5,339 research outputs found

### String Junctions and Non-Simply Connected Gauge Groups

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

We study discrete fluxes in four dimensional SU(N) gauge theories with a mass
gap by using brane compactifications which give ${\cal{N}} = 1$ or ${\cal{N}} =
0$ supersymmetry. We show that when such theories are compactified further on a
torus, the t'Hooft magnetic flux $m$ is related to the NS two-form modulus $B$
by $B = 2\pi {m\over N}$. These values of $B$ label degenerate brane vacua,
giving a simple demonstration of magnetic screening. Furthermore, for these
values of $B$ one has a conventional gauge theory on a commutative torus,
without having to perform any T-dualities. Because of the mass gap, a generic
$B$ 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 $B=2\pi {m\over N}$. Finally we show that $2\pi
{m\over N}$ behaves like a two form modulus of the QCD string. This confirms a
previous conjecture based on properties of large $N$ 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

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

- â€¦