How we see a symmetry in a regularized theory

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1. Symmetry and exact renormalisation groupA regularization introduced in the exact renormalization group often conflicts with symmetry of a theory. Earlier we have formulated the problem in the Batalin-Vilokovitsky's anti-field formalism and found that the master equation guarantees the presence of symmetry even in a regularized theory. One research during the project clarified how the flow equation respects a symmetry, which appears as a BRS symmetry in our formalism. The result was first obtained for a fermionic system with the chiral symmetry, and recently the similar result was produced for QED. We reported these results in international conferences.2. Supersymmetry on LatticeLattice gauge theory has been a powerful formulation for non-perturbative study. No convincing formulation of a supersymmetric theory on lattice has been known. Earlier, So, Itoh and others found a Grassmannian symmetry for the system of the staggered fermion coupled to link variables with a novel modification of coupling constants, namely the distribution of the coupling constants in the Ichimatsu-pattern. The presence of the symmetry may imply the emergence of supersymmtery in a continuum limit. In order to achieve that, we have to clarify the degrees of freedom both for the fermionic and bosonic part of the theory. Along this line of this thought, we have formulated the staggered fermion respecting the SO(2D) hidden symmetry. Based on that, So and3. Other subjectsWe also abtained some other results on the string field theory and lattice gauge theory. As for the former subject, our result is related to the large gauge symmetry of the SFT and its relation to various solutions that is believed to describe the tachyon condensation. As for the latter, results are obtained on the analogue of Witten's global anomaly and properties of an overlap-type Dirac operator in a gravitational background.