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

Less is More: Non-renormalization Theorems from Lower Dimensional Superspace

We discuss a new class of non-renormalization theorems in N=4 and N=2 Super-Yang-Mills theory, obtained by using a superspace which makes a lower dimensional subgroup of the full supersymmetry manifest. Certain Wilson loops (and Wilson lines) belong to the chiral ring of the lower dimensional supersymmetry algebra, and their expectation values can be computed exactly.Comment: 8 pages, based on talk given by Z. Guralnik at 8th Workshop on Non-perturbative QCD, Paris, June 200

Strong Coupling Phenomena on the Noncommutative Plane

We study strong coupling phenomena in U(1) gauge theory on the non-commutative plane. To do so, we make use of a T-dual description in terms of an $N\to\infty$ limit of U(N) gauge theory on a commutative torus. The magnetic flux on this torus is taken to be $m=N-1$, while the area scales like 1/N, keeping $\Lambda_{QCD}$ fixed. With a few assumptions, we argue that the speed of high frequency light in pure non-commutative QED is modified in the non-commutative directions by the factor $1 + \Lambda_{QCD}^4 \theta^2$, where $\theta$ is the non-commutative parameter. If charged flavours are included, there is an upper bound on the momentum of a photon propagating in the non-commutative directions, beyond which it is unstable against production of charged pairs. We also discuss a particular $\theta\to\infty$ limit of pure non-commutative QED which is T-dual to a more conventional $N\to\infty$ limit with $m/N$ fixed. In the non-commutative description, this limit gives rise to an exotic theory of open strings.Comment: 24 pages, latex, 2 figures, corrected typo in eqn 6.

On the Polarization of Unstable D0-Branes into Non-Commutative Odd Spheres

We consider the polarization of unstable type IIB D0-branes in the presence of a background five-form field strength. This phenomenon is studied from the point of view of the leading terms in the non-abelian Born Infeld action of the unstable D0-branes. The equations have SO(4) invariant solutions describing a non-commutative 3-sphere, which becomes a classical 3-sphere in the large N limit. We discuss the interpretation of these solutions as spherical D3-branes. The tachyon plays a tantalizingly geometrical role in relating the fuzzy S^3 geometry to that of a fuzzy S^4.Comment: 18 pages, Te

Wilson line correlators in two-dimensional noncommutative Yang-Mills theory

We study the correlator of two parallel Wilson lines in two-dimensional noncommutative Yang-Mills theory, following two different approaches. We first consider a perturbative expansion in the large-N limit and resum all planar diagrams. The second approach is non-perturbative: we exploit the Morita equivalence, mapping the two open lines on the noncommutative torus (which eventually gets decompacted) in two closed Wilson loops winding around the dual commutative torus. Planarity allows us to single out a suitable region of the variables involved, where a saddle-point approximation of the general Morita expression for the correlator can be performed. In this region the correlator nicely compares with the perturbative result, exhibiting an exponential increase with respect to the momentum p.Comment: 21 pages, 1 figure, typeset in JHEP style; some formulas corrected in Sect.3, one reference added, results unchange

Torons and D-Brane Bound States

We interpret instantons on a torus with twisted boundary conditions, in terms of bound states of branes. The interplay between the SU(N) and U(1) parts of the U(N) theory of N 4-branes allows the construction of a variety of bound states. The SU(N) and U(1) parts can contribute fractional amounts to the total instanton number which is integral. The geometry of non-self intersecting two-cycles in $T^4$ sheds some light on a number of properties of these solutions.Comment: 13 pages, harvmac bi