1,438 research outputs found

### 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

### 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

### 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

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### Chern-Simons: Fano and Calabi-Yau

We present the complete classification of smooth toric Fano threefolds, known to the algebraic geometry literature, and perform some preliminary analyses in the context of brane-tilings and Chern-Simons theory on M2-branes probing Calabi-Yau fourfold singularities. We emphasise that these 18 spaces should be as intensely studied as their well-known counter-parts: the del Pezzo surfaces

### 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

### Understanding Confinement in QCD: Elements of a Big Picture

I give a brief review of advances in the strong interaction theory. This talk
was delivered at the Conference in honor of Murray Gell-Mann's 80th birthday,
24-26 February 2010, Singapore.Comment: I give a brief review of advances in the strong interaction theory.
This talk was delivered at the Conference in honor of Murray Gell-Mann's 80th
birthday, 24-26 February 2010, Singapor

### Stepwise Projection: Toward Brane Setups for Generic Orbifold Singularities

The construction of brane setups for the exceptional series E6,E7,E8 of SU(2)
orbifolds remains an ever-haunting conundrum. Motivated by techniques in some
works by Muto on non-Abelian SU(3) orbifolds, we here provide an algorithmic
outlook, a method which we call stepwise projection, that may shed some light
on this puzzle. We exemplify this method, consisting of transformation rules
for obtaining complex quivers and brane setups from more elementary ones, to
the cases of the D-series and E6 finite subgroups of SU(2). Furthermore, we
demonstrate the generality of the stepwise procedure by appealing to Frobenius'
theory of Induced Representations. Our algorithm suggests the existence of
generalisations of the orientifold plane in string theory.Comment: 22 pages, 3 figure

### Orientifold Points in M Theory

We identify the lift to M theory of the four types of orientifold points, and
show that they involve a chiral fermion on an orbifold fixed circle. From this
lift, we compute the number of normalizable ground states for the SO(N) and
$Sp(N)$ supersymmetric quantum mechanics with sixteen supercharges. The results
agree with known results obtained by the mass deformation method. The mass of
the orientifold is identified with the Casimir energy.Comment: 11 pages, Latex, references adde

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### M2-Branes and Quiver Chern-Simons: A Taxonomic Study

We initiate a systematic investigation of the space of 2+1 dimensional quiver gauge theories, emphasising a succinct "forward algorithm". Few "order parametres" are introduced such as the number of terms in the superpotential and the number of gauge groups. Starting with two terms in the superpotential, we find a generating function, with interesting geometric interpretation, which counts the number of inequivalent theories for a given number of gauge groups and fields. We demonstratively list these theories for some low numbers thereof. Furthermore, we show how these theories arise from M2-branes probing toric Calabi-Yau 4-folds by explicitly obtaining the toric data of the vacuum moduli space. By observing equivalences of the vacua between markedly different theories, we see a new emergence of "toric duality"

### Brane Boxes: Bending and Beta Functions

We study the type IIB brane box configurations recently introduced by Hanany
and Zaffaroni. We show that even at finite string coupling, one can construct
smooth configurations of branes with fairly arbitrary gauge and flavor
structure. Limiting our attention to the better understood case where NS-branes
do not intersect over a four dimensional surface gives some restrictions on the
theories, but still permits many examples, both anomalous and non-anomalous. We
give several explicit examples of such configurations and discuss what
constraints can be imposed on brane-box theories from bending considerations.
We also discuss the relation between brane bending and beta-functions for
brane-box configurations.Comment: latex, 18 pages, 8 figure

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