2,344 research outputs found
Brane tilings and supersymmetric gauge theories
In the last few years, brane tilings have proven to be an efficient and
convenient way of studying supersymmetric gauge theories living on D3-branes or
M2-branes. In these pages we present a quick and simple introduction to the
subject, hoping this could tickle the reader's curiosity to learn more on this
extremely fascinating subject.Comment: 3 pages, 2 figures, based on a presentation given by G.T. at the 2010
Cargese Summer School (June 21-July 3), to appear in the proceeding
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
Counting Orbifolds
We present several methods of counting the orbifolds C^D/Gamma. A
correspondence between counting orbifold actions on C^D, brane tilings, and
toric diagrams in D-1 dimensions is drawn. Barycentric coordinates and scaling
mechanisms are introduced to characterize lattice simplices as toric diagrams.
We count orbifolds of C^3, C^4, C^5, C^6 and C^7. Some remarks are made on
closed form formulas for the partition function that counts distinct orbifold
actions.Comment: 69 pages, 9 figures, 24 tables; minor correction
The Hilbert Series of Adjoint SQCD
We use the plethystic exponential and the Molien-Weyl formula to compute the
Hilbert series (generating funtions), which count gauge invariant operators in
N=1 supersymmetric SU(N_c), Sp(N_c), SO(N_c) and G_2 gauge theories with 1
adjoint chiral superfield, fundamental chiral superfields, and zero classical
superpotential. The structure of the chiral ring through the generators and
relations between them is examined using the plethystic logarithm and the
character expansion technique. The palindromic numerator in the Hilbert series
implies that the classical moduli space of adjoint SQCD is an affine Calabi-Yau
cone over a weighted projective variety.Comment: 53 pages, 1 figure and 2 tables. Version 2: Section 4.4.1 added,
Section 4.4 improved, typos fixed, published in Nuclear Physics
The covariant perturbative string spectrum
We provide generating functions for the perturbative massive string spectrum
which are covariant with respect to the SO(9) little group, and which contain
all the representation theoretic content of the spectrum. Generating functions
for perturbative bosonic, Type II, Heterotic and Type I string theories are
presented, and generalizations are discussed.Comment: 15 pages, typos correcte
The Hilbert series of U/SU SQCD and Toeplitz Determinants
We present a new technique for computing Hilbert series of N=1 supersymmetric
QCD in four dimensions with unitary and special unitary gauge groups. We show
that the Hilbert series of this theory can be written in terms of determinants
of Toeplitz matrices. Applying related theorems from random matrix theory, we
compute a number of exact Hilbert series as well as asymptotic formulae for
large numbers of colours and flavours -- many of which have not been derived
before.Comment: 49 pages, 6 figures. Version 2: references adde
Calabi-Yau Orbifolds and Torus Coverings
The theory of coverings of the two-dimensional torus is a standard part of
algebraic topology and has applications in several topics in string theory, for
example, in topological strings. This paper initiates applications of this
theory to the counting of orbifolds of toric Calabi-Yau singularities, with
particular attention to Abelian orbifolds of C^D. By doing so, the work
introduces a novel analytical method for counting Abelian orbifolds, verifying
previous algorithm results. One identifies a p-fold cover of the torus T^{D-1}
with an Abelian orbifold of the form C^D/Z_p, for any dimension D and a prime
number p. The counting problem leads to polynomial equations modulo p for a
given Abelian subgroup of S_D, the group of discrete symmetries of the toric
diagram for C^D. The roots of the polynomial equations correspond to orbifolds
of the form C^D/Z_p, which are invariant under the corresponding subgroup of
S_Ds. In turn, invariance under this subgroup implies a discrete symmetry for
the corresponding quiver gauge theory, as is clearly seen by its brane tiling
formulation.Comment: 33 pages, 5 figures, 7 tables; version published on JHE
Highest Weight Generating Functions for Hilbert Series
We develop a new method for representing Hilbert series based on the highest
weight Dynkin labels of their underlying symmetry groups. The method draws on
plethystic functions and character generating functions along with Weyl
integration. We give explicit examples showing how the use of such highest
weight generating functions (HWGs) permits an efficient encoding and analysis
of the Hilbert series of the vacuum moduli spaces of classical and exceptional
SQCD theories and also of the moduli spaces of instantons. We identify how the
HWGs of gauge invariant operators of a selection of classical and exceptional
SQCD theories result from the interaction under symmetrisation between a
product group and the invariant tensors of its gauge group. In order to
calculate HWGs, we derive and tabulate character generating functions for low
rank groups by a variety of methods, including a general character generating
function, based on the Weyl Character Formula, for any classical or exceptional
group.Comment: 76 page
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