have been widely explored in terrestrial ecosystems, but less in marine and coastal ecosystems, calling for further research in this direction. This work focuses on the mosaic of submerged habitats in the Venice lagoon, Italy. It aims to describe the habitats’ spatial patterns at multiple spatial scales, and to explore their linkages with the ecological status defined according to the EU Water Framework Directive (WFD, 2000/60/EC). The submerged habitats’ mosaic has been analysed by calculating a set of seascape metrics at different spatial scales. These metrics have been linked with the biological quality elements (BQEs) that are monitored in the lagoon in compliance to the WFD. The results show that the habitats’ spatial patterns differ between the areas of the lagoon with marine-like features and the areas which still retain more lagoon characteristics. The similarity between the pattern found in the whole lagoon and those found in marine-like areas suggests a general loss of lagoon characteristics at the lagoon scale. Regarding the ecological status, every BQE seems to be associated with a different habitat configuration at the water body scale. This does not facilitate the joint improvement of the BQEs, as required by the Directive. If we cannot achieve that, at some point we will probably have to choose what to prioritize. On a broader perspective, this calls for a reflection on what lagoon we want for the future, a vision that should be shared and account for the lagoon’s complexity, current trends and challenges
Supersymmetric black holes in 2D dilaton supergravity: baldness and extremality
We present a systematic discussion of supersymmetric solutions of 2D dilaton
supergravity. In particular those solutions which retain at least half of the
supersymmetries are ground states with respect to the bosonic Casimir function
(essentially the ADM mass). Nevertheless, by tuning the prepotential
appropriately, black hole solutions may emerge with an arbitrary number of
Killing horizons. The absence of dilatino and gravitino hair is proven.
Moreover, the impossibility of supersymmetric dS ground states and of
nonextremal black holes is confirmed, even in the presence of a dilaton. In
these derivations the knowledge of the general analytic solution of 2D dilaton
supergravity plays an important role. The latter result is addressed in the
more general context of gPSMs which have no supergravity interpretation.
Finally it is demonstrated that the inclusion of non-minimally coupled
matter, a step which is already nontrivial by itself, does not change these
features in an essential way.Comment: 30 pages, LaTeX, v2: mayor revision (rearranged title, shortened
abstract, revised introduction, inserted section from appendix to main text,
added subsection with new material on non-SUGRA gPSMs, added clarifying
remarks at some places, updated references); v3: corrected minor misprints,
added note with a new referenc
Classical and Quantum Integrability of 2D Dilaton Gravities in Euclidean space
Euclidean dilaton gravity in two dimensions is studied exploiting its
representation as a complexified first order gravity model. All local classical
solutions are obtained. A global discussion reveals that for a given model only
a restricted class of topologies is consistent with the metric and the dilaton.
A particular case of string motivated Liouville gravity is studied in detail.
Path integral quantisation in generic Euclidean dilaton gravity is performed
non-perturbatively by analogy to the Minkowskian case.Comment: 27 p., LaTeX, v2: included new refs. and a footnot
Graded Poisson-Sigma Models and Dilaton-Deformed 2D Supergravity Algebra
Fermionic extensions of generic 2d gravity theories obtained from the graded
Poisson-Sigma model (gPSM) approach show a large degree of ambiguity. In
addition, obstructions may reduce the allowed range of fields as given by the
bosonic theory, or even prohibit any extension in certain cases. In our present
work we relate the finite W-algebras inherent in the gPSM algebra of
constraints to algebras which can be interpreted as supergravities in the usual
sense (Neuveu-Schwarz or Ramond algebras resp.), deformed by the presence of
the dilaton field. With very straightforward and natural assumptions on them
--like demanding rigid supersymmetry in a certain flat limit, or linking the
anti-commutator of certain fermionic charges to the Hamiltonian constraint-- in
the ``genuine'' supergravity obtained in this way the ambiguities disappear, as
well as the obstructions referred to above. Thus all especially interesting
bosonic models (spherically reduced gravity, the Jackiw-Teitelboim model etc.)\
under these conditions possess a unique fermionic extension and are free from
new singularities. The superspace supergravity model of Howe is found as a
special case of this supergravity action. For this class of models the relation
between bosonic potential and prepotential does not introduce obstructions as
well.Comment: 22 pages, LaTeX, JHEP class. v3: Final version, to appear in JHE
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