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L. Castellani

Publications and source records attributed to L. Castellani.

At least 19 recordsLinked to original sources
arXiv2025

The $L_\infty$ structure of Free Differential Algebras and $d=11$ Supergravity

We discuss free differential algebras (FDA's), a generalization of the Cartan-Maurer equations for the group manifold vielbein, appropriate for theories containing $p$-forms ($p >1$). Their dual formulation is an extension of Lie algebras, called $L_\infty$ algebras, and we illustrate this duality in a simple example. Finally we review the FDA structure and the dual $L_\infty$ structure of $d=11$ supergravity.

hep-th↗
arXiv2020

Overhaul and Installation of the ICARUS-T600 Liquid Argon TPC Electronics for the FNAL Short Baseline Neutrino Program

The ICARUS T600 liquid argon (LAr) time projection chamber (TPC) underwent a major overhaul at CERN in 2016-2017 to prepare for the operation at FNAL in the Short Baseline Neutrino (SBN) program. This included a major upgrade of the photo-multiplier system and of the TPC wire read-out electronics. The full TPC wire read-out electronics together with the new wire biasing and interconnection scheme are described. The design of a new signal feed-through flange is also a fundamental piece of this overhaul whose major feature is the integration of all electronics components onto the signal flange. Initial functionality tests of the full TPC electronics chain installed in the T600 detector at FNAL are also described.

physics.ins-det↗
arXiv2020

Chern-Simons Supergravity on Supergroup Manifolds

We construct N=1 d=3 AdS supergravity within the group manifold approach and compare it with Achucarro-Townsend Chern-Simons formulation of the same theory. We clarify the relation between the off-shell super gauge transformations of the Chern-Simons theory and the off-shell worldvolume supersymmetry transformations of the group manifold action. We formulate the Achucarro-Townsend model in a double supersymmetric action where the Chern-Simons theory with a supergroup gauge symmetry is constructed on a supergroup manifold. This framework is useful to establish a correspondence of degrees of freedom and auxiliary fields between the two descriptions of d=3 supergravity.

hep-th↗
arXiv2018

New read-out electronics for ICARUS-T600 liquid Argon TPC. Description, simulation and tests of the new front-end and ADC system

The ICARUS T600, a liquid argon time projection chamber (LAr-TPC) detector mainly devoted to neutrino physics, underwent a major overhauling at CERN in 2016-2017, which included also a new design of the read-out electronics, in view of its operation in Fermilab on the Short Baseline Neutrino (SBN) beam from 2019. The new more compact electronics showed capability of handling more efficiently the signals also in the intermediate Induction 2 wire plane with a significant increase of signal to noise (S/N), allowing for charge measurement also in this view. The new front-end and the analog to digital conversion (ADC) system are presented together with the results of the tests on 50 liters liquid argon TPC performed at CERN with cosmic rays.

physics.ins-det↗
arXiv2017

Wess-Zumino and Super Yang-Mills Theories in D=4 Integral Superspace

We reconstruct the action of $N=1, D=4$ Wess-Zumino and $N=1, 2, D=4$ super-Yang-Mills theories, using integral top forms on the supermanifold ${\cal M}^{(4|4)}$. Choosing different Picture Changing Operators, we show the equivalence of their rheonomic and superspace actions. The corresponding supergeometry and integration theory are discussed in detail. This formalism is an efficient tool for building supersymmetric models in a geometrical framework.

hep-th↗
arXiv2017

Super Quantum Mechanics in the Integral Form Formalism

We reformulate Super Quantum Mechanics in the context of integral forms. This framework allows to interpolate between different actions for the same theory, connected by different choices of Picture Changing Operators (PCO). In this way we retrieve component and superspace actions, and prove their equivalence. The PCO are closed integral forms, and can be interpreted as super Poincaré duals of bosonic submanifolds embedded into a supermanifold.. We use them to construct Lagrangians that are top integral forms, and therefore can be integrated on the whole supermanifold. The $D=1, ~N=1$ and the $D=1,~ N=2$ cases are studied, in a flat and in a curved supermanifold. In this formalism we also consider coupling with gauge fields, Hilbert space of quantum states and observables.

