229 research outputs found
Geometric Aspects of D-branes and T-duality
We explore the differential geometry of T-duality and D-branes. Because
D-branes and RR-fields are properly described via K-theory, we discuss the
(differential) K-theoretic generalization of T-duality and its application to
the coupling of D-branes to RR-fields. This leads to a puzzle involving the
transformation of the A-roof genera in the coupling.Comment: 26 pages, JHEP format, uses dcpic.sty; v2: references added, v3:
minor change
Overview Of K-Theory Applied To Strings
K-theory provides a framework for classifying Ramond-Ramond (RR) charges and
fields. K-theory of manifolds has a natural extension to K-theory of
noncommutative algebras, such as the algebra considered in noncommutative
Yang-Mills theory or in open string field theory. In a number of concrete
problems, the K-theory analysis proceeds most naturally if one starts out with
an infinite set of D-branes, reduced by tachyon condensation to a finite set.
This suggests that string field theory should be reconsidered for N=infinity.Comment: 20 p
Stability of flux vacua in the presence of charged black holes
In this letter we consider a charged black hole in a flux compactification of
type IIB string theory. Both the black hole and the fluxes will induce
potentials for the complex structure moduli. We choose the compact dimensions
to be described locally by a deformed conifold, creating a large hierarchy. We
demonstrate that the presence of a black hole typically will not change the
minimum of the moduli potential in a substantial way. However, we also point
out a couple of possible loop-holes, which in some cases could lead to
interesting physical consequences such as changes in the hierarchy.Comment: 14 pages. Published versio
Abelian duality on globally hyperbolic spacetimes
We study generalized electric/magnetic duality in Abelian gauge theory by combining techniques from locally covariant quantum field theory and Cheeger-Simons differential cohomology on the category of globally hyperbolic Lorentzian manifolds. Our approach generalizes previous treatments using the Hamiltonian formalism in a manifestly covariant way and without the assumption of compact Cauchy surfaces. We construct semi-classical configuration spaces and corresponding presymplectic Abelian groups of observables, which are quantized by the CCR-functor to the category of C*-algebras. We demonstrate explicitly how duality is implemented as a natural isomorphism between quantum field theories. We apply this formalism to develop a fully covariant quantum theory of self-dual fields
Twisted K-Theory of Lie Groups
I determine the twisted K-theory of all compact simply connected simple Lie
groups. The computation reduces via the Freed-Hopkins-Teleman theorem to the
CFT prescription, and thus explains why it gives the correct result. Finally I
analyze the exceptions noted by Bouwknegt et al.Comment: 16 page
Classifying A-field and B-field configurations in the presence of D-branes
We "solve" the Freed-Witten anomaly equation, i.e., we find a geometrical
classification of the B-field and A-field configurations in the presence of
D-branes that are anomaly-free. The mathematical setting being provided by the
geometry of gerbes, we find that the allowed configurations are jointly
described by a coset of a certain hypercohomology group. We then describe in
detail various cases that arise according to such classification. As is
well-known, only under suitable hypotheses the A-field turns out to be a
connection on a canonical gauge bundle. However, even in these cases, there is
a residual freedom in the choice of the bundle, naturally arising from the
hypercohomological description. For a B-field which is flat on a D-brane,
fractional or irrational charges of subbranes naturally appear; for a suitable
gauge choice, they can be seen as arising from "gauge bundles with not integral
Chern class": we give a precise geometric interpretation of these objects.Comment: 28 pages, no figure
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
A Torsion Correction to the RR 4-Form Fieldstrength
The shifted quantization condition of the M-theory 4-form G_4 is well-known.
The most naive generalization to type IIA string theory fails, an orientifold
counterexample was found by Hori in hep-th/9805141. In this note we use
D2-brane anomaly cancellation to find the corresponding shifted quantization
condition in IIA. Our analysis is consistent with the known O4-plane tensions
if we include a torsion correction to the usual construction of G_4 from C_3, B
and G_2. The resulting Bianchi identities enforce that RR fluxes lift to
K-theory classes.Comment: 10 Pages, 1 eps figur
Some Relations between Twisted K-theory and E8 Gauge Theory
Recently, Diaconescu, Moore and Witten provided a nontrivial link between
K-theory and M-theory, by deriving the partition function of the Ramond-Ramond
fields of Type IIA string theory from an E8 gauge theory in eleven dimensions.
We give some relations between twisted K-theory and M-theory by adapting the
method of Diaconescu-Moore-Witten and Moore-Saulina. In particular, we
construct the twisted K-theory torus which defines the partition function, and
also discuss the problem from the E8 loop group picture, in which the
Dixmier-Douady class is the Neveu-Schwarz field. In the process of doing this,
we encounter some mathematics that is new to the physics literature. In
particular, the eta differential form, which is the generalization of the eta
invariant, arises naturally in this context. We conclude with several open
problems in mathematics and string theory.Comment: 23 pages, latex2e, corrected minor errors and typos in published
versio
Ramond-Ramond Fields, Fractional Branes and Orbifold Differential K-Theory
We study D-branes and Ramond-Ramond fields on global orbifolds of Type II
string theory with vanishing H-flux using methods of equivariant K-theory and
K-homology. We illustrate how Bredon equivariant cohomology naturally realizes
stringy orbifold cohomology. We emphasize its role as the correct cohomological
tool which captures known features of the low-energy effective field theory,
and which provides new consistency conditions for fractional D-branes and
Ramond-Ramond fields on orbifolds. We use an equivariant Chern character from
equivariant K-theory to Bredon cohomology to define new Ramond-Ramond couplings
of D-branes which generalize previous examples. We propose a definition for
groups of differential characters associated to equivariant K-theory. We derive
a Dirac quantization rule for Ramond-Ramond fluxes, and study flat
Ramond-Ramond potentials on orbifolds.Comment: 46 pages; v2: typos correcte
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