Relating U(N)xU(N) to SU(N)xSU(N) Chern-Simons Membrane theories

By integrating out the U(1)_B gauge field, we show that the U(n)xU(n) ABJM theory at level k is equivalent to a Z_k identification of the (SU(n)xSU(n))/Z_n Chern-Simons theory, but only when n and k are coprime. As a consequence, the k=1 ABJM model for two M2-branes in R^8 can be identified with the N=8 (SU(2)xSU(2))/Z_2 theory. We also conjecture that the U(2)xU(2) ABJM model at k=2 is equivalent to the N=8 SU(2)xSU(2)-theory.Comment: 16 pages, Latex; v2: references added; v3: Clarifications adde

The Phase Diagram of Three-Dimensional SU(3) + Adjoint Higgs Theory

We study the phase diagram of the three-dimensional SU(3)+adjoint Higgs theory with lattice Monte Carlo simulations. A critical line consisting of a first order line, a tricritical point and a second order line, divides the phase diagram into two parts distinguished by =0 and /=0. The location and the type of the critical line are determined by measuring the condensates and , and the masses of scalar and vector excitations. Although in principle there can be different types of broken phases, corresponding perturbatively to unbroken SU(2)xU(1) or U(1)xU(1) symmetries, we find that dynamically only the broken phase with SU(2)xU(1)-like properties is realized. The relation of the phase diagram to 4d finite temperature QCD is discussed.Comment: 21 pages, 8 figure

Yang-Mills instantons and dyons on homogeneous G_2-manifolds

We consider Lie G-valued Yang-Mills fields on the space R x G/H, where G/H is a compact nearly K"ahler six-dimensional homogeneous space, and the manifold R x G/H carries a G_2-structure. After imposing a general G-invariance condition, Yang-Mills theory with torsion on R x G/H is reduced to Newtonian mechanics of a particle moving in R^6, R^4 or R^2 under the influence of an inverted double-well-type potential for the cases G/H = SU(3)/U(1)xU(1), Sp(2)/Sp(1)xU(1) or G_2/SU(3), respectively. We analyze all critical points and present analytical and numerical kink- and bounce-type solutions, which yield G-invariant instanton configurations on those cosets. Periodic solutions on S^1 x G/H and dyons on iR x G/H are also given.Comment: 1+26 pages, 14 figures, 6 miniplot

Towards an Anomaly-Free Quantum Dynamics for a Weak Coupling Limit of Euclidean Gravity: Diffeomorphism Covariance

The G-->0 limit of Euclidean gravity introduced by Smolin is described by a generally covariant U(1)xU(1)xU(1) gauge theory. In an earlier paper, Tomlin and Varadarajan constructed the quantum Hamiltonian constraint of density weight 4/3 for this U(1)xU(1)xU(1) theory so as to produce a non-trivial anomaly free LQG-type representation of the Poisson bracket between a pair of Hamiltonian constraints. These constructions involved a choice of regulating coordinate patches. The use of these coordinate patches is in apparent conflict with spatial diffeomorphism covariance. In this work we show how an appropriate choice of coordinate patches together with suitable modifications of these constructions results in the diffeomorphism covariance of the continuum limit action of the Hamiltonian constraint operator, while preserving the anomaly free property of the continuum limit action of its commutator.Comment: 56 pages, No figure

Structural and optical properties of MOCVD AllnN epilayers

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