부산대학교 도서관

Summary: ``We explore the notion of $c$-functions in renormalizationgroup flows between theories in different spacetime dimensions. Wediscuss functions connecting central charges of the UV and IR fixedpoint theories on the one hand, and functions which are monotonic alongthe flow on the other. First, using the geometric properties of theholographic dual RG flows across dimensions and the constraints fromthe null energy condition, we construct a monotonic holographic$c$-function and thereby establish a holographic $c$-theorem acrossdimensions. Second, we use entanglement entropies for two differenttypes of entangling regions in a field theory along the RG flow acrossdimensions to construct candidate cfunctions which satisfy one of thetwo criteria but not both. In due process we also discuss aninteresting connection between corner contributions to the entanglemententropy and the topology of the compact internal space. As concreteexamples for both approaches, we holographically study twistedcompactifications of 4d $\Cal N=4$ SYM and compactifications of 6d$\Cal N=(2,0)$ theories.''