Abstract
Recent results of A. Sen on quantum field theory models with self-dual field strengths use string field theory as a starting point. In the present work, we show that combining string field theory and supergeometry we can provide a constructive method for all these models, for any superspace representation and for any given background. The analysis is based on the new concept of pseudoform, emerging in supergeometry, which opens a new page in quantum field theory and, in particular, in supergravity. The present work deals with an explicit example, the case of the N=1 chiral boson supermultiplet in d=2.
Highlights
We show that combining string field theory and supergeometry we can provide a constructive method for all these models, for any superspace representation and for any given background
The analysis is based on the new concept of pseudoform, emerging in supergeometry, which opens a new page in quantum field theory and, in particular, in supergravity
1To our knowledge, the case of the chiral boson has not been analysed in the rheonomic framework, in several works ([13, 14, 15]) the authors propose some solutions to deal with self-dual field strengths. Those solutions are not satisfactory since the rheonomic variation principle does not include self-dual conditions. Problem in this context is that once the Lagrangian is projected via any Picture Changing Operator (PCO), the resulting equations of motion do not correspond to the single chiral boson as one would expect
Summary
Let us briefly explain the basic geometry. We consider two bosonic coordinates (z, z) (defined as complex coordinates) and two Grassmann odd coordinates (θ, θ), corresponding to the superspace N = 1, d = 2. It is an easy task to see that they imply the on-shell differentials (1.10), the equations of motion (1.11) and the relations for the new auxiliary fields in terms of Φ ξ = ∂Φ , ξ = −∂ ̄Φ. It can be verified that it is closed, only by using the algebraic equations of motion for ξ and ξ (1.16) and the curvature parametrisation dΦ, dW, dWand dF given in (1.8). If we eliminate ξ0, ξ0 and φθθvia their algebraic equation of motion, we obtain the usual action of d = 2 free sigma model [19]:. If we eliminate the superfields W and Wvia their algebraic equations of motion, we obtain the usual free d = 2 superspace action in flat background: DΦD Φ. We want to stress the fact that we already knew a priori that the two actions describe the same field content, since the Lagrangian is closed, there is no dependence on the choice of the PCO (again, see the Appendix for further comments)
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