5,908 research outputs found
Near-flat space limit and Einstein manifolds
We study the near-flat space limit for strings on AdS(5)xM(5), where the
internal manifold M(5) is equipped with a generic metric with U(1)xU(1)xU(1)
isometry. In the bosonic sector, the limiting sigma model is similar to the one
found for AdS(5)xS(5), as the global symmetries are reduced in the most general
case. When M(5) is a Sasaki-Einstein space like T(1,1), Y(p,q) and L(p,q,r),
whose dual CFT's have N=1 supersymmetry, the near-flat space limit gives the
same bosonic sector of the sigma model found for AdS(5)xS(5). This indicates
the generic presence of integrable subsectors in AdS/CFT.Comment: 30 pages, 1 figur
Implications of Hadron Collider Observables on Parton Distribution Function Uncertainties
Standard parton distribution function sets do not have rigorously quantified
uncertainties. In recent years it has become apparent that these uncertainties
play an important role in the interpretation of hadron collider data. In this
paper, using the framework of statistical inference, we illustrate a technique
that can be used to efficiently propagate the uncertainties to new observables,
assess the compatibility of new data with an initial fit, and, in case the
compatibility is good, include the new data in the fit.Comment: 22 pages, 5 figure
Zonotopes and four-dimensional superconformal field theories
The a-maximization technique proposed by Intriligator and Wecht allows us to
determine the exact R-charges and scaling dimensions of the chiral operators of
four-dimensional superconformal field theories. The problem of existence and
uniqueness of the solution, however, has not been addressed in general setting.
In this paper, it is shown that the a-function has always a unique critical
point which is also a global maximum for a large class of quiver gauge theories
specified by toric diagrams. Our proof is based on the observation that the
a-function is given by the volume of a three dimensional polytope called
"zonotope", and the uniqueness essentially follows from Brunn-Minkowski
inequality for the volume of convex bodies. We also show a universal upper
bound for the exact R-charges, and the monotonicity of a-function in the sense
that a-function decreases whenever the toric diagram shrinks. The relationship
between a-maximization and volume-minimization is also discussed.Comment: 29 pages, 15 figures, reference added, typos corrected, version
published in JHE
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"
journa
Central Extensions of Finite Heisenberg Groups in Cascading Quiver Gauge Theories
Many conformal quiver gauge theories admit nonconformal generalizations.
These generalizations change the rank of some of the gauge groups in a
consistent way, inducing a running in the gauge couplings. We find a group of
discrete transformation that acts on a large class of these theories. These
transformations form a central extension of the Heisenberg group, generalizing
the Heisenberg group of the conformal case, when all gauge groups have the same
rank. In the AdS/CFT correspondence the nonconformal quiver gauge theory is
dual to supergravity backgrounds with both five-form and three-form flux. A
direct implication is that operators counting wrapped branes satisfy a central
extension of a finite Heisenberg group and therefore do not commute.Comment: 25 pages, 12 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
Finite Heisenberg Groups in Quiver Gauge Theories
We show by direct construction that a large class of quiver gauge theories
admits actions of finite Heisenberg groups. We consider various quiver gauge
theories that arise as AdS/CFT duals of orbifolds of C^3, the conifold and its
orbifolds and some orbifolds of the cone over Y(p,q). Matching the gauge theory
analysis with string theory on the corresponding spaces implies that the
operators counting wrapped branes do not commute in the presence of flux.Comment: 25 pages, 13 figure
Scaling in many-body systems and proton structure function
The observation of scaling in processes in which a weakly interacting probe
delivers large momentum to a many-body system simply reflects the
dominance of incoherent scattering off target constituents. While a suitably
defined scaling function may provide rich information on the internal dynamics
of the target, in general its extraction from the measured cross section
requires careful consideration of the nature of the interaction driving the
scattering process. The analysis of deep inelastic electron-proton scattering
in the target rest frame within standard many-body theory naturally leads to
the emergence of a scaling function that, unlike the commonly used structure
functions and , can be directly identified with the intrinsic proton
response.Comment: 11 pages, 4 figures. Proceedings of the 11th Conference on Recent
Progress in Many-Body Theories, Manchester, UK, July 9-13 200
Finite Heisenbeg Groups and Seiberg Dualities in Quiver Gauge Theories
A large class of quiver gauge theories admits the action of finite Heisenberg
groups of the form Heis(Z_q x Z_q). This Heisenberg group is generated by a
manifest Z_q shift symmetry acting on the quiver along with a second Z_q
rephasing (clock) generator acting on the links of the quiver. Under Seiberg
duality, however, the action of the shift generator is no longer manifest, as
the dualized node has a different structure from before. Nevertheless, we
demonstrate that the Z_q shift generator acts naturally on the space of all
Seiberg dual phases of a given quiver. We then prove that the space of Seiberg
dual theories inherits the action of the original finite Heisenberg group,
where now the shift generator Z_q is a map among fields belonging to different
Seiberg phases. As examples, we explicitly consider the action of the
Heisenberg group on Seiberg phases for C^3/Z_3, Y^{4,2} and Y^{6,3} quiver.Comment: 22 pages, five figure
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
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