28 research outputs found
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
M2-Branes and Fano 3-folds
A class of supersymmetric gauge theories arising from M2-branes probing
Calabi-Yau 4-folds which are cones over smooth toric Fano 3-folds is
investigated. For each model, the toric data of the mesonic moduli space is
derived using the forward algorithm. The generators of the mesonic moduli space
are determined using Hilbert series. The spectrum of scaling dimensions for
chiral operators is computed.Comment: 128 pages, 39 figures, 42 table
Counting Chiral Operators in Quiver Gauge Theories
We discuss in detail the problem of counting BPS gauge invariant operators in
the chiral ring of quiver gauge theories living on D-branes probing generic
toric CY singularities. The computation of generating functions that include
counting of baryonic operators is based on a relation between the baryonic
charges in field theory and the Kaehler moduli of the CY singularities. A study
of the interplay between gauge theory and geometry shows that given geometrical
sectors appear more than once in the field theory, leading to a notion of
"multiplicities". We explain in detail how to decompose the generating function
for one D-brane into different sectors and how to compute their relevant
multiplicities by introducing geometric and anomalous baryonic charges. The
Plethystic Exponential remains a major tool for passing from one D-brane to
arbitrary number of D-branes. Explicit formulae are given for few examples,
including C^3/Z_3, F_0, and dP_1.Comment: 75 pages, 22 figure
Baryonic Generating Functions
We show how it is possible to use the plethystic program in order to compute
baryonic generating functions that count BPS operators in the chiral ring of
quiver gauge theories living on the world volume of D branes probing a non
compact CY manifold. Special attention is given to the conifold theory and the
orbifold C^2/Z_2 times C, where exact expressions for generating functions are
given in detail. This paper solves a long standing problem for the
combinatorics of quiver gauge theories with baryonic moduli spaces. It opens
the way to a statistical analysis of quiver theories on baryonic branches.
Surprisingly, the baryonic charge turns out to be the quantized Kahler modulus
of the geometry.Comment: 44 pages, 7 figures; fonts change
Brane Tilings and M2 Branes
Brane tilings are efficient mnemonics for Lagrangians of N=2
Chern-Simons-matter theories. Such theories are conjectured to arise on
M2-branes probing singular toric Calabi-Yau fourfolds. In this paper, a simple
modification of the Kasteleyn technique is described which is conjectured to
compute the three dimensional toric diagram of the non-compact moduli space of
a single probe. The Hilbert Series is used to compute the spectrum of
non-trivial scaling dimensions for a selected set of examples.Comment: 47 pages, 23 figure
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
N=2 solutions of massive type IIA and their Chern-Simons duals
We find explicit AdS4 solutions of massive type IIA with N=2 supersymmetry
obtained deforming with a Roman mass the type IIA supersymmetric reduction of
the M theory background AdS4 times M111. The family of solutions have SU(3)
times SU(3) structure and isometry SU(3) times U(1)^2. They are conjectured to
be dual to three-dimensional N=2 Chern-Simons theories with generic
Chern-Simons couplings and gauge group ranks.Comment: 20 pages, 1 figure, comments and references adde
Master Space, Hilbert Series and Seiberg Duality
We analyze the action of Toric (Seiberg) duality on the combined mesonic and
baryonic moduli space of quiver gauge theories obtained from D3 branes at
Calabi-Yau singularities. We analyze in particular the structure of the master
space, the complete moduli space for one brane, for different toric phases of a
given singularity. We show that the Hilbert Series for the largest component of
the master space of different phases is the same, when refined with all the non
anomalous charges. This reflects the fact that the quiver gauge theories
associated with different phases are related by Seiberg duality when the number
of branes is greater than one.Comment: 32 pages, 7 figures, 7 tables; minor correction