Power of Supersymmetry in D-particle Dynamics

A new systematic method is developed to study to what extent the symmetry requirements alone, above all the invariance under 16 supersymmetries (SUSY), determine the completely off-shell effective action $\Gamma$ of a D-particle, i.e. without imposing any restrictions on its position $r^m(\tau)$ and spin $\theta_\alpha(\tau)$. Our method consists of (i) writing down the proper closure relations for general SUSY transformations $\delta_\epsilon$ (which necessarily involves $\Gamma$ itself) together with the invariance condition $\delta_\epsilon\Gamma=0$ (ii) and solving this coupled system of functional differential equations for $\delta_\epsilon$ and $\Gamma$ simultaneously, modulo field redefinitions, in a consistent derivative expansion scheme. Our analysis is facilitated by a novel classification scheme introduced for the terms in $\Gamma$. At order 2 and 4, although no assumption is made on the underlying theory, we reproduce the effective action previously obtained at the tree and the 1-loop level in Matrix theory respectively (modulo two constants), together with the quantum-corrected SUSY transformations which close properly. This constitutes a complete unambiguous proof of off-shell non-renormalization theorems.Comment: 44 pages, v2: typos corrected, published versio

Fully Off-shell Effective Action and its Supersymmetry in Matrix Theory

As a step toward clarification of the power of supersymmetry (SUSY) in Matrix theory, a complete calculation, including all the spin effects, is performed of the effective action of a probe D-particle, moving along an arbitrary trajectory in interaction with a large number of coincident source D-particles, at one loop at order 4 in the derivative expansion. Furthermore, exploiting the SUSY Ward identity developed previously, the quantum-corrected effective supersymmetry transformation laws are obtained explicitly to the relevant order and are used to verify the SUSY-invariance of the effective action. Assuming that the agreement with 11-dimensional supergravity persists, our result can be regarded as a prediction for supergravity calculation, which, yet unavailable, is known to be highly non-trivial.Comment: 27 page

A Theorem on the Power of Supersymmetry in Matrix Theory

For the so-called source-probe configuration in Matrix theory, we prove the following theorem concerning the power of supersymmetry (SUSY): Let $\delta$ be a quantum-corrected effective SUSY transformation operator expandable in powers of the coupling constant $g$ as $\delta = \sum_{n\ge 0} g^{2n} \delta^{(n)}$, where $\delta^{(0)}$ is of the tree-level form. Then, apart from an overall constant, the SUSY Ward identity $\delta \Gamma=0$ determines the off-shell effective action $\Gamma$ uniquely to arbitrary order of perturbation theory, provided that the $SO(9)$ symmetry is preserved. Our proof depends only on the properties of the tree-level SUSY transformation laws and does not require the detailed knowledge of quantum corrections.Comment: 20 page

On quantum deformation of conformal symmetry: Gauge dependence via field redefinitions

The effective action in gauge theories is known to depend on a choice of gauge fixing conditions. This dependence is such that any change of gauge conditions is equivalent to a field redefinition in the effective action. In this sense, the quantum deformation of conformal symmetry in the N = 4 super Yang-Mills theory, which was computed in 't Hooft gauge in hep-th/9808039 and hep-th/0203236, is gauge dependent. The deformation is an intrinsic property of the theory in that it cannot be eliminated by a local choice of gauge (although we sketch a field redefinition induced by a nonlocal gauge which, on the Coulomb branch of the theory, converts the one-loop quantum-corrected conformal transformations to the classical ones). We explicitly compute the deformed conformal symmetry in R_\xi gauge. The conformal transformation law of the gauge field turns out to be \xi-independent. We construct the scalar field redefinition which relates the 't Hooft and R_\xi gauge results. A unique feature of 't Hooft gauge is that it makes it possible to consistently truncate the one-loop conformal deformation to the terms of first order in derivatives of the fields such that the corresponding transformations form a field realization of the conformal algebra.Comment: 14 pages, latex, no figures; references and comments added, the final version to appear in PL

Interaction of D-string with F-string: A Path-Integral Formalism

A path integral formalism is developed to study the interaction of an arbitrary curved Dirichlet (D-) string with elementary excitations of the fundumental (F-) string in bosonic string theory. Up to the next to leading order in the derivative expansion, we construct the properly renormalized vertex operator, which generalizes the one previously obtained for a D-particle moving along a curved trajectory. Using this vertex, an attempt is further made to quantize the D-string coordinates and to compute the quantum amplitude for scattering between elementary excitations of the D- and F-strings. By studying the dependence on the Liouville mode for the D-string, it is found that the vertex in our approximation consists of an infinite tower of local vertex operators which are conformally invariant on their respective mass-shell. This analysis indicates that, unlike the D-particle case, an off-shell extension of the interaction vertex would be necessary to compute the full amplitude and that the realization of symmetry can be quite non-trivial when the dual extended objects are simultaneously present. Possible future directions are suggested.Comment: 23 pages, latex, no figure

Poincare Polynomials and Level Rank Dualities in the N=2N=2 Coset Construction

We review the coset construction of conformal field theories; the emphasis is on the construction of the Hilbert spaces for these models, especially if fixed points occur. This is applied to the $N=2$ superconformal cosets constructed by Kazama and Suzuki. To calculate heterotic string spectra we reformulate the Gepner con- struction in terms of simple currents and introduce the so-called extended Poincar\'e polynomial. We finally comment on the various equivalences arising between models of this class, which can be expressed as level rank dualities. (Invited talk given at the III. International Conference on Mathematical Physics, String Theory and Quantum Gravity, Alushta, Ukraine, June 1993. To appear in Theor. Math. Phys.)Comment: 14 pages in LaTeX, HD-THEP-93-4

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

Generalized symmetries and invariant matter couplings in two-dimensional dilaton gravity

New features of the generalized symmetries of generic two-dimensional dilaton models of gravity are presented and invariant gravity-matter couplings are introduced. We show that there is a continuum set of Noether symmetries, which contains half a de Witt algebra. Two of these symmetries are area-preserving transformations. We show that gravity-matter couplings which are invariant under area preserving transformations only contribute to the dynamics of the dilaton-gravity sector with a reshaping of the dilaton potential. The interaction with matter by means of invariant metrics is also considered. We show in a constructive way that there are metrics which are invariant under two of the symmetries. The most general metrics and minimal couplings that fulfil this condition are found.Comment: LateX file, no macros, 14pp: minor changes have been made and some misprints have been correcte