4,847 research outputs found
ICMP lecture on Heterotic/F-theory duality
The heterotic string compactified on an (n-1)-dimensional elliptically
fibered Calabi-Yau Z-->B is conjectured to be dual to F-theory compactified on
an n-dimensional Calabi-Yau X-->B, fibered over the same base with elliptic K3
fibers. In particular, the moduli of the two theories should be isomorphic. The
cases most relevant to the physics are n=2, 3, 4, i.e. the compactification is
to dimensions d=8, 6 or 4 respectively. Mathematically, the richest picture
seems to emerge for n=3, where the moduli space involves an analytically
integrable system whose fibers admit rather different descriptions in the two
theories. The purpose of this talk is to review some of what is known and what
is not yet known about this conjectural isomorphism. Some of the underlying
mathematics of principal bundles on elliptic fibrations is reviewed in the
accompanying Taniguchi talk (hep-th/9802094).Comment: 9 pages, Late
Taniguchi Lecture on Principal Bundles on Elliptic Fibrations
In this talk we discuss the description of the moduli space of principal
G-bundles on an elliptic fibration X-->S in terms of cameral covers and their
distinguished Prym varieties. We emphasize the close relationship between this
problem and the integrability of Hitchin's system and its generalizations. The
discussion roughly parallels that of [D2], but additional examples are included
and some important steps of the argument are illustrated. Some of the
applications to heterotic/F-theory duality were described in the accompanying
ICMP talk (hep-th/9802093).Comment: 17 pages, Late
Principal bundles on elliptic fibrations
A central role in recent investigations of the duality of F-theory and
heterotic strings is played by the moduli of principal bundles, with various
structure groups G, over an elliptically fibered Calabi-Yau manifold on which
the heterotic theory is compactified. In this note we propose a simple
algebro-geometric technique for studying the moduli spaces of principal
G-bundles on an arbitrary variety X which is elliptically fibered over a base
S: The moduli space itself is naturally fibered over a weighted projective base
parametrizing spectral covers of S, and the fibers are identified
as translates of distinguished Pryms of these covers. In nice situations, the
generic Prym fiber is isogenous to the product of a finite group and an abelian
subvariety of .Comment: 11 pages, Plain TeX. This is the published version, containing minor
correction
The Virial Correction to the Ideal Gas Law: A Primer
The virial expansion of a gas is a correction to the ideal gas law that is
usually discussed in advanced courses in statistical mechanics. In this note we
outline this derivation in a manner suitable for advanced undergraduate and
introductory graduate classroom presentations. We introduce a physically
meaningful interpretation of the virial expansion that has heretofore escaped
attention, by showing that the virial series is actually an expansion in a
parameter that is the ratio of the effective volume of a molecule to its mean
volume. Using this interpretation we show why under normal conditions ordinary
gases such as O_2 and N_2 can be regarded as ideal gases.Comment: Revised title and abstract, and slightly lengthened tex
Abelian solitons
We describe a new algebraically completely integrable system, whose integral
manifolds are co-elliptic subvarieties of Jacobian varieties. This is a
multi-periodic extension of the Krichever-Treibich-Verdier system, which
consists of elliptic solitons
The Heterotic String, the Tangent Bundle, and Derived Categories
We consider the compactification of the E8xE8 heterotic string on a K3
surface with "the spin connection embedded in the gauge group" and the dual
picture in the type IIA string (or F-theory) on a Calabi-Yau threefold X. It
turns out that the same X arises also as dual to a heterotic compactification
on 24 point-like instantons. X is necessarily singular, and we see that this
singularity allows the Ramond-Ramond moduli on X to split into distinct
components, one containing the (dual of the heterotic) tangent bundle, while
another component contains the point-like instantons. As a practical
application we derive the result that a heterotic string compactified on the
tangent bundle of a K3 with ADE singularities acquires nonperturbatively
enhanced gauge symmetry in just the same fashion as a type IIA string on a
singular K3 surface. On a more philosophical level we discuss how it appears to
be natural to say that the heterotic string is compactified using an object in
the derived category of coherent sheaves. This is necessary to properly extend
the notion of T-duality to the heterotic string on a K3 surface.Comment: 34 pages, 3 figures (published version
Synthesis from Knowledge-Based Specifications
In program synthesis, we transform a specification into a program that is
guaranteed to satisfy the specification. In synthesis of reactive systems, the
environment in which the program operates may behave nondeterministically,
e.g., by generating different sequences of inputs in different runs of the
system. To satisfy the specification, the program needs to act so that the
specification holds in every computation generated by its interaction with the
environment. Often, the program cannot observe all attributes of its
environment. In this case, we should transform a specification into a program
whose behavior depends only on the observable history of the computation. This
is called synthesis with incomplete information. In such a setting, it is
desirable to have a knowledge-based specification, which can refer to the
uncertainty the program has about the environment's behavior. In this work we
solve the problem of synthesis with incomplete information with respect to
specifications in the logic of knowledge and time. We show that the problem has
the same worst-case complexity as synthesis with complete information.Comment: An extended abstract of this paper appeared in CONCUR'9
A Logic for SDSI's Linked Local Name Spaces
Abadi has introduced a logic to explicate the meaning of local names in SDSI,
the Simple Distributed Security Infrastructure proposed by Rivest and Lampson.
Abadi's logic does not correspond precisely to SDSI, however; it draws
conclusions about local names that do not follow from SDSI's name resolution
algorithm. Moreover, its semantics is somewhat unintuitive. This paper presents
the Logic of Local Name Containment, which does not suffer from these
deficiencies. It has a clear semantics and provides a tight characterization of
SDSI name resolution. The semantics is shown to be closely related to that of
logic programs, leading to an approach to the efficient implementation of
queries concerning local names. A complete axiomatization of the logic is also
provided.Comment: To appear, Journal of Computer Securit
A logical reconstruction of SPKI
SPKI/SDSI is a proposed public key infrastructure standard that incorporates
the SDSI public key infrastructure. SDSI's key innovation was the use of local
names. We previously introduced a Logic of Local Name Containment that has a
clear semantics and was shown to completely characterize SDSI name resolution.
Here we show how our earlier approach can be extended to deal with a number of
key features of SPKI, including revocation, expiry dates, and tuple reduction.
We show that these extensions add relatively little complexity to the logic. In
particular, we do not need a nonmonotonic logic to capture revocation. We then
use our semantics to examine SPKI's tuple reduction rules. Our analysis
highlights places where SPKI's informal description of tuple reduction is
somewhat vague, and shows that extra reduction rules are necessary in order to
capture general information about binding and authorization.Comment: This is an updated version of a paper that appears in the Proceedings
of the 14th IEEE Computer Security Foundations Workshop. It will appear in a
special issue of the Journal of Computer Security devoted to papers from that
conferenc
Complete Axiomatizations for Reasoning About Knowledge and Time
Sound and complete axiomatizations are provided for a number of different
logics involving modalities for knowledge and time. These logics arise from
different choices for various parameters. All the logics considered involve the
discrete time linear temporal logic operators `next' and `until' and an
operator for the knowledge of each of a number of agents. Both the single agent
and multiple agent cases are studied: in some instances of the latter there is
also an operator for the common knowledge of the group of all agents. Four
different semantic properties of agents are considered: whether they have a
unique initial state, whether they operate synchronously, whether they have
perfect recall, and whether they learn. The property of no learning is
essentially dual to perfect recall. Not all settings of these parameters lead
to recursively axiomatizable logics, but sound and complete axiomatizations are
presented for all the ones that do.Comment: To appear, SIAM Journal on Computin
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