2,416 research outputs found
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
Global symmetries and 't Hooft anomalies in brane tilings
We investigate the relation between gauge theories and brane configurations
described by brane tilings. We identify U(1)_B (baryonic), U(1)_M (mesonic),
and U(1)_R global symmetries in gauge theories with gauge symmetries in the
brane configurations. We also show that U(1)_MU(1)_B^2 and U(1)_RU(1)_B^2 't
Hooft anomalies are reproduced as gauge transformations of the classical brane
action.Comment: 41 pages, 6 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
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
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
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
Anomaly Cancellations in Brane Tilings
We re-interpret the anomaly cancellation conditions for the gauge symmetries
and the baryonic flavor symmetries in quiver gauge theories realized by the
brane tilings from the viewpoint of flux conservation on branes.Comment: 10 pages, LaTeX; v2: minor corrections, a note on the zero-form flux
adde
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
A-D-E Quivers and Baryonic Operators
We study baryonic operators of the gauge theory on multiple D3-branes at the
tip of the conifold orbifolded by a discrete subgroup Gamma of SU(2). The
string theory analysis predicts that the number and the order of the fixed
points of Gamma acting on S^2 are directly reflected in the spectrum of
baryonic operators on the corresponding quiver gauge theory constructed from
two Dynkin diagrams of the corresponding type. We confirm the prediction by
developing techniques to enumerate baryonic operators of the quiver gauge
theory which includes the gauge groups with different ranks. We also find that
the Seiberg dualities act on the baryonic operators in a non-Abelian fashion.Comment: 46 pages, 17 figures; v2: minor corrections, note added in section 1,
references adde
Toric AdS4/CFT3 duals and M-theory Crystals
We study the recently proposed crystal model for three dimensional
superconformal field theories arising from M2-branes probing toric Calabi-Yau
four-fold singularities. We explain the algorithms mapping a toric Calabi-Yau
to a crystal and vice versa, and show how the spectrum of BPS meson states fits
into the crystal model.Comment: 24 pages, 24 figure
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