13,825 research outputs found
On the twisted chiral potential in 2d and the analogue of rigid special geometry for 4-folds
We discuss how to obtain an N=(2,2) supersymmetric SU(3) gauge theory in two
dimensions via geometric engineering from a Calabi-Yau 4-fold and compute its
non-perturbative twisted chiral potential. The relevant compact part of the
4-fold geometry consists of two intersecting P^1's fibered over P^2. The rigid
limit of the local mirror of this geometry is a complex surface that
generalizes the Seiberg-Witten curve and on which there exist two holomorphic
2-forms. These stem from the same meromorphic 2-form as derivatives w.r.t. the
two moduli, respectively. The middle periods of this meromorphic form give
directly the twisted chiral potential. The explicit computation of these and of
the four-point Yukawa couplings allows for a non-trivial test of the analogue
of rigid special geometry for a 4-fold with several moduli.Comment: 20 pages, LaTeX, no figures; v2: discussion of FI-couplings in
section 3 and appendix enlarged, version to appear in JHE
Reverse geometric engineering of singularities
One can geometrically engineer supersymmetric field theories theories by
placing D-branes at or near singularities. The opposite process is described,
where one can reconstruct the singularities from quiver theories. The
description is in terms of a noncommutative quiver algebra which is constructed
from the quiver diagram and the superpotential. The center of this
noncommutative algebra is a commutative algebra, which is the ring of
holomorphic functions on a variety V. If certain algebraic conditions are met,
then the reverse geometric engineering produces V as the geometry that D-branes
probe. It is also argued that the identification of V is invariant under
Seiberg dualities.Comment: 17 pages, Latex. v2: updates reference
Geometric Engineering, Mirror Symmetry and 6d (1,0) -> 4d, N=2
We study compactification of 6 dimensional (1,0) theories on T^2. We use
geometric engineering of these theories via F-theory and employ mirror symmetry
technology to solve for the effective 4d N=2 geometry for a large number of the
(1,0) theories including those associated with conformal matter. Using this we
show that for a given 6d theory we can obtain many inequivalent 4d N=2 SCFTs.
Some of these respect the global symmetries of the 6d theory while others
exhibit SL(2,Z) duality symmetry inherited from global diffeomorphisms of the
T^2. This construction also explains the 6d origin of moduli space of 4d affine
ADE quiver theories as flat ADE connections on T^2. Among the resulting 4d N=2
CFTs we find theories whose vacuum geometry is captured by an LG theory (as
opposed to a curve or a local CY geometry). We obtain arbitrary genus curves of
class S with punctures from toroidal compactification of (1,0) SCFTs where the
curve of the class S theory emerges through mirror symmetry. We also show that
toroidal compactification of the little string version of these theories can
lead to class S theories with no punctures on arbitrary genus Riemann surface.Comment: 58 pages, 8 figures, v2: references added, typos fixed, table 2
update
D-branes on Singularities: New Quivers from Old
In this paper we present simplifying techniques which allow one to compute
the quiver diagrams for various D-branes at (non-Abelian) orbifold
singularities with and without discrete torsion. The main idea behind the
construction is to take the orbifold of an orbifold. Many interesting discrete
groups fit into an exact sequence . As such, the orbifold
is easier to compute as and we present graphical rules which
allow fast computation given the quiver.Comment: 25 pages, 13 figures, LaTe
Chiral field theories from conifolds
We discuss the geometric engineering and large n transition for an N=1 U(n)
chiral gauge theory with one adjoint, one conjugate symmetric, one
antisymmetric and eight fundamental chiral multiplets. Our IIB realization
involves an orientifold of a non-compact Calabi-Yau A_2 fibration, together
with D5-branes wrapping the exceptional curves of its resolution as well as the
orientifold fixed locus. We give a detailed discussion of this background and
of its relation to the Hanany-Witten realization of the same theory. In
particular, we argue that the T-duality relating the two constructions maps the
Z_2 orientifold of the Hanany-Witten realization into a Z_4 orientifold in type
IIB. We also discuss the related engineering of theories with SO/Sp gauge
groups and symmetric or antisymmetric matter.Comment: 34 pages, 8 figures, v2: References added, minor correction
OPE Selection Rules for Schur Multiplets in 4D Superconformal Field Theories
We compute general expressions for two types of three-point functions of
(semi-)short multiplets in four-dimensional superconformal
field theories. These (semi-)short multiplets are called "Schur multiplets" and
play an important role in the study of associated chiral algebras. The first
type of the three-point functions we compute involves two half-BPS Schur
multiplets and an arbitrary Schur multiplet, while the second type involves one
stress tensor multiplet and two arbitrary Schur multiplets. From these
three-point functions, we read off the corresponding OPE selection rules for
the Schur multiplets. Our results particularly imply that there are non-trivial
selection rules on the quantum numbers of Schur operators in these multiplets.
We also give a conjecture on the selection rules for general Schur multiplets.Comment: 39 page
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