Abstract
We construct a Liouville superconformal field theory with eight real supercharges in four dimensions. The Liouville superfield is an mathcal{N} = 2 chiral superfield with sixteen bosonic and sixteen fermionic component fields. Its lowest component is a logcorrelated complex scalar field whose real part carries a background charge. The theory is non-unitary with a continuous spectrum of scaling dimensions. We study its quantum dynamics on the supersymmetric 4-sphere and show that the classical background charge is not corrected quantum mechanically. We calculate the super-Weyl anomaly coefficients and find that c vanishes, while a is negative and depends on the background charge. We derive an integral expression for the correlation functions of superfield vertex operators in mathcal{N} = 2 superspace and analyze them in the semiclassical approximation by using a quaternionic formalism for the mathcal{N} = 2 superconformal algebra.
Highlights
Background chargeWe define Liouville superconformal field theory (SCFT) on the N = 2 supermanifold extension of S4 [20]
We derive an integral expression for the correlation functions of superfield vertex operators in N = 2 superspace and analyze them in the semiclassical approximation by using a quaternionic formalism for the N = 2 superconformal algebra
2 N = 2 Liouville SCFT in four dimensions
Summary
Where E is the chiral density [13]. The Liouville superfield Φ is an N = 2 chiral superfield [13, 14], which satisfies the conditions: Diα Φ = 0, i = {1, 2} ,. In the Liouville action, Qis an N = 2 supersymmetric extension of the conformally covariant Q-curvature [18] given by [11]: Q This supersymmetric extension is chiral and satisfies Diα Q = 0. The reduced chiral superfield carries 8 + 8 degrees of freedom (bosonic and fermionic), while the chiral one used in (2.1) carries 16 + 16 degrees of freedom These two models yield the same super-Weyl variation. That the field equations in the non-supersymmetric four-dimensional Liouville field theory studied in [4] have a real positive cosmological constant parameter μ and their solutions can be viewed as Weyl factors that transform the background curved space into a constant negative Q-curvature one
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