Sim(2) and SUSY

The proposal of hep-ph/0601236, that the laws of physics in flat spacetime need be invariant only under a SIM(2) subgroup of the Lorentz group, is extended to include supersymmetry. $\mathcal{N}=1$ SUSY gauge theories which include SIM(2) couplings for the fermions in chiral multiplets are formulated. These theories contain two conserved supercharges rather than the usual four.Comment: 10 pages, revtex4. Note added and sign correcte

A Generalization of Slavnov-Extended Non-Commutative Gauge Theories

We consider a non-commutative U(1) gauge theory in 4 dimensions with a modified Slavnov term which looks similar to the 3-dimensional BF model. In choosing a space-like axial gauge fixing we find a new vector supersymmetry which is used to show that the model is free of UV/IR mixing problems, just as in the previously discussed model in arXiv:hep-th/0604154. Finally, we present generalizations of our proposed model to higher dimensions.Comment: 25 pages, no figures; v2 minor correction

Confinement in Covariant Gauges

We examine the weak coupling limit of Euclidean SU(n) gauge theory in covariant gauges. Following an earlier suggestion, an equivariant BRST-construction is used to define the continuum theory on a finite torus. The equivariant gauge fixing introduces constant ghost fields as moduli of the model. We study the parameter- and moduli- space perturbatively. For $n_f \leq n$ quark flavors, the moduli flow to a non-trivial fixed point in certain critical covariant gauges and the one-loop effective potential indicates that the global SU(n) color symmetry of the gauge fixed model is spontaneously broken to $U(1)^{n-1}$. Ward identities and renormalization group arguments imply that the longitudinal gauge boson propagator at long range is dominated by $n(n-1)$ Goldstone bosons in these critical covariant gauges. In the large $n$ limit, we derive a nonlinear integral equation for the expectation value of large Wilson loops assuming that the exchange of Goldstone bosons dominates the interaction at long range in critical covariant gauges. We find numerically that the expectation value of large circular Wilson loops decreases exponentially with the enclosed area in the absence of dynamical fermions. The gauge invariance of this mechanism for confinement in critical covariant gauges is discussed.Comment: 45 pages, Latex, uses psfig.sty and epsfig.sty to include postscript-figure

Wrapped fivebranes and N=2 super Yang-Mills theory

We construct D=10 supergravity solutions corresponding to type IIB fivebranes wrapping a two-sphere in a Calabi-Yau two-fold. These are related in the IR to the large N limit of pure N=2 SU(N) super Yang-Mills theory. We show that the singularities in the IR correspond to the wrapped branes being distributed on a ring. We analyse the dynamics of a probe fivebrane and show that it incorporates the full perturbative structure of the gauge theory. For a class of solutions the two-dimensional moduli space is non-singular and we match the result for the corresponding slice of the Coulomb branch of the gauge theory.Comment: 24 Latex pages, two figures;v2 typos corrected, references adde

Exactly Marginal Deformations and Global Symmetries

We study the problem of finding exactly marginal deformations of N=1 superconformal field theories in four dimensions. We find that the only way a marginal chiral operator can become not exactly marginal is for it to combine with a conserved current multiplet. Additionally, we find that the space of exactly marginal deformations, also called the "conformal manifold," is the quotient of the space of marginal couplings by the complexified continuous global symmetry group. This fact explains why exactly marginal deformations are ubiquitous in N=1 theories. Our method turns the problem of enumerating exactly marginal operators into a problem in group theory, and substantially extends and simplifies the previous analysis by Leigh and Strassler. We also briefly discuss how to apply our analysis to N=2 theories in three dimensions.Comment: 23 pages, 2 figure

Investigating Yang-Mills theory and Confinement as a function of the spatial volume

We study the volume dependence of electric flux energies for SU(2) gauge theory with twisted boundary conditions. The curves interpolate smoothly between the perturbative semiclassicalresults and the Confinement regime. On the basis of our results, we propose that the Confinement property might be caused by a class of non-dilute multi-instanton configurations.Comment: Postscript - paper.ps and sig_lt3c.eps (Fig 1). 25 pages of text and 1 figur

N=1 Supersymmetric Product Group Theories in the Coulomb Phase

We study the low-energy behavior of N=1 supersymmetric gauge theories with product gauge groups SU(N)^M and M chiral superfields transforming in the fundamental representation of two of the SU(N) factors. These theories are in the Coulomb phase with an unbroken U(1)^(N-1) gauge group. For N >= 3, M >= 3 the theories are chiral. The low-energy gauge kinetic functions can be obtained from hyperelliptic curves which we derive by considering various limits of the theories. We present several consistency checks of the curves including confinement through the addition of mass perturbations and other limits.Comment: 22 pages, LaTeX, minor changes. Eqs. (20) and (42) correcte

Instantons and Matter in N=1/2 Supersymmetric Gauge Theory

We extend the instanton calculus for N=1/2 U(2) supersymmetric gauge theory by including one massless flavor. We write the equations of motion at leading order in the coupling constant and we solve them exactly in the non(anti)commutativity parameter C. The profile of the matter superfield is deformed through linear and quadratic corrections in C. Higher order corrections are absent because of the fermionic nature of the back-reaction. The instanton effective action, in addition to the usual 't Hooft term, includes a contribution of order C^2 and is N=1/2 invariant. We argue that the N=1 result for the gluino condensate is not modified by the presence of the new term in the effective action.Comment: 33 pages, harvmac; v2: minor changes, added references; v3: added analysis of the instanton measure in section

Dualities of the Matrix Model from T-Duality of the Type II String

We investigate in the Matrix theory framework, the subgroup of dualities of the DLCQ of M-theory compactified on three-tori, which corresponds to T-duality in the auxiliary Type II string theory. We show how these dualities are realized in the supersymmetric Yang-Mills gauge theories on dual noncommutative three-tori.Comment: 37 pages, LaTeX, no figures, typos correcte