22 research outputs found
Twisted Homology
D-branes are classified by twisted K-theory. Yet twisted K-theory is often
hard to calculate. We argue that, in the case of a compactification on a
simply-connected six manifold, twisted K-theory is isomorphic to a much simpler
object, twisted homology. Unlike K-theory, homology can be twisted by a class
of any degree and so it classifies not only D-branes but also M-branes. Twisted
homology classes correspond to cycles in a certain bundle over spacetime, and
branes may decay via Kachru-Pearson-Verlinde transitions only if this cycle is
trivial. We provide a spectral sequence which calculates twisted homology, the
kth step treats D(p-2k)-branes ending on Dp-branes.Comment: 29 pages, 3 eps figures, added Report-n
F-theory on singular spaces
We propose a framework for treating F-theory directly, without resolving or
deforming its singularities. This allows us to explore new sectors of gauge
theories, including exotic bound states such as T-branes, in a global context.
We use the mathematical framework known as Eisenbud's matrix factorizations for
hypersurface singularities. We display the usefulness of this technique by way
of examples, including affine singularities of both conifold and orbifold type,
as well as a class of full-fledged compact elliptically fibered Calabi-Yau
fourfolds.Comment: 35 pages, 4 figures, minor revision
New F-theory lifts
In this note, a procedure is developed to explicitly construct non-trivial
F-theory lifts of perturbative IIB orientifold models on Calabi-Yau complete
intersections in toric varieties. This procedure works on Calabi-Yau
orientifolds where the involution coordinate can have arbitrary projective
weight, as opposed to the well-known hypersurface cases where it has half the
weight of the equation defining the CY threefold. This opens up the possibility
of lifting more general setups, such as models that have O3-planes.Comment: 13 pages, 4 tables; added references, 1 table, and some
acknowledgements; minor modifications and clarification
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
T-branes through 3d mirror symmetry
T-branes are exotic bound states of D-branes, characterized by mutually
non-commuting vacuum expectation values for the worldvolume scalars. The
M/F-theory geometry lifting D6/D7-brane configurations is blind to the T-brane
data. In this paper, we make this data manifest, by probing the geometry with
an M2-brane. We find that the effect of a T-brane is to deform the membrane
worldvolume superpotential with monopole operators, which partially break the
three-dimensional flavor symmetry, and reduce supersymmetry from N=4 to N=2.
Our main tool is 3d mirror symmetry. Through this language, a very concrete
framework is developed for understanding T-branes in M-theory. This leads us to
uncover a new class of N=2 quiver gauge theories, whose Higgs branches mimic
those of membranes at ADE singularities, but whose Coulomb branches differ from
their N=4 counterparts.Comment: 36 page
Magnetized E3-brane instantons in F-theory
We discuss E3-brane instantons in N=1 F-theory compactifications to four
dimensions and clarify the structure of E3-E3 zero modes for general
world-volume fluxes. We consistently incorporate SL(2,Z) monodromies and
highlight the relation between F-theory and perturbative IIB results. We
explicitly show that world-volume fluxes can lift certain fermionic zero-modes,
whose presence would prevent the generation of non-perturbative superpotential
terms, and we discuss in detail the geometric interpretation of the zero-mode
lifting mechanism. We provide a IIB derivation of the index for generation of
superpotential terms and of its modification to include world-volume fluxes,
which reproduces and generalizes available results. We apply our general
analysis to the explicit, though very simple, example of compactification on
P^3 and its orientifold weak-coupling limit. In particular, we provide an
example in which a non-rigid divisor with fluxes contributes to the
superpotential.Comment: 58 pages, 1 figure. v2: minor changes and typos correcte
Genus zero Gopakumar-Vafa invariants from open strings
Abstract: We propose a new way to compute the genus zero Gopakumar-Vafa invariants
for two families of non-toric non-compact Calabi-Yau threefolds that admit simple flops:
Reid’s Pagodas, and Laufer’s examples. We exploit the duality between M-theory on these
threefolds, and IIA string theory with D6-branes and O6-planes. From this perspective,
the GV invariants are detected as five-dimensional open string zero modes. We propose
a definition for genus zero GV invariants for threefolds that do not admit small crepant
resolutions. We find that in most cases, non-geometric T-brane data is required in order
to fully specify the invariants
Higgs branches of 5d rank-zero theories from geometry
Abstract: We study the Higgs branches of five-dimensional N = 1 rank-zero theories obtained
from M-theory on two classes non-toric non-compact Calabi-Yau threefolds: Reid’s
pagodas, and Laufer’s examples. Our approach consists in reducing to IIA with D6-branes
and O6-planes, and computing the open-string spectra giving rise to hypermultiplets. Starting
with the seven-dimensional worldvolume theories, we switch on T-brane backgrounds
to give rise to bound states with angles. We observe that the resulting partially Higgsed
5d theories have discrete gauge groups, from which we readily deduce the geometry of the
Higgs branches as orbifolds of quaternionic varieties
Supersymmetric Yang-Mills theory at order alpha'^3
We construct the order alpha'^3 terms in the supersymmetric Yang-Mills action
in ten dimensions for an arbitrary gauge group. The result can be expressed in
terms of the structure constants of the Yang-Mills group, and is therefore
independent of abelian factors. The alpha'^3 invariant obtained here is
independent of the alpha'^2 invariant, and we argue that additional
superinvariants will occur at all odd orders of alpha'.Comment: 15 pages LaTe