How we see a symmetry in a regularized theory

1.对称性与精确重正化群在精确重正化群中引入的正则化经常与理论的对称性相冲突。早些时候，我们在巴达林-维洛科维奇的反场形式主义中阐述了这个问题，并发现即使在正则化理论中，主方程也保证对称性的存在。项目期间的一项研究阐明了流动方程如何尊重对称性，在我们的形式主义中，对称性表现为BRS对称性。这一结果首先是对手征对称性的费米子系统得到的，最近对QED也得到了类似的结果。我们在国际会议上报道了这些结果。格子上的超对称性格子规范理论一直是非微扰研究的有力提法。关于格子上的超对称理论，目前还没有令人信服的表述。早些时候，Itoh和其他人发现了交错费米子与连接变量耦合的系统具有Grassman对称性，并对耦合常数进行了新的修改，即耦合常数在Ichiatsu模式中的分布。对称性的存在可能意味着超对称在连续统极限中的出现。为了实现这一点，我们必须澄清该理论中费米子和玻色子部分的自由度。沿着这条思路，我们得到了考虑SO(2D)隐藏对称性的交错费米子的公式。基于这一点，所以和3。我们还得到了一些关于弦场理论和格点规范理论的其他结果。对于前一个主题，我们的结果与SFT的大规范对称性以及它与被认为描述快子凝聚的各种解的关系有关。对于后者，给出了引力背景下Witten整体反常的类比和重叠型Dirac算符的性质。

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.