359 research outputs found
M-theory, the signature theorem, and geometric invariants
The equations of motion and the Bianchi identity of the C-field in M-theory
are encoded in terms of the signature operator. We then reformulate the
topological part of the action in M-theory using the signature, which leads to
connections to the geometry of the underlying manifold, including positive
scalar curvature. This results in a variation on the miraculous cancellation
formula of Alvarez-Gaum\'e and Witten in twelve dimensions and leads naturally
to the Kreck-Stolz s-invariant in eleven dimensions. Hence M-theory detects
diffeomorphism type of eleven-dimensional (and seven-dimensional) manifolds,
and in the restriction to parallelizable manifolds classifies topological
eleven-spheres. Furthermore, requiring the phase of the partition function to
be anomaly-free imposes restrictions on allowed values of the s-invariant.
Relating to string theory in ten dimensions amounts to viewing the bounding
theory as a disk bundle, for which we study the corresponding phase in this
formulation.Comment: 17 page
Quantum discontinuity between zero and infinitesimal graviton mass with a Lambda term
We show that the recently demonstrated absence of the usual discontinuity for
massive spin 2 with a Lambda term is an artifact of the tree approximation, and
that the discontinuity reappears at one loop.Comment: 8 pages, revtex 3.1, title changed (version to appear in Phys. Rev.
Lett.
The Elliptic curves in gauge theory, string theory, and cohomology
Elliptic curves play a natural and important role in elliptic cohomology. In
earlier work with I. Kriz, thes elliptic curves were interpreted physically in
two ways: as corresponding to the intersection of M2 and M5 in the context of
(the reduction of M-theory to) type IIA and as the elliptic fiber leading to
F-theory for type IIB. In this paper we elaborate on the physical setting for
various generalized cohomology theories, including elliptic cohomology, and we
note that the above two seemingly unrelated descriptions can be unified using
Sen's picture of the orientifold limit of F-theory compactification on K3,
which unifies the Seiberg-Witten curve with the F-theory curve, and through
which we naturally explain the constancy of the modulus that emerges from
elliptic cohomology. This also clarifies the orbifolding performed in the
previous work and justifies the appearance of the w_4 condition in the elliptic
refinement of the mod 2 part of the partition function. We comment on the
cohomology theory needed for the case when the modular parameter varies in the
base of the elliptic fibration.Comment: 23 pages, typos corrected, minor clarification
Duality symmetry and the form fields of M-theory
In previous work we derived the topological terms in the M-theory action in
terms of certain characters that we defined. In this paper, we propose the
extention of these characters to include the dual fields. The unified treatment
of the M-theory four-form field strength and its dual leads to several
observations. In particular we elaborate on the possibility of a twisted
cohomology theory with a twist given by degrees greater than three.Comment: 12 pages, modified material on the differentia
Quantum M^2 -> 2Lambda/3 discontinuity for massive gravity with a Lambda term
In a previous paper we showed that the absence of the van
Dam-Veltman-Zakharov discontinuity as M^2 -> 0 for massive spin-2 with a Lambda
term is an artifact of the tree approximation, and that the discontinuity
reappears at one loop, as a result of going from five degrees of freedom to
two. In this paper we show that a similar classical continuity but quantum
discontinuity arises in the "partially massless" limit M^2 -> 2Lambda/3, as a
result of going from five degrees of freedom to four.Comment: 8 pages, REVTe
Principal infinity-bundles - General theory
The theory of principal bundles makes sense in any infinity-topos, such as
that of topological, of smooth, or of otherwise geometric
infinity-groupoids/infinity-stacks, and more generally in slices of these. It
provides a natural geometric model for structured higher nonabelian cohomology
and controls general fiber bundles in terms of associated bundles. For suitable
choices of structure infinity-group G these G-principal infinity-bundles
reproduce the theories of ordinary principal bundles, of bundle
gerbes/principal 2-bundles and of bundle 2-gerbes and generalize these to their
further higher and equivariant analogs. The induced associated infinity-bundles
subsume the notions of gerbes and higher gerbes in the literature.
