Non-commutativity and Supersymmetry

We study the extent to which the gauge symmetry of abelian Yang-Mills can be deformed under two conditions: first, that the deformation depend on a two-form scale. Second, that the deformation preserve supersymmetry. We show that (up to a single parameter) the only allowed deformation is the one determined by the star product. We then consider the supersymmetry algebra satisfied by NCYM expressed in commutative variables. The algebra is peculiar since the supercharges are not gauge-invariant. However, the action, expressed in commutative variables, appears to be quadratic in fermions to all orders in theta.Comment: 21 pages, LaTeX; a reference adde

Structure in Supersymmetric Yang-Mills Theory

We show that requiring sixteen supersymmetries in quantum mechanical gauge theory implies the existence of a web of constrained interactions. Contrary to conventional wisdom, these constraints extend to arbitrary orders in the momentum expansion.Comment: 22 pages, LaTe

Effective Dynamics of the Matrix Big Bang

We study the leading quantum effects in the recently introduced Matrix Big Bang model. This amounts to a study of supersymmetric Yang-Mills theory compactified on the Milne orbifold. We find a one-loop potential that is attractive near the Big Bang. Surprisingly, the potential decays very rapidly at late times, where it appears to be generated by D-brane effects. Usually, general covariance constrains the form of any effective action generated by renormalization group flow. However, the form of our one-loop potential seems to violate these constraints in a manner that suggests a connection between the cosmological singularity and long wavelength, late time physics.Comment: 22 pages, LaTeX; some minor changes; an improved discussion of the potentia

Analyzing Multi-Field Tunneling With Exact Bounce Solutions

We study multi-field tunneling using exact solutions for additive potentials. We introduce a binomial potential with non-integer powers that could be considered a generalization of the $4D$ Fubini instanton potential. Using scaling arguments, we show that for multi-field potentials taller and wider barriers may still lead to a smaller bounce action.Comment: 16 pages, 2 figures, 1 tabl

Duals of noncommutative supersymmetric U(1) gauge theory

Parent actions for component fields are utilized to derive the dual of supersymmetric U(1) gauge theory in 4 dimensions. Generalization of the Seiberg-Witten map to the component fields of noncommutative supersymmetric U(1) gauge theory is analyzed. Through this transformation we proposed parent actions for noncommutative supersymmetric U(1) gauge theory as generalization of the ordinary case.Duals of noncommutative supersymmetric U(1) gauge theory are obtained. Duality symmetry under the interchange of fields with duals accompanied by the replacement of the noncommutativity parameter \Theta_{\mu\nu} with \tilde{\Theta}_{\mu \nu} = \epsilon_{\mu\nu\rho\sigma}\Theta^{\rho\sigma} of the non--supersymmetric case is broken at the level of actions. We proposed a noncommutative parent action for the component fields which generates actions possessing this duality symmetry.Comment: Typos corrected. Version which will appear in JHE

Leptogenesis from Pseudo-Scalar Driven Inflation

We examine recent claims for a considerable amount of leptogenesis, in some inflationary scenarios, through the gravitational anomaly in the lepton number current. We find that when the short distances contributions are properly included the amount of lepton number generated is actually much smaller.Comment: JHEP style, 11 pages. Corrected typ

Conformal Symmetry and A New Gauge in the Matrix Model

We generalize the background gauge in the Matrix model to propose a new gauge which is useful for discussing the conformal symmetry. In this gauge, the special conformal transformation (SCT) as the isometry of the near-horizon geometry of the D-particle solution is directly reproduced with the correct coefficient as the quantum correction to the SCT in the Matrix model. We also present a general argument for the relation between the gauge choice and the field redefinition in the Matrix model.Comment: 17 pages, LaTeX, no figures; v2: Introduction modified, references added and typos corrected; v3: Introduction changed; v4: Eq.(12) corrected; v5: final version to appear in Phys. Rev.