15,392 research outputs found

### On G/H geometry and its use in M-theory compactifications

The Riemannian geometry of coset spaces is reviewed, with emphasis on its
applications to supergravity and M-theory compactifications. Formulae for the
connection and curvature of rescaled coset manifolds are generalized to the
case of nondiagonal Killing metrics.
The example of the N^{010} spaces is discussed in detail. These are a
subclass of the coset manifolds N^{pqr}=G/H = SU(3) x U(1)/U(1) x U(1), the
integers p,q,r characterizing the embedding of H in G. We study the realization
of N^{010} as G/H=SU(3) x SU(2)/U(1) x SU(2) (with diagonal embedding of the
SU(2) \in H into G). For a particular G-symmetric rescaling there exist three
Killing spinors, implying N=3 supersymmetry in the AdS_4 \times N^{010}
compactification of D=11 supergravity. This rescaled N^{010} space is of
particular interest for the AdS_4/CFT_3 correspondence, and its SU(3) x SU(2)
isometric realization is essential for the OSp(4|3) classification of the
Kaluza-Klein modes.Comment: 12 page

### Supergravity in the group-geometric framework: a primer

We review the group-geometric approach to supergravity theories, in the
perspective of recent developments and applications. Usual diffeomorphisms,
gauge symmetries and supersymmetries are unified as superdiffeomorphisms in a
supergroup manifold. Integration on supermanifolds is briefly revisited, and
used as a tool to provide a bridge between component and superspace actions. As
an illustration of the constructive techniques, the cases of $d=3,4$ off-shell
supergravities and $d=5$ Chern-Simons supergravity are discussed in detail. A
cursory account of $d=10+2$ supergravity is also included. We recall a
covariant canonical formalism, well adapted to theories described by
Lagrangians $d$-forms, that allows to define a form hamiltonian and to recast
constrained hamiltonian systems in a covariant form language. Finally, group
geometry and properties of spinors and gamma matrices in $d=s+t$ dimensions are
summarized in Appendices.Comment: LaTeX, 65 pages, 2 Tables, 1 figure. v2: included Figure missing in
v1, ref.s added. v3: added missing term in eq. (9.3). v4: eq. (9.41)
corrected. Matches published version. v5: added missing terms in eq.s (7.21),
(7.24), (7.27), (9.38), added a paragraph in Sect. 11, added re

### The complete N=3 Kaluza Klein spectrum of 11D supergravity on AdS_4 x N^{010}

We derive the invariant operators of the zero-form, the one-form, the
two-form and the spinor from which the mass spectrum of Kaluza Klein of
eleven-dimensional supergravity on AdS_4 x N^{010} can be derived by means of
harmonic analysis. We calculate their eigenvalues for all representations of
SU(3)xSO(3). We show that the information contained in these operators is
sufficient to reconstruct the complete N=3 supersymmetry content of the
compactified theory. We find the N=3 massless graviton multiplet, the Betti
multiplet and the SU(3) Killing vector multiplet.Comment: 1+50 pages, LaTe

### The structure of N=3 multiplets in AdS_4 and the complete Osp(3|4) X SU(3) spectrum of M-theory on AdS_4 X N^{010}

In this paper, relying on previous results of one of us on harmonic analysis,
we derive the complete spectrum of Osp(3|4) X SU(3) multiplets that one obtains
compactifying D=11 supergravity on the unique homogeneous space N^{0,1,0} that
has a tri-sasakian structure, namely leads to N=3 supersymmetry both in the
four-dimensional bulk and on the three-dimensional boundary. As in previously
analyzed cases the knowledge of the Kaluza Klein spectrum, together with
general information on the geometric structure of the compact manifold is an
essential ingredient to guess and construct the corresponding superconformal
field theory. This is work in progress. As a bonus of our analysis we derive
and present the explicit structure of all unitary irreducible representations
of the superalgebra Osp(3|4) with maximal spin content s_{max}>=2.Comment: Latex2e, 13+1 page

### The Lagrangian of q-Poincare' Gravity

The gauging of the q-Poincar\'e algebra of ref. hep-th 9312179 yields a
non-commutative generalization of the Einstein-Cartan lagrangian. We prove its
invariance under local q-Lorentz rotations and, up to a total derivative, under
q-diffeomorphisms. The variations of the fields are given by their q-Lie
derivative, in analogy with the q=1 case. The algebra of q-Lie derivatives is
shown to close with field dependent structure functions. The equations of
motion are found, generalizing the Einstein equations and the zero-torsion
condition.Comment: 12 pp., LaTeX, DFTT-01/94 (extra blank lines introduced by mailer,
corrupting LaTeX syntax, have been hopefully eliminated

### 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}.Comment: 18 pages, LaTe

### A locally supersymmetric $SO(10,2)$ invariant action for $D=12$ supergravity

We present an action for $N=1$ supergravity in $10+2$ dimensions, containing
the gauge fields of the $OSp(1|64)$ superalgebra, i.e. one-forms $B^{(n)}$ with
$n$=1,2,5,6,9,10 antisymmetric D=12 Lorentz indices and a Majorana gravitino
$\psi$. The vielbein and spin connection correspond to $B^{(1)}$ and $B^{(2)}$
respectively. The action is not gauge invariant under the full $OSp(1|64)$
superalgebra, but only under a subalgebra ${\tilde F}$ (containing the $F$
algebra $OSp(1|32)$), whose gauge fields are $B^{(2)}$, $B^{(6)}$, $B^{(10)}$
and the Weyl projected Majorana gravitino ${1 \over 2} (1+\Gamma_{13}) \psi$.
Supersymmetry transformations are therefore generated by a Majorana-Weyl
supercharge and, being part of a gauge superalgebra, close off-shell. The
action is simply $\int STr ({\bf R}^6 {\bf \Gamma})$ where ${\bf R}$ is the
$OSp(1|64)$ curvature supermatrix two-form, and ${\bf \Gamma}$ is a constant
supermatrix involving $\Gamma_{13}$ and breaking $OSp(1|64)$ to its ${\tilde
F}$ subalgebra. The action includes the usual Einstein-Hilbert term.Comment: LaTeX, 13 pages. Added a reference, a Table in Appendix A for the
gamma commutations in d=12, and corrected eq. (4.14) for the Einstein-Hilbert
term; v4: corrected formulas (A.3), (A.4) and (A.10), modified last paragraph
of Section 5, added acknowledgement

### Differential calculi on finite groups

A brief review of bicovariant differential calculi on finite groups is given,
with some new developments on diffeomorphisms and integration. We illustrate
the general theory with the example of the nonabelian finite group S_3.Comment: LaTeX, 16 pages, 1 figur

### Reductionism, Emergence, and Effective Field Theories

In recent years, a change in attitude in particle physics has led to our
understanding current quantum field theories as effective field theories
(EFTs). The present paper is concerned with the significance of this EFT
approach, especially from the viewpoint of the debate on reductionism in
science. In particular, it is a purpose of this paper to clarify how EFTs may
provide an interesting case-study in current philosophical discussion on
reduction, emergence and inter-level relationships in general.Comment: 18 pages, LateX2e, to appear in Studies in History and Philosophy of
Modern Physic

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