Super-Weyl Invariant 2D Supergravity, Anomaly and WZ Action

We present a candidate of anomaly and Wess Zumino action of the two dimensional supergravity coupling with matters in a super-Weyl invariant regularization. It is a generalization of the Weyl and the area preserving \Diff invariant formulation of two dimensional gravity theory.Comment: 9 pages, Late

Brane Dualities in Non-relativistic Limit

We analyze brane dualities in the non-relativistic limit of the worldvolume actions. In particular we have analyzed how the non-relativistic M2-brane is related via these dualities to non-relativistic D2-brane, non-relativistic IIA fundamental string and also, by using T-duality, to non-relativistic D1-string. These actions coincide with ones obtained from relativistic actions by taking non-relativistic limit, showing that the non-relativistic limit and the dualities commute in these cases.Comment: 21 pages, 1 figur

Nambu-Goldstone Fields, Anomalies and WZ Terms

We construct the Wess-Zumino terms from anomalies in case of quasigroups for the following situations. One is effective gauge field theories of Nambu-Goldstone fields associated with spontaneously broken global symmetries and the other is anomalous gauge theories. The formalism that we will develop can be seen as a generalization of the non-linear realization method of Lie groups. As an example we consider 2d gravity with a Weyl invariant regularizationComment: 19 pages, Late

Mirror Symmetry And Loop Operators

Wilson loops in gauge theories pose a fundamental challenge for dualities. Wilson loops are labeled by a representation of the gauge group and should map under duality to loop operators labeled by the same data, yet generically, dual theories have completely different gauge groups. In this paper we resolve this conundrum for three dimensional mirror symmetry. We show that Wilson loops are exchanged under mirror symmetry with Vortex loop operators, whose microscopic definition in terms of a supersymmetric quantum mechanics coupled to the theory encode in a non-trivial way a representation of the original gauge group, despite that the gauge groups of mirror theories can be radically different. Our predictions for the mirror map, which we derive guided by branes in string theory, are confirmed by the computation of the exact expectation value of Wilson and Vortex loop operators on the three-sphere.Comment: 92 pages, v2: minor clarifications in the introduction, to be published in JHE