372 research outputs found
On factorizations in perturbative quantum gravity
Some features of Einstein gravity are most easily understood from string
theory but are not manifest at the level of the usual Lagrangian formulation.
One example is the factorization of gravity amplitudes into gauge theory
amplitudes. Based on the recently constructed `double field theory' and a
geometrical frame-like formalism developed by Siegel, we provide a framework of
perturbative Einstein gravity coupled to a 2-form and a dilaton in which, as a
consequence of T-duality, the Feynman rules factorize to all orders in
perturbation theory. We thereby establish the precise relation between the
field variables in different formulations and discuss the Lagrangian that, when
written in terms of these variables, makes a left-right factorization manifest.Comment: 18 pages, v2: reference added, to appear in JHE
Double Field Theory Formulation of Heterotic Strings
We extend the recently constructed double field theory formulation of the
low-energy theory of the closed bosonic string to the heterotic string. The
action can be written in terms of a generalized metric that is a covariant
tensor under O(D,D+n), where n denotes the number of gauge vectors, and n
additional coordinates are introduced together with a covariant constraint that
locally removes these new coordinates. For the abelian subsector, the action
takes the same structural form as for the bosonic string, but based on the
enlarged generalized metric, thereby featuring a global O(D,D+n) symmetry.
After turning on non-abelian gauge couplings, this global symmetry is broken,
but the action can still be written in a fully O(D,D+n) covariant fashion, in
analogy to similar constructions in gauged supergravities.Comment: 28 pages, v2: minor changes, version published in JHE
Massive Type II in Double Field Theory
We provide an extension of the recently constructed double field theory
formulation of the low-energy limits of type II strings, in which the RR fields
can depend simultaneously on the 10-dimensional space-time coordinates and
linearly on the dual winding coordinates. For the special case that only the RR
one-form of type IIA carries such a dependence, we obtain the massive
deformation of type IIA supergravity due to Romans. For T-dual configurations
we obtain a `massive' but non-covariant formulation of type IIB, in which the
10-dimensional diffeomorphism symmetry is deformed by the mass parameter.Comment: 21 page
Differential geometry with a projection: Application to double field theory
In recent development of double field theory, as for the description of the
massless sector of closed strings, the spacetime dimension is formally doubled,
i.e. from D to D+D, and the T-duality is realized manifestly as a global O(D,D)
rotation. In this paper, we conceive a differential geometry characterized by a
O(D,D) symmetric projection, as the underlying mathematical structure of double
field theory. We introduce a differential operator compatible with the
projection, which, contracted with the projection, can be covariantized and may
replace the ordinary derivatives in the generalized Lie derivative that
generates the gauge symmetry of double field theory. We construct various gauge
covariant tensors which include a scalar and a tensor carrying two O(D,D)
vector indices.Comment: 1+22 pages, No figure; a previous result on 4-index tensor removed,
presentation improve
Hermitian Yang-Mills instantons on resolutions of Calabi-Yau cones
We study the construction of Hermitian Yang-Mills instantons over resolutions
of Calabi-Yau cones of arbitrary dimension. In particular, in d complex
dimensions, we present an infinite family, parametrised by an integer k and a
continuous modulus, of SU(d) instantons. A detailed study of their properties,
including the computation of the instanton numbers is provided. We also explain
how they can be used in the construction of heterotic non-Kahler
compactifications.Comment: 20 pages, 1 figure; typos corrected, section 3.1 expande
Yang-Mills instantons and dyons on homogeneous G_2-manifolds
We consider Lie G-valued Yang-Mills fields on the space R x G/H, where G/H is
a compact nearly K"ahler six-dimensional homogeneous space, and the manifold R
x G/H carries a G_2-structure. After imposing a general G-invariance condition,
Yang-Mills theory with torsion on R x G/H is reduced to Newtonian mechanics of
a particle moving in R^6, R^4 or R^2 under the influence of an inverted
double-well-type potential for the cases G/H = SU(3)/U(1)xU(1),
Sp(2)/Sp(1)xU(1) or G_2/SU(3), respectively. We analyze all critical points and
present analytical and numerical kink- and bounce-type solutions, which yield
G-invariant instanton configurations on those cosets. Periodic solutions on S^1
x G/H and dyons on iR x G/H are also given.Comment: 1+26 pages, 14 figures, 6 miniplot
On the Riemann Tensor in Double Field Theory
Double field theory provides T-duality covariant generalized tensors that are
natural extensions of the scalar and Ricci curvatures of Riemannian geometry.
We search for a similar extension of the Riemann curvature tensor by developing
a geometry based on the generalized metric and the dilaton. We find a duality
covariant Riemann tensor whose contractions give the Ricci and scalar
curvatures, but that is not fully determined in terms of the physical fields.
This suggests that \alpha' corrections to the effective action require \alpha'
corrections to T-duality transformations and/or generalized diffeomorphisms.
Further evidence to this effect is found by an additional computation that
shows that there is no T-duality invariant four-derivative object built from
the generalized metric and the dilaton that reduces to the square of the
Riemann tensor.Comment: 36 pages, v2: minor changes, ref. added, v3: appendix on frame
formalism added, version to appear in JHE
Incorporation of fermions into double field theory
Based on the stringy differential geometry we proposed earlier, we
incorporate fermions such as gravitino and dilatino into double field theory in
a manifestly covariant manner with regard to O(D,D) T-duality, diffeomorphism,
one-form gauge symmetry for B-field and a pair of local Lorentz symmetries. We
note that there are two kinds of fermions in double field theory: O(D,D)
singlet and non-singlet which may be identified, respectively as the common and
the non-common fermionic sectors in type IIA and IIB supergravities. For each
kind, we construct corresponding covariant Dirac operators. Further, we derive
a simple criterion for an O(D,D) rotation to flip the chirality of the O(D,D)
non-singlet chiral fermions, which implies the exchange of type IIA and IIB
supergravities.Comment: (v1) 1+21 pages, no figure; (v2) Refs. added, to appear in JHEP; (v3)
minor change, a comment in the last section removed and Eq.(3.22) correcte
Double field theory of type II strings
We use double field theory to give a unified description of the low energy limits of type IIA and type IIB superstrings. The Ramond-Ramond potentials fit into spinor representations of the duality group O(D, D) and field-strengths are obtained by acting with the Dirac operator on the potentials. The action, supplemented by a Spin+ (D, D)-covariant self-duality condition on field strengths, reduces to the IIA and IIB theories in different frames. As usual, the NS-NS gravitational variables are described through the generalized metric. Our work suggests that the fundamental gravitational variable is a hermitian element of the group Spin(D, D) whose natural projection to O(D, D) gives the generalized metric.United States. Dept. of Energy (cooperative research agreement DE-FG02-05ER41360)
- …