1,438 research outputs found

    Anomaly Cancellations in Brane Tilings

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    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

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    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

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    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

    Calabi-Yau Orbifolds and Torus Coverings

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    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

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    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

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    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

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    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)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

    Brane Boxes: Bending and Beta Functions

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    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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