6,080 research outputs found
The Toric Phases of the Y^{p,q} Quivers
We construct all connected toric phases of the recently discovered
quivers and show their IR equivalence using Seiberg duality. We also compute
the R and global U(1) charges for a generic toric phase of .Comment: 14 pages, 3 figure
From Sasaki-Einstein spaces to quivers via BPS geodesics: Lpqr
The AdS/CFT correspondence between Sasaki-Einstein spaces and quiver gauge
theories is studied from the perspective of massless BPS geodesics. The
recently constructed toric Lpqr geometries are considered: we determine the
dual superconformal quivers and the spectrum of BPS mesons. The conformal
anomaly is compared with the volumes of the manifolds. The U(1)^2_F x U(1)_R
global symmetry quantum numbers of the mesonic operators are successfully
matched with the conserved momenta of the geodesics, providing a test of
AdS/CFT duality. The correspondence between BPS mesons and geodesics allows to
find new precise relations between the two sides of the duality. In particular
the parameters that characterize the geometry are mapped directly to the
parameters used for a-maximization in the field theory. The analysis simplifies
for the special case of the Lpqq models, which are shown to correspond to the
known "generalized conifolds". These geometries can break conformal invariance
through toric deformations of the complex structure.Comment: 30 pages, 8 figures, LaTeX. v2: One more figure. References added,
typos correcte
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
Comments on Anomalies and Charges of Toric-Quiver Duals
We obtain a simple expression for the triangle `t Hooft anomalies in quiver
gauge theories that are dual to toric Sasaki-Einstein manifolds. We utilize the
result and simplify considerably the proof concerning the equivalence of
a-maximization and Z-minimization. We also resolve the ambiguity in defining
the flavor charges in quiver gauge theories. We then compare coefficients of
the triangle anomalies with coefficients of the current-current correlators and
find perfect agreement.Comment: 22 pages, 3 figure
Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics
We develop a systematic and efficient method of counting single-trace and
multi-trace BPS operators with two supercharges, for world-volume gauge
theories of D-brane probes for both and finite . The
techniques are applicable to generic singularities, orbifold, toric, non-toric,
complete intersections, et cetera, even to geometries whose precise field
theory duals are not yet known. The so-called ``Plethystic Exponential''
provides a simple bridge between (1) the defining equation of the Calabi-Yau,
(2) the generating function of single-trace BPS operators and (3) the
generating function of multi-trace operators. Mathematically, fascinating and
intricate inter-relations between gauge theory, algebraic geometry,
combinatorics and number theory exhibit themselves in the form of plethystics
and syzygies.Comment: 59+1 pages, 7 Figure
Brane Tilings and Exceptional Collections
Both brane tilings and exceptional collections are useful tools for
describing the low energy gauge theory on a stack of D3-branes probing a
Calabi-Yau singularity. We provide a dictionary that translates between these
two heretofore unconnected languages. Given a brane tiling, we compute an
exceptional collection of line bundles associated to the base of the
non-compact Calabi-Yau threefold. Given an exceptional collection, we derive
the periodic quiver of the gauge theory which is the graph theoretic dual of
the brane tiling. Our results give new insight to the construction of quiver
theories and their relation to geometry.Comment: 46 pages, 37 figures, JHEP3; v2: reference added, figure 13 correcte
Knowledge, Food and Place: a way of producing a way of knowing
The article examines the dynamics of knowledge in the valorisation of local food, drawing on the results from the CORASON project (A cognitive approach to rural sustainable development: the dynamics of expert and lay knowledge), funded by the EU under its Framework Programme 6. It is based on the analysis of several in-depth case studies on food relocalisation carried out in 10 European countries
Cascading Quivers from Decaying D-branes
We use an argument analogous to that of Kachru, Pearson and Verlinde to argue
that cascades in L^{a,b,c} quiver gauge theories always preserve the form of
the quiver, and that all gauge groups drop at each step by the number M of
fractional branes. In particular, we demonstrate that an NS5-brane that sweeps
out the S^3 of the base of L^{a,b,c} destroys M D3-branes.Comment: 11 pages, 1 figure; v2: references adde
A Meinardus theorem with multiple singularities
Meinardus proved a general theorem about the asymptotics of the number of
weighted partitions, when the Dirichlet generating function for weights has a
single pole on the positive real axis. Continuing \cite{GSE}, we derive
asymptotics for the numbers of three basic types of decomposable combinatorial
structures (or, equivalently, ideal gas models in statistical mechanics) of
size , when their Dirichlet generating functions have multiple simple poles
on the positive real axis. Examples to which our theorem applies include ones
related to vector partitions and quantum field theory. Our asymptotic formula
for the number of weighted partitions disproves the belief accepted in the
physics literature that the main term in the asymptotics is determined by the
rightmost pole.Comment: 26 pages. This version incorporates the following two changes implied
by referee's remarks: (i) We made changes in the proof of Proposition 1; (ii)
We provided an explanation to the argument for the local limit theorem. The
paper is tentatively accepted by "Communications in Mathematical Physics"
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