156 research outputs found
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
D3-branes on partial resolutions of abelian quotient singularities of Calabi-Yau threefolds
We investigate field theories on the worldvolume of a D3-brane transverse to
partial resolutions of a Calabi-Yau threefold quotient
singularity. We deduce the field content and lagrangian of such theories and
present a systematic method for mapping the moment map levels characterizing
the partial resolutions of the singularity to the Fayet-Iliopoulos parameters
of the D-brane worldvolume theory. As opposed to the simpler cases studied
before, we find a complex web of partial resolutions and associated
field-theoretic Fayet-Iliopoulos deformations. The analysis is performed by
toric methods, leading to a structure which can be efficiently described in the
language of convex geometry. For the worldvolume theory, the analysis of the
moduli space has an elegant description in terms of quivers. As a by-product,
we present a systematic way of extracting the birational geometry of the
classical moduli spaces, thus generalizing previous work on resolution of
singularities by D-branes.Comment: 52 pages, 9 figure
The Runaway Quiver
We point out that some recently proposed string theory realizations of
dynamical supersymmetry breaking actually do not break supersymmetry in the
usual desired sense. Instead, there is a runaway potential, which slides down
to a supersymmetric vacuum at infinite expectation values for some fields. The
runaway direction is not on a separated branch; rather, it shows up as
a"tadpole" everywhere on the moduli space of field expectation values.Comment: 12 pages, no figures. v2: reference chang
Dibaryons from Exceptional Collections
We discuss aspects of the dictionary between brane configurations in del
Pezzo geometries and dibaryons in the dual superconformal quiver gauge
theories. The basis of fractional branes defining the quiver theory at the
singularity has a K-theoretic dual exceptional collection of bundles which can
be used to read off the spectrum of dibaryons in the weakly curved dual
geometry. Our prescription identifies the R-charge R and all baryonic U(1)
charges Q_I with divisors in the del Pezzo surface without any Weyl group
ambiguity. As one application of the correspondence, we identify the cubic
anomaly tr R Q_I Q_J as an intersection product for dibaryon charges in large-N
superconformal gauge theories. Examples can be given for all del Pezzo surfaces
using three- and four-block exceptional collections. Markov-type equations
enforce consistency among anomaly equations for three-block collections.Comment: 47 pages, 11 figures, corrected ref
Duality cascades and duality walls
We recast the phenomenon of duality cascades in terms of the Cartan matrix
associated to the quiver gauge theories appearing in the cascade. In this
language, Seiberg dualities for the different gauge factors correspond to Weyl
reflections. We argue that the UV behavior of different duality cascades
depends markedly on whether the Cartan matrix is affine ADE or not. In
particular, we find examples of duality cascades that can't be continued after
a finite energy scale, reaching a "duality wall", in terminology due to M.
Strassler. For these duality cascades, we suggest the existence of a UV
completion in terms of a little string theory.Comment: harvmac, 24 pages, 4 figures. v2: references added. v3: reference
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Quiver theories, soliton spectra and Picard-Lefschetz transformations
Quiver theories arising on D3-branes at orbifold and del Pezzo singularities
are studied using mirror symmetry. We show that the quivers for the orbifold
theories are given by the soliton spectrum of massive 2d N=2 theory with
weighted projective spaces as target. For the theories obtained from the del
Pezzo singularities we show that the geometry of the mirror manifold gives
quiver theories related to each other by Picard-Lefschetz transformations, a
subset of which are simple Seiberg duals. We also address how one indeed
derives Seiberg duality on the matter content from such geometrical transitions
and how one could go beyond and obtain certain ``fractional Seiberg duals.''
Moreover, from the mirror geometry for the del Pezzos arise certain Diophantine
equations which classify all quivers related by Picard-Lefschetz. Some of these
Diophantine equations can also be obtained from the classification results of
Cecotti-Vafa for the 2d N=2 theories.Comment: 34 pages, 11 figure
The Generalized Green-Schwarz Mechanism for Type IIB Orientifolds with D3- and D7-Branes
In this paper, we work out in detail the tadpole cancellation conditions as
well as the generalized Green-Schwarz mechanism for type IIB orientifold
compactifications with D3- and D7-branes. We find that not only the well-known
D3- and D7-tadpole conditions have to be satisfied, but in general also the
vanishing of the induced D5-brane charges leads to a non-trivial constraint. In
fact, for the case the latter condition is important for
the cancellation of chiral anomalies. We also extend our analysis by including
D9- as well as D5-branes and determine the rules for computing the chiral
spectrum of the combined system.Comment: 33+7 pages; 2 figures; v2: references added; v3: published versio
Supersymmetric (non-)Abelian Bundles in the Type I and SO(32) Heterotic String
We discuss perturbative four-dimensional compactifications of both the SO(32)
heterotic and the Type I string on smooth Calabi-Yau manifolds endowed with
general non-abelian and abelian bundles. We analyse the generalized
Green-Schwarz mechanism for multiple anomalous U(1) factors and derive the
generically non-universal one-loop threshold corrections to the gauge kinetic
function as well as the one-loop corrected Fayet-Iliopoulos terms. The latter
can be interpreted as a stringy one-loop correction to the
Donaldson-Uhlenbeck-Yau condition. Applying S-duality, for the Type I string we
obtain the perturbative Pi-stability condition for non-abelian bundles on
curved spaces. Some simple examples are given, and we qualitatively discuss
some generic phenomenological aspects of this kind of string vacua. In
particular, we point out that in principle an intermediate string scale
scenario with TeV scale large extra dimensions might be possible for the
heterotic string.Comment: LaTeX, 32 pages, v2: refs adde
Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2d qYM theory
We study the WZW, Chern-Simons, and 2d qYM theories with gauge group U(N).
The U(N) WZW model is only well-defined for odd level K, and this model is
shown to exhibit level-rank duality in a much simpler form than that for SU(N).
The U(N) Chern-Simons theory on Seifert manifolds exhibits a similar duality,
distinct from the level-rank duality of SU(N) Chern-Simons theory on S^3. When
q = e^{2 pi i/(N+K)}, the observables of the 2d U(N) qYM theory can be
expressed as a sum over a finite subset of U(N) representations. When N and K
are odd, the qYM theory exhibits N K duality, provided q = e^{2 pi
i/(N+K)} and theta = 0 mod 2 pi /(N+K).Comment: 19 pages; v2: minor typo corrected, 1 paragraph added, published
versio
Strings on conifolds from strong coupling dynamics, part I
A method to solve various aspects of the strong coupling expansion of the
superconformal field theory duals of AdS_5 x X geometries from first principles
is proposed. The main idea is that at strong coupling the configurations that
dominate the low energy dynamics of the field theory compactified on a three
sphere are given by certain non-trivial semi-classical configurations in the
moduli space of vacua.
We show that this approach is self-consistent and permits one to express most
of the dynamics in terms of an effective N=4 SYM dynamics. This has the
advantage that some degrees of freedom that move the configurations away from
moduli space can be treated perturbatively, unifying the essential low energy
dynamics of all of these theories. We show that with this formalism one can
compute the energies of strings in the BMN limit in the Klebanov-Witten theory
from field theory considerations, matching the functional form of results found
using AdS geometry. This paper also presents various other technical results
for the semiclassical treatment of superconformal field theories.Comment: 52 pages, JHEP3 styl
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