Coadjoint Orbits, Cocycles and Gravitational Wess-Zumino

About 30 years ago, in a joint work with L. Faddeev we introduced a geometric action on coadjoint orbits. This action, in particular, gives rise to a path integral formula for characters of the corresponding group $G$. In this paper, we revisit this topic and observe that the geometric action is a 1-cocycle for the loop group $LG$. In the case of $G$ being a central extension, we construct Wess-Zumino (WZ) type terms and show that the cocycle property of the geometric action gives rise to a Polyakov-Wiegmann (PW) formula. In particular, we obtain a PW type formula for the Polyakov's gravitational WZ action. After quantization, this formula leads to an interesting bulk-boundary decoupling phenomenon previously observed in the WZW model. We explain that this decoupling is a general feature of the Wess-Zumino terms obtained from geometric actions, and that in this case the path integral is expressed in terms of the 2-cocycle which defines the central extension. In memory of our teacher Ludwig Faddeev.Comment: 15 pages, v2: references adde

Two-dimensional Conformal Field Theories on AdS_{2d+1} Backgrounds

Various exact two-dimensional conformal field theories with AdS_{2d+1} target space are constructed. These models can be solved using bosonization techniques. Some examples are presented that can be used in building perturbative superstring theories with AdS backgrounds, including AdS_5.Comment: 36 pages, harvma

On Non-Supersymmetric CFT in Four Dimensions

We show that the $\mathcal{N}=0$ theories on the self-dual D3-branes of Type 0 string theory are in the class of the previously considered tadpole-free orbifolds of $\mathcal{N} = 4$ theory (although they have SO(6) global symmetry) and hence have vanishing beta function in the planar limit to all orders in 't Hooft coupling. Also, all planar amplitudes in this theory are equal to those of $\mathcal{N} = 4$ theory, up to a rescaling of the coupling.Comment: harvmac, 4 pp; v2. Z_4 field content corrected, references reworke

M&m's

We consider M theory 5-branes with compact transverse dimensions. In certain limits the theory on the 5-brane decouples and defines ``little string theories'' in 5+1 dimensions. We show that the familiar structure of IIA/IIB,M,F- theory in 10,11,12 dimensions respectively has a perfect parallel in a theory of strings and membranes in 6,7,8 dimensions. We call these theories $a/b,m,f$ theories. They have a coupling constant but no gravity. This construction clarifies some mysteries in F-theory and leads to several speculations about the phase structure of M theory.Comment: harvmac, 24 page