hep-th↗
arXiv2016

Integral representations in supermanifolds: super Hodge duals, PCOs and Liouville forms

We present few types of integral transforms and integral representations that are very useful for extending to supergeometry many familiar concepts of differential geometry. Among them we discuss the construction of the super Hodge dual, the integral representation of picture changing operators of string theories and the construction of the super-Liouville form of a symplectic supermanifold.

hep-th↗
arXiv2016

The Integral Form of Supergravity

By using integral forms we derive the superspace action of D=3, N=1 supergravity as an integral on a supermanifold. The construction is based on target space picture changing operators, here playing the role of Poincare' duals to the lower-dimensional spacetime surfaces embedded into the supermanifold. We show how the group geometrical action based on the group manifold approach interpolates between the superspace and the component supergravity actions, thus providing another proof of their equivalence.

hep-th↗
arXiv2015

The Hodge Operator Revisited

We present a new construction for the Hodge operator for differential manifolds based on a Fourier (Berezin)-integral representation. We find a simple formula for the Hodge dual of the wedge product of differential forms, using the (Berezin)-convolution. The present analysis is easily extended to supergeometry and to non-commutative geometry.

hep-th↗
arXiv2015

The Geometry of Supermanifolds and New Supersymmetric Actions

We construct the Hodge dual for supermanifolds by means of the Grassmannian Fourier transform of superforms. In the case of supermanifolds it is known that the superforms are not sufficient to construct a consistent integration theory and that the integral forms are needed. They are distribution-like forms which can be integrated on supermanifolds as a top form can be integrated on a conventional manifold. In our construction of the Hodge dual of superforms they arise naturally. The compatibility between Hodge duality and supersymmetry is exploited and applied to several examples. We define the irreducible representations of supersymmetry in terms of integral and superforms in a new way which can be easily generalised to several models in different dimensions. The construction of supersymmetric actions based on the Hodge duality is presented and new supersymmetric actions with higher derivative terms are found. These terms are required by the invertibility of the Hodge operator.

hep-th↗
arXiv2014

Supergravity Actions with Integral Forms

Integral forms provide a natural and powerful tool for the construction of supergravity actions. They are generalizations of usual differential forms and are needed for a consistent theory of integration on supermanifolds. The group geometrical approach to supergravity and its variational principle are reformulated and clarified in this language. Central in our analysis is the Poincare' dual of a bosonic manifold embedded into a supermanifold. Finally, using integral forms we provide a proof of Gates' so-called "Ectoplasmic Integration Theorem", relating superfield actions to component actions.

hep-th↗
arXiv2012

Noncommutative gauge fields coupled to noncommutative gravity

We present a noncommutative (NC) version of the action for vielbein gravity coupled to gauge fields. Noncommutativity is encoded in a twisted star product between forms, with a set of commuting background vector fields defining the (abelian) twist. A first order action for the gauge fields avoids the use of the Hodge dual. The NC action is invariant under diffeomorphisms and twisted gauge transformations. The Seiberg-Witten map, adapted to our geometric setting and generalized for an arbitrary abelian twist, allows to re-express the NC action in terms of classical fields: the result is a deformed action, invariant under diffeomorphisms and usual gauge transformations. This deformed action is a particular higher derivative extension of the Einstein-Hilbert action coupled to Yang-Mills fields, and to the background vector fields defining the twist. Here noncommutativity of the original NC action dictates the precise form of this extension. We explicitly compute the first order correction in the NC parameter of the deformed action, and find that it is proportional to cubic products of the gauge field strength and to the symmetric anomaly tensor D_{IJK}.

