Non-renormalization theorems of Supersymmetric QED in the Wess-Zumino gauge

The non-renormalization theorem of chiral vertices and the generalized non-renormalization theorem of the photon self energy are derived in SQED on the basis of algebraic renormalization. For this purpose the gauge coupling is extended to an external superfield. This extension already provides detailed insight into the divergence structure. Moreover, using the local supercoupling together with an additional external vector multiplet that couples to the axial current, the model becomes complete in the sense of multiplicative renormalization, with two important implications. First, a Slavnov--Taylor identity describing supersymmetry, gauge symmetry, and axial symmetry including the axial anomaly can be established to all orders. Second, from this Slavnov-Taylor identity we can infer a Callan-Symanzik equation expressing all aspects of the non-renormalization theorems. In particular, the gauge $\beta$-function appears explicitely in the closed form.Comment: Latex, 47 page

Domain Walls and Superpotentials from M Theory on Calabi-Yau Three-Folds

Compactification of M theory in the presence of G-fluxes yields N=2 five-dimensional gauged supergravity with a potential that lifts all supersymmetric vacua. We derive the effective superpotential directly from the Kaluza-Klein reduction of the eleven-dimensional action on a Calabi-Yau three-fold and compare it with the superpotential obtained by means of calibrations. We discuss an explicit domain wall solution, which represents five-branes wrapped over holomorphic cycles. This solution has a ``running volume'' and we comment on the possibility that quantum corrections provide a lower bound allowing for an AdS_5 vacuum of the 5-dimensional supergravity.Comment: 21 pages, harvmac, 1 figure, minor corrections and refs adde

Strong/Weak Coupling Duality from the Dual String

On compactification to six spacetime dimensions, the fundamental heterotic string admits as a soliton a dual string whose effective worldsheet action couples to the background fields of the dual formulation of six-dimensional supergravity. On further toroidal compactification to four spacetime dimensions, the dual string acquires an $O(2,2;Z)$ target-space duality. This contains as a subgroup the axion-dilaton $SL(2,Z)$ which corresponds to a strong/weak coupling duality for the fundamental string. The dual string also provides a new non-perturbative mechanism for enhancement of the gauge symmetry.Comment: 23 pages LATE

Supergravity Unification

A review is given of the historical developments of 1982 that lead to the supergravity unified model (SUGRA)with gravity mediated breaking of supersymmetry. Further developments and applications of the model in the period 1982-85 are also discussed. The supergravity unified model and its minimal version (mSUGRA) are currently among the leading candidates for physics beyond the Standard Model. A brief note on the developments from the present vantage point is included.Comment: Contribution to the Proceedings "Thirty Years of Supersymmetry", October 13-15, 2000, Minnesota, US

Out of Equilibrium Dynamics of Supersymmetry at High Energy Density

We investigate the out of equilibrium dynamics of global chiral supersymmetry at finite energy density. We concentrate on two specific models. The first is the massive Wess-Zumino model which we study in a selfconsistent one-loop approximation. We find that for energy densities above a certain threshold, the fields are driven dynamically to a point in field space at which the fermionic component of the superfield is massless. The state, however is found to be unstable, indicating a breakdown of the one-loop approximation. To investigate further, we consider an O(N) massive chiral model which is solved exactly in the large $N$ limit. For sufficiently high energy densities, we find that for late times the fields reach a nonperturbative minimum of the effective potential degenerate with the perturbative minimum. This minimum is a true attractor for O(N) invariant states at high energy densities, and this provides a mechanism for determining which of the otherwise degenerate vacua is chosen by the dynamics. The final state for large energy density is a cloud of massless particles (both bosons and fermions) around this new nonperturbative supersymmetric minimum. By introducing boson masses which softly break the supersymmetry, we demonstrate a see-saw mechanism for generating small fermion masses. We discuss some of the cosmological implications of our results.Comment: 31 pages, 15 figure

Twenty Years of SUGRA

A brief review is given of the developments of mSUGRA and its extensions since the formulation of these models in 1982. Future directions and prospects are also discussed.Comment: Invited talk at the International Conference BEYOND-2003, Schloss Ringberg, Germany, June 10-14, 2003; 21 pages, Late

Non-renormalization theorems in softly broken SQED and the soft β\beta-functions

The renormalization of softly broken SQED is related to the one of supersymmetric QED by using the construction with a local gauge supercoupling and by taking into account softly broken anomalous axial U(1) symmetry. From this extended model one obtains the non-renormalization theorems of SQED and the counterterms of the soft breaking parameters as functions of the supersymmetric counterterms. Due to the Adler-Bardeen anomaly of the axial current an invariant regularization scheme does not exist, and therefore the $\beta$-functions of soft breaking parameters are derived from an algebraic construction of the Callan-Symanzik equation and of the renormalization group equation. We obtain the soft $\beta$-functions in terms of the gauge $\beta$-function and of the anomalous dimension of the supersymmetric matter mass. In particular, we find that the X-term of the scalar mass $\beta$-function as well as the gauge $\beta$-function in $l\geq 2$ are due to the Adler-Bardeen anomaly of the axial symmetry.Comment: 28 page

Stochastic and parastochastic aspects of supersymmetric functional measures

This collection of selected reprints presents as broad a selection as possible, emphasizing formal and numerical aspects of Stochastic Quantization. It reviews and explains the most important concepts placing selected reprints and crucial papers into perspective and compact form