We discuss here this general theory of principal infinity-bundles, intimately
related to the axioms of Giraud, Toen-Vezzosi, Rezk and Lurie that characterize
infinity-toposes. We show a natural equivalence between principal
infinity-bundles and intrinsic nonabelian cocycles, implying the classification
of principal infinity-bundles by nonabelian sheaf hyper-cohomology. We observe
that the theory of geometric fiber infinity-bundles associated to principal
infinity-bundles subsumes a theory of infinity-gerbes and of twisted
infinity-bundles, with twists deriving from local coefficient infinity-bundles,
which we define, relate to extensions of principal infinity-bundles and show to
be classified by a corresponding notion of twisted cohomology, identified with
the cohomology of a corresponding slice infinity-topos.
In a companion article [NSSb] we discuss explicit presentations of this
theory in categories of simplicial (pre)sheaves by hyper-Cech cohomology and by
simplicial weakly-principal bundles; and in [NSSc] we discuss various examples
and applications of the theory.Comment: 46 pages, published versio
Integral group actions on symmetric spaces and discrete duality symmetries of supergravity theories
For a split, simply connected, semisimple Lie group of rank
and the maximal compact subgroup of , we give a method for computing
Iwasawa coordinates of using the Chevalley generators and the Steinberg
presentation. When is a scalar coset for a supergravity theory in
dimensions , we determine the action of the integral form
on . We give explicit results for the action of the
discrete --duality groups and on the
scalar cosets and
for type IIB supergravity
in ten dimensions and 11--dimensional supergravity in dimensions,
respectively. For the former, we use this to determine the discrete U--duality
transformations on the scalar sector in the Borel gauge and we describe the
discrete symmetries of the dyonic charge lattice. We determine the
spectrum--generating symmetry group for fundamental BPS solitons of type IIB
supergravity in dimensions at the classical level and we propose an
analog of this symmetry at the quantum level. We indicate how our methods can
be used to study the orbits of discrete U--duality groups in general
Effects of Moringa (Moringa oleifera Lam.) Leaf Meal on Performance, Carcass, Organs, Eggs and Meat of Japanese Quails
There are several reports on the utilisation of Moringa oleifera in poultry diets due to its essential bioactive compounds yet,little is known about its influence on Japanese quail eggs and meat qualities. Hence, the need to examine performance, eggs and meat qualities of Japanese quail hens fed M.oleifera leaf. To achieve this, 240 Japanese quail chicks were allocated to three dietary treatments: D1: control, 0.0% (without M. oleifera leaf meal),D2: (0.5% M. oleifera leaf meal) and D3: (1% M.oleifera leaf meal). Data on performance, carcass, organs, eggs and meat qualities were collected and subjected to ANOVA at 0.05. Results revealed that feed consumption was lowest (2,701g) in D1 and highest (2,800g) in D2, carcass weight varied from 100 - 100.67g, thigh weight (12.66 - 13.58g) and breast weight was highest (40.41g) in D3. Liver weight was lowest (3.25g) in D1, kidney was largest (0.91g) in D3 whereas, the heart, gizzard and spleen weights ranged from 1.00 - 1.16g, 3.08 - 3.50g and 0.04 - 0.08g, respectively. In the eggs, crude protein (10.94%), crude fat (6.71%), ash (1.36%), high-density lipoprotein (96.12mg/100g) and low-density lipoprotein (120.67mg/100g) were highest in D1. Total cholesterol (364.08mg/100g) and triglycerides (147.27mg/100g) were least in D1 and the caloric value varied from 1.46 -1.47kcal/g. In the meat, crude protein (17.14%) and energy value (1.96kcal/g) were best in D2 but, crude fat (12.62%), ash (2.85%) and carbohydrates(1.31%) were superior in D3. In both eggs and meat, no crude fibre (0.0%) was detected. In any case, all the parameter values were within the normal ranges given in healthy Japanese quails at similar age. Consequently,addition of M. oleifera leaf meal at 1.0% to Japanese quail diets might not depress performance, affect carcass quality, cause organs dysfunctions but may improve nutritional quality of the eggs and meat
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