hep-th↗
arXiv2003

Discretized Yang-Mills and Born-Infeld actions on finite group geometries

Discretized nonabelian gauge theories living on finite group spaces G are defined by means of a geometric action \int Tr F \wedge *F. This technique is extended to obtain discrete versions of the Born-Infeld action. The discretizations are in 1-1 correspondence with differential calculi on finite groups. A consistency condition for duality invariance of the discretized field equations is derived for discretized U(1) actions S[F] living on a 4-dimensional abelian G. Discretized electromagnetism satisfies this condition and therefore admits duality rotations. Yang-Mills and Born-Infeld theories are also considered on product spaces M^D x G, and we find the corresponding field theories on M^D after Kaluza-Klein reduction on the G discrete internal spaces. We examine in some detail the case G=Z_N, and discuss the limit N -> \infty. A self-contained review on the noncommutative differential geometry of finite groups is included.

hep-th↗
arXiv2002

Noncommutative de Rham cohomology of finite groups

We study de Rham cohomology for various differential calculi on finite groups G up to order 8. These include the permutation group S_3, the dihedral group D_4 and the quaternion group Q. Poincare' duality holds in every case, and under some assumptions (essentially the existence of a top form) we find that it must hold in general. A short review of the bicovariant (noncommutative) differential calculus on finite G is given for selfconsistency. Exterior derivative, exterior product, metric, Hodge dual, connections, torsion, curvature, and biinvariant integration can be defined algebraically. A projector decomposition of the braiding operator is found, and used in constructing the projector on the space of 2-forms. By means of the braiding operator and the metric a knot invariant is defined for any finite group.

math-ph↗
arXiv2000

New AdS(3) x G/H compactifications of chiral IIB supergravity

We present a new class of solutions of D=10, N=2 chiral supergravity. A nonvanishing background for the field strength G_{MNR} of the complex two-form triggers AdS_3 x M_7 compactifications, where M_7 is a 7-dimensional compact manifold. When M_7 is a nonsymmetric coset space G/H, we can always find a set of constants G_{MNR} covariantly conserved and thus satisfying the field equations. For example the structure constants of G with indices in the G/H directions are a covariantly conserved tensor. In some symmetric G/H, where these structure constants vanish, there may still exist conserved 3-forms, yielding AdS_3 x G/H solutions. The conditions for supersymmetry of the AdS_3 x M_7 compactifications are derived, and tested for the supersymmetric solutions AdS_3 x S^3 x T^4 and AdS_3 x S^3 x S^3 x S^1. Finally, we show that the AdS_3 x S^3 x T^4 supersymmetric background can be seen as the sigma = 0 limit in a one-parameter class of solutions of the form AdS_3 x S^3 x CP^2, the parameter sigma being the inverse "radius" of CP^2. For sigma different from 0 all supersymmetries are broken.

hep-th↗
arXiv1998

G/H M-branes and AdS_{p+2} Geometries

We prove the existence of a new class of BPS saturated M-branes. They are in one-to-one correspondence with the Freund--Rubin compactifications of M-theory on either (AdS_4) x (G/H) or (AdS_7) x (G/H), where G/H is the seven (or four) dimensional Einstein coset manifolds classified long ago in the context of Kaluza Klein supergravity. The G/H M-branes are solitons that interpolate between flat space at infinity and the old Kaluza-Klein compactifications at the horizon. They preserve N/2 supersymmetries where N is the number of Killing spinors of the (AdS) x (G/H) vacuum. A crucial ingredient in our discussion is the identification of a solvable Lie algebra parametrization of the Lorentzian non compact coset SO(2,p+1)/SO(1,p+1) corresponding to anti de Sitter space AdS_{p+2} . The solvable coordinates are those naturally emerging from the near horizon limit of the G/H p-brane and correspond to the Bertotti Robinson form of the anti-de-Sitter metric. The pull-back of anti-de-Sitter isometries on the p-brane world-volume contain, in particular, the broken conformal transformations recently found in the literature.

hep-th↗