42 research outputs found
On quantizations of complex contact manifolds
A (holomorphic) quantization of a complex contact manifold is a filtered
algebroid stack which is locally equivalent to the ring E of microdifferential
operators and which has trivial graded. The existence of a canonical
quantization has been proved by Kashiwara. In this paper we consider the
classification problem, showing that the above quantizations are classified by
the first cohomology group with values in a certain sheaf of homogeneous forms.
Secondly, we consider the problem of existence and classification for
quantizations given by algebras.Comment: Final published version (with a slightly different title from the
previous arXiv versions
Stacks of quantization-deformation modules on complex symplectic manifolds
On a complex symplectic manifold, we construct the stack of
quantization-deformation modules, that is, (twisted) modules of
microdifferential operators with an extra central parameter, a substitute to
the lack of homogeneity. We also quantize involutive submanifolds of contact
manifolds.Comment: In this new version, we have deleted from the previous one Lemma 7.6,
Proposition 7.7 and Proposition 7.8 which were erroneou
Deformation-Quantization of Complex Involutive Submanifolds
The sheaf of rings of WKB operators provides a deformation-quantization of
the cotangent bundle to a complex manifold. On a complex symplectic manifold
there may not exist a sheaf of rings locally isomorphic to a ring of WKB
operators. The idea is then to consider the whole family of locally defined
sheaves of WKB operators as the deformation-quantization of . To state it
precisely, one needs the notion of algebroid stack, introduced by Kontsevich.
In particular, the stack of WKB modules over defined in Polesello-Schapira
(see also Kashiwara for the contact case) is better understood as the stack of
modules over the algebroid stack of deformation-quantization of .
Let be an involutive submanifold of , and assume for simplicity that
the quotient of by its bicharacteristic leaves is isomorphic to a complex
symplectic manifold . The algebra of endomorphisms of a simple WKB module
along is locally (anti-)isomorphic to the pull-back of WKB operators on
. Hence we may say that a simple module provides a deformation-quantization
of . Again, since in general there do not exist globally defined simple WKB
modules, the idea is to consider the algebroid stack of locally defined simple
WKB modules as the deformation-quantization of .
In this paper we start by defining what an algebroid stack is, and how it is
locally described. We then discuss the algebroid stack of WKB operators on a
complex symplectic manifold , and define the deformation-quantization of an
involutive submanifold by means of simple WKB modules along . Finally,
we relate this deformation-quantization to that given by WKB operators on the
quotient of by its bicharacteristic leaves.Comment: 11 page
Higher Monodromy
For a given category C and a topological space X, the constant stack on X
with stalk C is the stack of locally constant sheaves with values in C. Its
global objects are classified by their monodromy, a functor from the Poincare
groupoid of X to C. In this paper we recall these notions from the point of
view of higher category theory and then define the 2-monodromy of a locally
constant stack with values in a 2-category as a 2-functor from the homotopy
2-groupoid into the 2-category. We show that 2-monodromy classifies locally
constant stacks on a reasonably well-behaved space X. As an application, we
show how to recover from this classification the cohomological version of a
classical theorem of Hopf, and we extend it to the non abelian case.Comment: 43 pages. This is a revised version of our preprint RIMS 1432
(11-2003
Stacks of twisted modules and integral transforms
Stacks were introduced by Grothendieck and Giraud and are, roughly speaking,
sheaves of categories. Kashiwara developed the theory of twisted modules, which
are objects of stacks locally equivalent to stacks of modules over sheaves of
rings. In this paper we recall these notions, and we develop the formalism of
operations for stacks of twisted modules. As an application, we state a twisted
version of an adjunction formula which is of use in the theory of integral
transforms for sheaves and D-modules.Comment: latex, 43 page
Morita classes of microdifferential algebroids
Projective cotangent bundles of complex manifolds are the local models of
complex contact manifolds. Such bundles are quantized by the algebra of
microdifferential operators (a localization of the algebra of differential
operators on the base manifold).
Kashiwara proved that any complex contact manifold is quantized by a
canonical microdifferential algebroid (a linear stack locally equivalent to an
algebra of microdifferential operators). Besides the canonical one, there can
be other microdifferential algebroids on . Our aim is to classify them. More
precisely, let be the symplectification of . We prove that Morita (resp.
equivalence) classes of microdifferential algebroids on are described by
. We also show that any linear stack locally
equivalent to a stack of microdifferential modules is in fact a stack of
modules over a microdifferential algebroid.
To obtain these results we use techniques of microlocal calculus, non-abelian
cohomology and Morita theory for linear stacks.Comment: Final version appeared in Publ. Res. Inst. Math. Sci., 42 page
Report from Working Group 3: Beyond the standard model physics at the HL-LHC and HE-LHC
This is the third out of five chapters of the final report [1] of the Workshop on Physics at HL-LHC, and perspectives on HE-LHC [2]. It is devoted to the study of the potential, in the search for Beyond the Standard Model (BSM) physics, of the High Luminosity (HL) phase of the LHC, defined as ab of data taken at a centre-of-mass energy of 14 TeV, and of a possible future upgrade, the High Energy (HE) LHC, defined as ab of data at a centre-of-mass energy of 27 TeV. We consider a large variety of new physics models, both in a simplified model fashion and in a more model-dependent one. A long list of contributions from the theory and experimental (ATLAS, CMS, LHCb) communities have been collected and merged together to give a complete, wide, and consistent view of future prospects for BSM physics at the considered colliders. On top of the usual standard candles, such as supersymmetric simplified models and resonances, considered for the evaluation of future collider potentials, this report contains results on dark matter and dark sectors, long lived particles, leptoquarks, sterile neutrinos, axion-like particles, heavy scalars, vector-like quarks, and more. Particular attention is placed, especially in the study of the HL-LHC prospects, to the detector upgrades, the assessment of the future systematic uncertainties, and new experimental techniques. The general conclusion is that the HL-LHC, on top of allowing to extend the present LHC mass and coupling reach by on most new physics scenarios, will also be able to constrain, and potentially discover, new physics that is presently unconstrained. Moreover, compared to the HL-LHC, the reach in most observables will, generally more than double at the HE-LHC, which may represent a good candidate future facility for a final test of TeV-scale new physics
Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector
A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements