174 research outputs found
Integral Grothendieck-Riemann-Roch theorem
We show that, in characteristic zero, the obvious integral version of the
Grothendieck-Riemann-Roch formula obtained by clearing the denominators of the
Todd and Chern characters is true (without having to divide the Chow groups by
their torsion subgroups). The proof introduces an alternative to Grothendieck's
strategy: we use resolution of singularities and the weak factorization theorem
for birational maps.Comment: 24 page
R-charges from toric diagrams and the equivalence of a-maximization and Z-minimization
We conjecture a general formula for assigning R-charges and multiplicities
for the chiral fields of all gauge theories living on branes at toric
singularities. We check that the central charge and the dimensions of all the
chiral fields agree with the information on volumes that can be extracted from
toric geometry. We also analytically check the equivalence between the volume
minimization procedure discovered in hep-th/0503183 and a-maximization, for the
most general toric diagram. Our results can be considered as a very general
check of the AdS/CFT correspondence, valid for all superconformal theories
associated with toric singularities.Comment: 43 pages, 17 figures; minor correction
Deformations of conformal theories and non-toric quiver gauge theories
We discuss several examples of non-toric quiver gauge theories dual to
Sasaki-Einstein manifolds with U(1)^2 or U(1) isometry. We give a general
method for constructing non-toric examples by adding relevant deformations to
the toric case. For all examples, we are able to make a complete comparison
between the prediction for R-charges based on geometry and on quantum field
theory. We also give a general discussion of the spectrum of conformal
dimensions for mesonic and baryonic operators for a generic quiver theory; in
the toric case we make an explicit comparison between R-charges of mesons and
baryons.Comment: 51 pages, 12 figures; minor corrections in appendix B, published
versio
Comments on the non-conformal gauge theories dual to Ypq manifolds
We study the infrared behavior of the entire class of Y(p,q) quiver gauge
theories. The dimer technology is exploited to discuss the duality cascades and
support the general belief about a runaway behavior for the whole family. We
argue that a baryonic classically flat direction is pushed to infinity by the
appearance of ADS-like terms in the effective superpotential. We also study in
some examples the IR regime for the L(a,b,c) class showing that the same
situation might be reproduced in this more general case as well.Comment: 48 pages, 27 figures; updated reference
A New Infinite Class of Quiver Gauge Theories
We construct a new infinite family of N=1 quiver gauge theories which can be
Higgsed to the Y^{p,q} quiver gauge theories. The dual geometries are toric
Calabi-Yau cones for which we give the toric data. We also discuss the action
of Seiberg duality on these quivers, and explore the different Seiberg dual
theories. We describe the relationship of these theories to five dimensional
gauge theories on (p,q) 5-branes. Using the toric data, we specify some of the
properties of the corresponding dual Sasaki-Einstein manifolds. These theories
generically have algebraic R-charges which are not quadratic irrational
numbers. The metrics for these manifolds still remain unknown.Comment: 29 pages, JHE
On operad structures of moduli spaces and string theory
Recent algebraic structures of string theory, including homotopy Lie
algebras, gravity algebras and Batalin-Vilkovisky algebras, are deduced from
the topology of the moduli spaces of punctured Riemann spheres. The principal
reason for these structures to appear is as simple as the following. A
conformal field theory is an algebra over the operad of punctured Riemann
surfaces, this operad gives rise to certain standard operads governing the
three kinds of algebras, and that yields the structures of such algebras on the
(physical) state space naturally.Comment: 33 pages (An elaboration of minimal area metrics and new references
are added
Primary thermometry in the intermediate Coulomb blockade regime
We investigate Coulomb blockade thermometers (CBT) in an intermediate
temperature regime, where measurements with enhanced accuracy are possible due
to the increased magnitude of the differential conductance dip. Previous
theoretical results show that corrections to the half width and to the depth of
the measured conductance dip of a sensor are needed, when leaving the regime of
weak Coulomb blockade towards lower temperatures. In the present work, we
demonstrate experimentally that the temperature range of a CBT sensor can be
extended by employing these corrections without compromising the primary nature
or the accuracy of the thermometer.Comment: 8 pages, 4 figure
Proximity Induced Josephson-Quasiparticle Process in a Single Electron Transistor
We have performed the first experiments in a superconductor - normal metal -
superconductor single electron transistor in which there is an extra
superconducting strip partially overlapping the normal metal island in good
metal-to-metal contact. Superconducting proximity effect gives rise to current
peaks at voltages below the quasiparticle threshold. We interpret these peaks
in terms of the Josephson-quasiparticle process and discuss their connection
with the proximity induced energy gap in the normal metal island.Comment: 4 pages + 4 figure
Exceptional collections and D-branes probing toric singularities
We demonstrate that a strongly exceptional collection on a singular toric
surface can be used to derive the gauge theory on a stack of D3-branes probing
the Calabi-Yau singularity caused by the surface shrinking to zero size. A
strongly exceptional collection, i.e., an ordered set of sheaves satisfying
special mapping properties, gives a convenient basis of D-branes. We find such
collections and analyze the gauge theories for weighted projective spaces, and
many of the Y^{p,q} and L^{p,q,r} spaces. In particular, we prove the strong
exceptionality for all p in the Y^{p,p-1} case, and similarly for the
Y^{p,p-2r} case.Comment: 49 pages, 6 figures; v2 refs added; v3 published versio
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