1,144 research outputs found
-symbols in exceptional field theory
We present the universal form of -symbols that can be applied to an
arbitrary exceptional field theory (EFT) up to . We then
express the -tensor, which governs the gauge algebra of EFT, as a quadratic
form of the -symbols. The usual definition of the -tensor strongly
depends on the dimension of the compactification torus while it is not the case
for our -tensor. Furthermore, using the -symbols, we propose a
universal form of the linear section equation. In particular, in the SL(5) EFT,
we explicitly show the equivalence to the known linear section equation.Comment: 41 pages; v2: typos corrected, clarifications added; v3: typos
corrected, to appear in PTEP; v4: typos corrected in Eq.(3.65) and Table
Propagators in de Sitter space
In a spacetime with no global timelike Killing vector, we do not have a
natural choice for the vacuum state of matter fields, leading to an ambiguity
in defining the Feynman propagators. In this paper, taking the vacuum state to
be the instantaneous ground state of the Hamiltonian at each moment, we develop
a method for calculating wave functions associated with the vacuum and the
corresponding in-in and in-out propagators. We apply this method to free scalar
field theory in de Sitter space and obtain de Sitter invariant propagators in
various coordinate patches. We show that the in-out propagator in the Poincare
patch has a finite massless limit in a de Sitter invariant form. We argue and
numerically check that our in-out propagators agree with those obtained by a
path integral with the standard i\epsilon prescription, and identify the
condition on a foliation of spacetime under which such coincidence can happen
for the foliation. We also show that the in-out propagators satisfy Polyakov's
composition law. Several applications of our framework are also discussed.Comment: 38 pages, 14 figures, v2: references added, discussion on the in-in
propagators improved, v3: typos corrected, v4: references added, discussions
improved, to appear in PR
Master equation for the Unruh-DeWitt detector and the universal relaxation time in de Sitter space
We derive the master equation that completely determines the time evolution
of the density matrix of the Unruh-DeWitt detector in an arbitrary background
geometry. We apply the equation to reveal a nonequilibrium thermodynamic
character of de Sitter space. This generalizes an earlier study on the
thermodynamic property of the Bunch-Davies vacuum that an Unruh-DeWitt detector
staying in the Poincare patch and interacting with a scalar field in the
Bunch-Davies vacuum behaves as if it is in a thermal bath of finite
temperature. In this paper, instead of the Bunch-Davies vacuum, we consider a
class of initial states of scalar field, for which the detector behaves as if
it is in a medium that is not in thermodynamic equilibrium and that undergoes a
relaxation to the equilibrium corresponding to the Bunch-Davies vacuum. We give
a prescription for calculating the relaxation times of the nonequilibrium
processes. We particularly show that, when the initial state of the scalar
field is the instantaneous ground state at a finite past, the relaxation time
is always given by a universal value of half the curvature radius of de Sitter
space. We expect that the relaxation time gives a nonequilibrium thermodynamic
quantity intrinsic to de Sitter space.Comment: 41 pages, 10 figures; v2: typos corrected; v3: typos corrected; v4:
clarifications and references added; v5: final version appearing in PR
Generalized gravity from modified DFT
Recently, generalized equations of type IIB supergravity have been derived
from the requirement of classical kappa-symmetry of type IIB superstring theory
in the Green-Schwarz formulation. These equations are covariant under
generalized T-duality transformations and hence one may expect a formulation
similar to double field theory (DFT). In this paper, we consider a modification
of the DFT equations of motion by relaxing a condition for the generalized
covariant derivative with an extra generalized vector. In this modified double
field theory (mDFT), we show that the flatness condition of the modified
generalized Ricci tensor leads to the NS-NS part of the generalized equations
of type IIB supergravity. In particular, the extra vector fields appearing in
the generalized equations correspond to the extra generalized vector in mDFT.
We also discuss duality symmetries and a modification of the string charge in
mDFT.Comment: 41 pages; v2: typos corrected, references added; v3: an addendum
added in Sec.5; v4: typos corrected, clarifications added, to appear in JHE
Weyl invariance for generalized supergravity backgrounds from the doubled formalism
It has recently been shown that a set of the generalized type IIB
supergravity equations follows from the requirement of kappa symmetry of the
type IIB Green-Schwarz superstring theory defined on an arbitrary background.
In this paper, we show that the whole bosonic part of the generalized type II
supergravity equations can be reproduced from the T-duality covariant equations
of motion of the double field theory by choosing a non-standard solution of the
strong constraint. Then, by using the doubled formalism, we show the Weyl
invariance of the bosonic string sigma model on a generalized gravity
background. According to the dual-coordinate dependence of the dilaton, the
Fradkin-Tseytlin term nicely removes the Weyl anomaly. This result seems likely
to support that string theories can be consistently defined on arbitrary
generalized supergravity backgrounds.Comment: 28 pages; v2: typos corrected, clarifications added; v3: typos
corrected, references added, to appear in PTE
Effective Action for Non-Geometric Fluxes from Duality Covariant Actions
The (heterotic) double field theories and the exceptional field theories are
recently developed for manifestly duality covariant formulation of various
supergravity theories, describing low-energy limit of various (heterotic)
superstring and M-theory compactifications. These field theories are known to
be reduced to the standard descriptions by introducing appropriately
parameterized generalized metric and by applying suitably chosen section
conditions. We generalize this development to non-geometric backgrounds by
utilizing dual fields pertinent to non-geometric fluxes. We introduce different
parameterizations for the generalized metric, in terms of the conventional
supergravity fields or the dual fields. Under certain simplifying assumptions,
we construct new effective action for non-geometric backgrounds. We then obtain
the non-geometric backgrounds sourced by exotic branes. From them, we construct
their -duality monodromy matrices. The charge of exotic branes obtained from
these monodromy matrices agrees perfectly with the charge obtained from the
non-geometric flux integral.Comment: cover + 101 pages; v2. published version in JHE
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