New Symmetries of Supersymmetric Effective Lagrangians

We consider the structure of effective lagrangians describing the low-energy dynamics of supersymmetric theories in which a global symmetry $G$ is spontaneously broken to a subgroup $H$ while supersymmetry is unbroken. In accordance with the supersymmetric Goldstone theorem, these lagrangians contain Nambu--Goldstone superfields associated with a coset space $G^c / \hat{H}$, where $G^c$ is the complexification of $G$ and $\hat{H}$ is the largest subgroup of $G^c$ that leaves the order parameter invariant. The lagrangian may also contain additional light matter fields. To analyze the effective lagrangian for the matter fields, we first consider the case where the effective lagrangian is obtained by integrating out heavy modes at weak coupling (but including non-perturbative effects such as instantons). We show that the superpotential of the matter fields is $\hat{H}$ invariant, which can give rise to non-trivial relations among independent $H$-invariants in the superpotential. We also show that the Kahler potential of the matter fields can be restricted by a remnant of $\hat{H}$ symmetry. These results are non-perturbative and have a simple group-theoretic interpretation. When we relax the weak-coupling constraint, there appear to be additional possibilities for the action of $\hat{H}$ on the matter fields, hinting that the constraints imposed by $\hat{H}$ may be even richer in strongly coupled theories.Comment: 23 pages, plain Te

Parity Conservation in Supersymmetric Vector-Like Theories

We show that parity is conserved in vector-like supersymmetric theories, such as supersymmetric QCD with massive quarks with no cubic couplings among chiral multiplets, based on fermionic path-integrals, originally developed by Vafa and Witten. We also look into the effect of supersymmetric breaking through gluino masses, and see that the parity-conservation is intact also in this case. Our conclusion is valid, when only bosonic parity-breaking observable terms are considered in path-integrals like the original Vafa-Witten formulation.Comment: 14 pages, latex, no figures; replaced with corrections of exponent in old eq.(2.8), misleading expressions in (3.19), comments on fermionic parity-breaking terms, and some references adde

Group Theory of Non-Abelian Vortices

We investigate the structure of the moduli space of multiple BPS non-Abelian vortices in U(N) gauge theory with N fundamental Higgs fields, focusing our attention on the action of the exact global (color-flavor diagonal) SU(N) symmetry on it. The moduli space of a single non-Abelian vortex, CP(N-1), is spanned by a vector in the fundamental representation of the global SU(N) symmetry. The moduli space of winding-number k vortices is instead spanned by vectors in the direct-product representation: they decompose into the sum of irreducible representations each of which is associated with a Young tableau made of k boxes, in a way somewhat similar to the standard group composition rule of SU(N) multiplets. The K\"ahler potential is exactly determined in each moduli subspace, corresponding to an irreducible SU(N) orbit of the highest-weight configuration.Comment: LaTeX 46 pages, 4 figure

Model-based interpretation of complex and variable images.

The ultimate goal of machine vision is image understanding-the ability not only to recover image structure but also to know what it represents. By definition, this involves the use of models which describe and label the expected structure of the world. Over the past decade, model-based vision has been applied successfully to images of man-made objects. It has proved much more difficult to develop model-based approaches to the interpretation of images of complex and variable structures such as faces or the internal organs of the human body (as visualized in medical images). In such cases it has been problematic even to recover image structure reliably, without a model to organize the often noisy and incomplete image evidence. The key problem is that of variability. To be useful, a model needs to be specific-that is, to be capable of representing only 'legal' examples of the modelled object(s). It has proved difficult to achieve this whilst allowing for natural variability. Recent developments have overcome this problem; it has been shown that specific patterns of variability in shape and grey-level appearance can be captured by statistical models that can be used directly in image interpretation. The details of the approach are outlined and practical examples from medical image interpretation and face recognition are used to illustrate how previously intractable problems can now be tackled successfully. It is also interesting to ask whether these results provide any possible insights into natural vision; for example, we show that the apparent changes in shape which result from viewing three-dimensional objects from different viewpoints can be modelled quite well in two dimensions; this may lend some support to the 'characteristic views' model of natural vision