5,339 research outputs found

    String Junctions and Non-Simply Connected Gauge Groups

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    Relations between the global structure of the gauge group in elliptic F-theory compactifications, fractional null string junctions, and the Mordell-Weil lattice of rational sections are discussed. We extend results in the literature, which pertain primarily to rational elliptic surfaces and obtain pi^1(G) where G is the semi-simple part of the gauge group. We show how to obtain the full global structure of the gauge group, including all U(1) factors. Our methods are not restricted to rational elliptic surfaces. We also consider elliptic K3's and K3-fibered Calabi-Yau three-folds.Comment: latex, 34 pages, 8 figure

    Strings and Discrete Fluxes of QCD

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    We study discrete fluxes in four dimensional SU(N) gauge theories with a mass gap by using brane compactifications which give N=1{\cal{N}} = 1 or N=0{\cal{N}} = 0 supersymmetry. We show that when such theories are compactified further on a torus, the t'Hooft magnetic flux mm is related to the NS two-form modulus BB by B=2Ď€mNB = 2\pi {m\over N}. These values of BB label degenerate brane vacua, giving a simple demonstration of magnetic screening. Furthermore, for these values of BB one has a conventional gauge theory on a commutative torus, without having to perform any T-dualities. Because of the mass gap, a generic BB does not give a four dimensional gauge theory on a non-commutative torus. The Kaluza-Klein modes which must be integrated out to give a four dimensional theory decouple only when B=2Ď€mNB=2\pi {m\over N}. Finally we show that 2Ď€mN2\pi {m\over N} behaves like a two form modulus of the QCD string. This confirms a previous conjecture based on properties of large NN QCD suggesting a T-duality invariance.Comment: references added, revised comments concerning non-commutative tor

    Complexified Path Integrals and the Phases of Quantum Field Theory

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    The path integral by which quantum field theories are defined is a particular solution of a set of functional differential equations arising from the Schwinger action principle. In fact these equations have a multitude of additional solutions which are described by integrals over a complexified path. We discuss properties of the additional solutions which, although generally disregarded, may be physical with known examples including spontaneous symmetry breaking and theta vacua. We show that a consideration of the full set of solutions yields a description of phase transitions in quantum field theories which complements the usual description in terms of the accumulation of Lee-Yang zeroes. In particular we argue that non-analyticity due to the accumulation of Lee-Yang zeros is related to Stokes phenomena and the collapse of the solution set in various limits including but not restricted to, the thermodynamic limit. A precise demonstration of this relation is given in terms of a zero dimensional model. Finally, for zero dimensional polynomial actions, we prove that Borel resummation of perturbative expansions, with several choices of singularity avoiding contours in the complex Borel plane, yield inequivalent solutions of the action principle equations.Comment: 15 pages, 9 figures (newer version has better images
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