Abstract
An N=(4,0) supersymmetric Liouville theory is formulated by the coadjoint orbit method. It is discovered that the action has symmetry under PSU(1,1|2).
Highlights
In the past few years there has been much interest in a duality between the SYK model and the D = 2 effective gravity
The differential geometrical aspects of the Schwarzian theory got clarified when it was reformulated by the coadjoint orbit method in [1]
In this letter we have formulated the N = (4, 0) super-Liouville theory by the coadjoint orbit method and have shown that it has all the properties which are characteristic in the lower symmetric Liouville theory, except for one
Summary
After this work the coadjoint orbit method was generalized to get the (1, 0) and (2, 0) supersymmetric Liouville theories in [7] and [8] respectively. Integrating this 1-form on the orbit O(b,c) gives an N = (4, 0) supersymmetric action We propose that this is the (4,0) super-Liouville theory. Γ is a function of h, ρηa, ξηa, which are the lowest component of the superfields f, φa, φa respectively With this γ put in (3.16) the N = (4, 0) super-Liouville action (3.13) gets a local expression in 1+1 dimensions as. Here we remember that the purely bosonic part of the action is identical with that of the non-supersymmetric Liouville theory The latter is invariant under SU(1,1)(∼=SL(2)), which is a subgroup of PSU(1,1|2).
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