219 research outputs found
Topological duality twist and brane instantons in F-theory
A variant of the topological twist, involving SL(2,Z) dualities and hence
named topological duality twist, is introduced and explicitly applied to
describe a U(1) N=4 super Yang-Mills theory on a Kaehler space with
holomorphically space-dependent coupling. Three-dimensional duality walls and
two-dimensional chiral theories naturally enter the formulation of the duality
twisted theory. Appropriately generalized, this theory is relevant for the
study of Euclidean D3-brane instantons in F-theory compactifications. Some of
its properties and implications are discussed.Comment: 39 pages, 7 figure
D-brane networks in flux vacua, generalized cycles and calibrations
We consider chains of generalized submanifolds, as defined by Gualtieri in
the context of generalized complex geometry, and define a boundary operator
that acts on them. This allows us to define generalized cycles and the
corresponding homology theory. Gauge invariance demands that D-brane networks
on flux vacua must wrap these generalized cycles, while deformations of
generalized cycles inside of a certain homology class describe physical
processes such as the dissolution of D-branes in higher-dimensional D-branes
and MMS-like instantonic transitions. We introduce calibrations that identify
the supersymmetric D-brane networks, which minimize their energy inside of the
corresponding homology class of generalized cycles. Such a calibration is
explicitly presented for type II N=1 flux compactifications to four dimensions.
In particular networks of walls and strings in compactifications on warped
Calabi-Yau's are treated, with explicit examples on a toroidal orientifold
vacuum and on the Klebanov-Strassler geometry.Comment: 42 pages, 4 eps figures, version to appear in JHE
Non-perturbative effects on seven-brane Yukawa couplings
We analyze non-perturbative corrections to the superpotential of seven-brane
gauge theories on type IIB and F-theory warped Calabi-Yau compactifications. We
show in particular that such corrections modify the holomorphic Yukawa
couplings by an exponentially suppressed contribution, generically solving the
Yukawa rank-one problem present in F-theory local models. We provide explicit
expressions for the non-perturbative correction to the seven-brane
superpotential, and check that it is related to a non-commutative deformation
to the tree-level superpotential via the Seiberg-Witten map.Comment: 4 pages. v2: minor changes, footnotes and citations added. Version to
be published in PR
Hidden Selection Rules, M5-instantons and Fluxes in F-theory
We introduce a new approach to investigate the selection rules governing the
contributions of fluxed M5-instantons to the F-theory four-dimensional
effective action, with emphasis on the generation of charged matter F-terms.
The structure of such couplings is unraveled by exploiting the perturbative and
non-perturbative homological relations, introduced in our companion paper
arXiv:1506.06764, which encode the interplay between the self-dual 3-form flux
on the M5-brane, the background 4-form flux and certain fibral curves. The
latter are wrapped by time-like M2-branes representing matter insertions in the
instanton path integral. In particular, we clarify how fluxed M5-instantons
detect the presence of geometrically massive s which are responsible for
`hidden' selection rules. We discuss how for non-generic embeddings the
M5-instanton can probe `locally massless' symmetries if the rank of its
Mordell-Weil group is enhanced compared to that of the bulk. As a
phenomenological off-spring we propose a new type of non-perturbative
corrections to Yukawa couplings which may change the rank of the Yukawa matrix.
