3 research outputs found
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Example of a quantum field theory based on a nonlinear Lie algebra
In this contribution to Tini Veltman's Festschrift we shall give a paedagogical account of our work on a new class of gauge theories called W gravities. They contain higher spin gauge fields, but the usual no-go theorems for interacting field theories with spins exceeding two do not apply since these theories are in two dimensions. It is, of course, well known that ghost-free interacting massless spin 2 fields ( the metric') are gauge fields, and correspond to the geometrical notion of general coordinate transformations in general relativity, but it is yet unknown what extension of these ideas is introduced by the presence of massless higher spin gauge fields. A parallel with supergravity may be drawn: there the presence of massless spin 3/2 fields (gravitinos) corresponds to local fermi-bose symmetries of which these gravitinos are the gauge fields. Their geometrical meaning becomes only clear if one introduces superspace (with bosonic and fermionic coordinates): they correspond to local transformations of the fermionic coordinates. For W gravity one might speculate on a kind of W-superspace with extra bosonic coordinates
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Induced gauge theories and W gravity
We review some aspects of induced gauge theories in two dimensions. We focus on W{sub 3} gravity, paying particular attention to the treatment of the non-linearities inherent to W gravity. We show that the induced action {Gamma}{sub ind}(h,b) for chiral W{sub 3} in the c {yields} {plus minus}infinity limit is obtained from the induced action of a gauged Sl(3,R) Wess-Zumino-Witten model by imposing constraints on some of the affine currents. Subsequently we investigate the effective action, which is obtained by integrating the induced action over the gauge fields. We show perturbatively that certain subleading terms which appear in the induced action for finite c (and which are related to nonlocal terms in the Ward identifies) get canceled by similar terms due to loop corrections, and we propose an all-order result for the effective action
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Quantum W sub 3 gravity
We briefly review some results in the theory of quantum W{sub 3} gravity in the chiral gauge. We compare them with similar results in the analogous but simpler cases of d = 2 induced gauge theories and d = 2 induced gravity