Necessary and sufficient conditions for non-perturbative equivalences of large N orbifold gauge theories

Large N coherent state methods are used to study the relation between U(N) gauge theories containing adjoint representation matter fields and their orbifold projections. The classical dynamical systems which reproduce the large N limits of the quantum dynamics in parent and daughter orbifold theories are compared. We demonstrate that the large N dynamics of the parent theory, restricted to the subspace invariant under the orbifold projection symmetry, and the large N dynamics of the daughter theory, restricted to the untwisted sector invariant under "theory space'' permutations, coincide. This implies equality, in the large N limit, between appropriately identified connected correlation functions in parent and daughter theories, provided the orbifold projection symmetry is not spontaneously broken in the parent theory and the theory space permutation symmetry is not spontaneously broken in the daughter. The necessity of these symmetry realization conditions for the validity of the large N equivalence is unsurprising, but demonstrating the sufficiency of these conditions is new. This work extends an earlier proof of non-perturbative large N equivalence which was only valid in the phase of the (lattice regularized) theories continuously connected to large mass and strong coupling.Comment: 21 page, JHEP styl

Comments on Condensates in Non-Supersymmetric Orbifold Field Theories

Non-supersymmetric orbifolds of N=1 super Yang-Mills theories are conjectured to inherit properties from their supersymmetric parent. We examine this conjecture by compactifying the Z_2 orbifold theories on a spatial circle of radius R. We point out that when the orbifold theory lies in the weakly coupled vacuum of its parent, fractional instantons do give rise to the conjectured condensate of bi-fundamental fermions. Unfortunately, we show that quantum effects render this vacuum unstable through the generation of twisted operators. In the true vacuum state, no fermion condensate forms. Thus, in contrast to super Yang-Mills, the compactified orbifold theory undergoes a chiral phase transition as R is varied.Comment: 10 Pages. Added clarifying comments, computational steps and a nice pretty pictur

Small volume expansion of almost supersymmetric large N theories

We consider the small-volume dynamics of nonsupersymmetric orbifold and orientifold field theories defined on a three-torus, in a test of the claimed planar equivalence between these models and appropriate supersymmetric ``parent models". We study one-loop effective potentials over the moduli space of flat connections and find that planar equivalence is preserved for suitable averages over the moduli space. On the other hand, strong nonlinear effects produce local violations of planar equivalence at special points of moduli space. In the case of orbifold models, these effects show that the "twisted" sector dominates the low-energy dynamics.Comment: 20 pages, 3 figures; added references, minor change

SU(3) Predictions for Weak Decays of Doubly Heavy Baryons -- including SU(3) breaking terms

We find expressions for the weak decay amplitudes of baryons containing two b quarks (or one b and one c quark -- many relationship are the same) in terms of unknown reduced matrix elements. This project was originally motivated by the request of the FNAL Run II b Physics Workshop organizers for a guide to experimentalists in their search for as yet unobserved hadrons. We include an analysis of linear SU(3) breaking terms in addition to relationships generated by unbroken SU(3) symmetry, and relate these to expressions in terms of the complete set of possible reduced matrix elements.Comment: 49 page

Non-Perturbative Planar Equivalence and the Absence of Closed String Tachyons

We consider 'orbifold' and 'orientifold' field theories from the dual closed string theory side. We argue that a necessary condition for planar equivalence to hold is the absence of a closed string tachyonic mode in the dual non-supersymmetric string. We analyze several gauge theories on R3xS1. In the specific case of U(N) theories with symmetric/anti-symmetric fermions ('orientifold field theories') the relevant closed string theory is tachyon-free at large compactification radius (due to winding modes), but it develops a tachyonic mode below a critical radius. Our finding is with agreement with field theory expectations of a phase transition from a C-parity violating phase to a C-parity preserving phase as the compactification radius increases. In the case of U(N)xU(N) theories with bi-fundamental matter ('orbifold field theories') a tachyon is always present in the string spectrum, at any compactification radius. We conclude that on R4 planar equivalence holds for 'orientfiold field theories', but fails for 'orbifold field theories' daughters of N=4 SYM and suggest the same for daughters of N=1 SYM. We also discuss examples of SO/Sp gauge theories with symmetric/anti-symmetric fermions. In this case planar equivalence holds at any compactification radius -in agreement with the absence of tachyons in the string dual.Comment: 14 pages, Latex. 3 eps figures. v2: ref. added. v3: clarifying sentences added in the abstract and at the end of section 4. version accepted to JHE