Along the way, we also gain new insights into the structure of massive
gauge fluxes in the stable degeneration limit.Comment: 42 pages; v2: references adde
Non-perturbative selection rules in F-theory
We discuss the structure of charged matter couplings in 4-dimensional
F-theory compactifications. Charged matter is known to arise from M2-branes
wrapping fibral curves on an elliptic or genus-one fibration Y. If a set of
fibral curves satisfies a homological relation in the fibre homology, a
coupling involving the states can arise without exponential volume suppression
due to a splitting and joining of the M2-branes. If the fibral curves only sum
to zero in the integral homology of the full fibration, no such coupling is
possible. In this case an M2-instanton wrapping a 3-chain bounded by the fibral
matter curves can induce a D-term which is volume suppressed. We elucidate the
consequences of this pattern for the appearance of massive U(1) symmetries in
F-theory and analyse the structure of discrete selection rules in the coupling
sector. The weakly coupled analogue of said M2-instantons is worked out to be
given by D1-F1 instantons. The generation of an exponentially suppressed F-term
requires the formation of half-BPS bound states of M2 and M5-instantons. This
effect and its description in terms of fluxed M5-instantons is discussed in a
companion paper.Comment: 49 pages, 9 figures; v2: references adde
On type II superstrings in bosonic backgrounds: the role of fermions and T-duality
We derive the actions for type II Green-Schwarz strings up to second order in
the fermions, for general bosonic backgrounds. We base our work on the
so-called normal coordinate expansion. The resulting actions are
-symmetric and, for the case of surviving background supersymmetries,
supersymmetric. We first obtain the type IIa superstring action from the 11D
supermembrane by double dimensional reduction. Then, by means of a
generalization of T-duality we derive the type IIb superstring action. The
resulting actions are surprisingly simple and elegant.Comment: 10 pages, latex. more typos correcte
Symmetries, Sum Rules and Constraints on Effective Field Theories
Using unitarity, analyticity and crossing symmetry, we derive universal sum
rules for scattering amplitudes in theories invariant under an arbitrary
symmetry group. The sum rules relate the coefficients of the energy expansion
of the scattering amplitudes in the IR to total cross sections integrated all
the way up to the UV. Exploiting the group structure of the symmetry, we
systematically determine all the independent sum rules and positivity
conditions on the expansion coefficients. For effective field theories the
amplitudes in the IR are calculable and hence the sum rules set constraints on
the parameters of the effective Lagrangian. We clarify the impact of gauging on
the sum rules for Goldstone bosons in spontaneously broken gauge theories. We
discuss explicit examples that are relevant for WW-scattering, composite Higgs
models, and chiral perturbation theory. Certain sum rules based on custodial
symmetry and its extensions provide constraints on the Higgs boson coupling to
the electroweak gauge bosons.Comment: 50 pages, 5 figures, 5 appendices; several typos fixed, discussions
improved, references added; results unchange
Freezing E3-brane instantons with fluxes
E3-instantons that generate non-perturbative superpotentials in IIB N=1
compactifications are more frequent than currently believed. Worldvolume fluxes
will typically lift the E3-brane geometric moduli and their fermionic
superpartners, leaving only the two required universal fermionic zero-modes. We
consistently incorporate SL(2, Z) monodromies and world-volume fluxes in the
effective theory of the E3-brane fermions and study the resulting zero-mode
spectrum, highlighting the relation between F-theory and perturbative IIB
results. This leads us to a IIB derivation of the index for generation of
superpotential terms, which reproduces and generalizes available results.
Furthermore, we show how worldvolume fluxes can be explicitly constructed in a
one-modulus compactification, such that an E3-instanton has exactly two
fermonic zero-modes. This construction is readily applicable to numerous
scenarios.Comment: 8 pages. Proceedings of the "XVII European Workshop on String Theory
2011", Padova, Italy, 5-9 September 201
Timelike structures of ten-dimensional supersymmetry
In several contexts, supersymmetry can be reformulated in terms of
calibrations, namely forms whose integrals measure minimal energies. It has
been conjectured that this should be possible in general. For type II
supergravity, we present a new system of equations which realizes this
expectation. Besides the customary D-brane calibrations, it also includes
NS5-brane and KK5-monopole calibrations. It is equivalent to supersymmetry
under the assumption that the Killing vector associated to supersymmetry is
timelike. No assumption is made on a factorization of spacetime. We also obtain
a version of the system which is manifestly S-invariant and we present an
application to near-horizon backgrounds. Using calibration, a definition of
central charges in purely gravitational terms is given.Comment: 61 pages; v2: matches published version, comments adde
Hamiltonian linearization of the rest-frame instant form of tetrad gravity in a completely fixed 3-orthogonal gauge: a radiation gauge for background-independent gravitational waves in a post-Minkowskian Einstein spacetime
In the framework of the rest-frame instant form of tetrad gravity, where the
Hamiltonian is the weak ADM energy , we define a special
completely fixed 3-orthogonal Hamiltonian gauge, corresponding to a choice of
{\it non-harmonic} 4-coordinates, in which the independent degrees of freedom
of the gravitational field are described by two pairs of canonically conjugate
Dirac observables (DO) , , . We define a Hamiltonian linearization of the
theory, i.e. gravitational waves, {\it without introducing any background
4-metric}, by retaining only the linear terms in the DO's in the
super-hamiltonian constraint (the Lichnerowicz equation for the conformal
factor of the 3-metric) and the quadratic terms in the DO's in . {\it We solve all the constraints} of the linearized theory: this
amounts to work in a well defined post-Minkowskian Christodoulou-Klainermann
space-time. The Hamilton equations imply the wave equation for the DO's
, which replace the two polarizations of the TT
harmonic gauge, and that {\it linearized Einstein's equations are satisfied} .
Finally we study the geodesic equation, both for time-like and null geodesics,
and the geodesic deviation equation.Comment: LaTeX (RevTeX3), 94 pages, 4 figure
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