(2,2) Supergravity in the Light-Cone gauge

Starting with the prepotential description of two-dimensional $(2,2)$ supergravity we use local supersymmetry transformations to go to light-cone gauge. We discuss properties of the theory in this gauge and derive Ward identities for correlation functions defined with respect to the induced supergravity action.Comment: Latex, 20 pages, 2 figures in separate compressed fil

A Critical Behaviour of Anomalous Currents, Electric-Magnetic Universality and CFT_4

We discuss several aspects of superconformal field theories in four dimensions (CFT_4), in the context of electric-magnetic duality. We analyse the behaviour of anomalous currents under RG flow to a conformal fixed point in N=1, D=4 supersymmetric gauge theories. We prove that the anomalous dimension of the Konishi current is related to the slope of the beta function at the critical point. We extend the duality map to the (nonchiral) Konishi current. As a byproduct we compute the slope of the beta function in the strong coupling regime. We note that the OPE of $T_{\mu\nu}$ with itself does not close, but mixes with a special additional operator $\Sigma$ which in general is the Konishi current. We discuss the implications of this fact in generic interacting conformal theories. In particular, a SCFT_4 seems to be naturally equipped with a privileged off-critical deformation $\Sigma$ and this allows us to argue that electric-magnetic duality can be extended to a neighborhood of the critical point. We also stress that in SCFT_4 there are two central charges, c and c', associated with the stress tensor and $\Sigma$, respectively; c and c' allow us to count both the vector multiplet and the matter multiplet effective degrees of freedom of the theory.Comment: harvmac tex, 28 pages, 3 figures. Version to be published in Nucl. Phys.

Direct Calculation of the Boundary SS Matrix for the Open Heisenberg Chain

We calculate the boundary $S$ matrix for the open antiferromagnetic spin $1/2$ isotropic Heisenberg chain with boundary magnetic fields. Our approach, which starts from the model's Bethe Ansatz solution, is an extension of the Korepin-Andrei-Destri method. Our result agrees with the boundary $S$ matrix for the boundary sine-Gordon model with $\beta^2 \rightarrow 8\pi$ and with ``fixed'' boundary conditions.Comment: 29 pages, plain TEX, UMTG-17

Effective K\"ahler Potentials

We compute the $1$-loop effective K\"ahler potential in the most general renormalizable $N=1$ $d=4$ supersymmetric quantum field theory.Comment: 11 pages, Late

The Quantum Geometry of N=(2,2) Non-Linear Sigma-Models

We consider a general N=(2,2) non-linear sigma-model in (2,2) superspace. Depending on the details of the complex structures involved, an off-shell description can be given in terms of chiral, twisted chiral and semi-chiral superfields. Using superspace techniques, we derive the conditions the potential has to satisfy in order to be ultra-violet finite at one loop. We pay particular attention to the effects due to the presence of semi-chiral superfields. A complete description of N=(2,2) strings follows from this.Comment: 9 pages, Late

k-Anomalies and Space-Time Supersymmetry in the Green-Schwarz Heterotic Superstring

The computation of $\kappa$-anomalies in the Green-Schwarz heterotic superstring sigma-model and the corresponding Wess-Zumino consistency condition constitute a powerful alternative approach for the derivation of manifestly supersymmetric string effective actions. With respect to the beta-function approach this technique presents the advantage that a result which is obtained with the computation of beta-functions at $n$ loops can be obtained through the calculation of $\kappa$-anomalies at \hbox{$n-1$} loops. In this paper we derive by a direct one-loop perturbative computation the $\kappa$-anomaly associated to the Yang-Mills Chern-Simons threeform and, for the first time, the one associated to the Lorentz Chern-Simons threeform. Contrary to what is often stated in the literature we show that the Lorentz $\kappa$-anomaly gets contributions from the integration over both the fermionic {\it and\/} bosonic degrees of freedom of the string. A careful analysis of the absolute coefficients of all these anomalies reveals that they can be absorbed by setting dH={\alpha'\over4}(\trace F^2-\trace R^2), where $\alpha'$ is the string tension, the expected result. We show that this relation ensures also the absence of gauge and Lorentz anomalies in the sigma-model effective action. We evidenciate the presence of infrared divergences.Comment: 50 pages, latex (uses equations.sty, feynman.tex and a4.sty), DFPD/94/TH/4

Planar Gravitational Corrections For Supersymmetric Gauge Theories

In this paper we discuss the contribution of planar diagrams to gravitational F-terms for N=1 supersymmetric gauge theories admitting a large N description. We show how the planar diagrams lead to a universal contribution at the extremum of the glueball superpotential, leaving only the genus one contributions, as was previously conjectured. We also discuss the physical meaning of gravitational F-terms.Comment: 20 pages, 4 figure