Non-perturbative equivalences among large N gauge theories with adjoint and bifundamental matter fields

We prove an equivalence, in the large N limit, between certain U(N) gauge theories containing adjoint representation matter fields and their orbifold projections. Lattice regularization is used to provide a non-perturbative definition of these theories; our proof applies in the strong coupling, large mass phase of the theories. Equivalence is demonstrated by constructing and comparing the loop equations for a parent theory and its orbifold projections. Loop equations for both expectation values of single-trace observables, and for connected correlators of such observables, are considered; hence the demonstrated non-perturbative equivalence applies to the large N limits of both string tensions and particle spectra.Comment: 40 pages, JHEP styl

A Mathematical Model of Liver Cell Aggregation In Vitro

The behavior of mammalian cells within three-dimensional structures is an area of intense biological research and underpins the efforts of tissue engineers to regenerate human tissues for clinical applications. In the particular case of hepatocytes (liver cells), the formation of spheroidal multicellular aggregates has been shown to improve cell viability and functionality compared to traditional monolayer culture techniques. We propose a simple mathematical model for the early stages of this aggregation process, when cell clusters form on the surface of the extracellular matrix (ECM) layer on which they are seeded. We focus on interactions between the cells and the viscoelastic ECM substrate. Governing equations for the cells, culture medium, and ECM are derived using the principles of mass and momentum balance. The model is then reduced to a system of four partial differential equations, which are investigated analytically and numerically. The model predicts that provided cells are seeded at a suitable density, aggregates with clearly defined boundaries and a spatially uniform cell density on the interior will form. While the mechanical properties of the ECM do not appear to have a significant effect, strong cell-ECM interactions can inhibit, or possibly prevent, the formation of aggregates. The paper concludes with a discussion of our key findings and suggestions for future work

D-Brane Probes of Special Holonomy Manifolds

Using D2-brane probes, we study various properties of M-theory on singular, non-compact manifolds of G_2 and Spin(7) holonomy. We derive mirror pairs of N=1 supersymmetric three-dimensional gauge theories, and apply this technique to realize exceptional holonomy manifolds as both Coulomb and Higgs branches of the D2-brane world-volume theory. We derive a ``G_2 quotient construction'' of non-compact manifolds which admit a metric of G_2 holonomy. We further discuss the moduli space of such manifolds, including the structure of geometrical transitions in each case. For completeness, we also include familiar examples of manifolds with SU(3) and Sp(2) holonomy, where some of the new ideas are clarified and tested.Comment: 79 pages, Late

Non-Abelian k-Vortex Dynamics in N=1^* theory and its Gravity Dual

We study magnetic flux tubes in the Higgs vacuum of the N=1^* mass deformation of SU(N_c), N=4 SYM and its large N_c string dual, the Polchinski-Strassler geometry. Choosing equal masses for the three adjoint chiral multiplets, for all N_c we identify a "colour-flavour locked" symmetry, SO(3)_{C+F} which leaves the Higgs vacuum invariant. At weak coupling, we find explicit non-Abelian k-vortex solutions carrying a Z_{N_c}-valued magnetic flux, with winding, 0 < k < N_c. These k-strings spontaneously break SO(3)_{C+F} to U(1)_{C+F} resulting in an S^2 moduli space of solutions. The world-sheet sigma model is a nonsupersymmetric CP^1 model with a theta angle \theta_{1+1} = k(N_c-k)\theta_{3+1} where \theta_{3+1} is the Yang-Mills vacuum angle. We find numerically that k-vortex tensions follow the Casimir scaling law T_k \propto k (N_c-k) for large N_c. In the large N_c IIB string dual, the SO(3)_{C+F} symmetry is manifest in the geometry interpolating between AdS_5 x S^5 and the interior metric due to a single D5-brane carrying D3-brane charge. We identify candidate k-vortices as expanded probe D3-branes formed from a collection of k D-strings. The resulting k-vortex tension exhibits precise Casimir scaling, and the effective world-sheet theta angle matches the semiclassical result. S-duality maps the Higgs to the confining phase so that confining string tensions at strong 't Hooft coupling also exhibit Casimir scaling in N=1^* theory in the large N_c limit.Comment: 48 pages, 5 figures. v2: typos correcte