[Paper Review] Classical and Quantum Nonlocal Supergravity

Stefano Giaccari, Leonardo Modesto|arXiv (Cornell University)|May 12, 2016

Cosmology and Gravitation Theories58 references7 citations

TL;DR

This paper constructs the N=1 supersymmetric extension of weakly nonlocal four-dimensional supergravity using superspace formalism, ensuring tree-level perturbative unitarity and ghost-freeness. The theory is super-renormalizable with the same spectrum as local supergravity, and quantum finiteness is achieved via 'super-killer' operators, though spacetime singularities persist despite nonlocality.

ABSTRACT

We derive the N=1 supersymmetric extension for a class of weakly nonlocal four dimensional gravitational theories.The construction is explicitly done in the superspace and the tree-level perturbative unitarity is explicitly proved both in the superfield formalism and in field components. For the minimal nonlocal supergravity the spectrum is the same as in the local theory and in particular it is ghost-free. The supersymmetric extension of the super-renormalizable Starobinsky theory and of two alternative massive nonlocal supergravities are found as straightforward applications of the formalism. Power-counting arguments ensure super-renormalizability with milder requirement for the asymptotic behavior of form factors than in ordinary nonlocal gravity. The most noteworthy result, common to ordinary supergravity, is the absence of quantum corrections to the cosmological constant in any regularization procedure. We cannot exclude the usual one-loop quadratic divergences. However, local vertices in the superfields, not undergoing renormalization, can be introduced to cancel out such divergences. Therefore, quantum finiteness is certainly achieved in dimensional regularization and most likely also in the cut-off regularization scheme. We also discuss the n-point scattering amplitudes making use of a general field redefinition theorem implemented in the superspace. Finally, we show that all the exact solutions of the local supergravity in vacuum are solutions of the nonlocal one too. In particular, we have the usual Schwarzschild singularity. We infer that the weak nonlocality, even in the presence of minimal supersymmetry, is not sufficient to solve the spacetime singularities issue, although the theory is finite at quantum level.

Motivation & Objective

• To extend weakly nonlocal, ghost-free gravity to a supersymmetric framework preserving unitarity and finiteness.
• To ensure the spectrum matches local N=1 supergravity, avoiding unphysical states.
• To demonstrate quantum finiteness through super-killer operators in dimensional and cut-off regularization.
• To investigate whether nonlocality resolves spacetime singularities in supergravity.
• To generalize field redefinition theorems to show tree-level scattering amplitudes match local supergravity.

Proposed method

• Constructing the nonlocal supergravity action in superspace with entire functions of the d’Alembertian operator.
• Using the superfield formalism to manifestly preserve off-shell N=1 supersymmetry.
• Deriving the component quadratic action, showing kinetic terms modified by exp[H(□)] with H entire.
• Applying power-counting arguments to establish super-renormalizability with milder UV form factor requirements.
• Introducing local, quartic superfield operators ('super-killer' terms) to cancel one-loop divergences.
• Generalizing a field redefinition theorem to prove equivalence of tree-level n-point amplitudes to local supergravity.

Experimental results

Research questions

• RQ1 Can a weakly nonlocal, ghost-free supergravity be consistently constructed in superspace with manifest off-shell supersymmetry?
• RQ2 Does the nonlocal extension preserve the same physical spectrum as local N=1 supergravity?
• RQ3 Can quantum finiteness be achieved in both dimensional and cut-off regularization via local counterterms?
• RQ4 Is the nonlocality sufficient to remove classical spacetime singularities, such as the Schwarzschild singularity?
• RQ5 Are tree-level scattering amplitudes in the nonlocal theory identical to those in local supergravity?

Key findings

• The N=1 supersymmetric extension of nonlocal supergravity is constructed in superspace, preserving off-shell supersymmetry and tree-level unitarity.
• The physical spectrum is identical to local N=1 supergravity, consisting of the graviton, gravitino, and auxiliary fields, with no ghosts.
• The theory is super-renormalizable with only one-loop divergences, and quantum finiteness is achievable via 'super-killer' operators in dimensional regularization.
• Even in cut-off regularization, finiteness is likely achievable by adding one extra local operator to cancel the Einstein-Hilbert divergence.
• All tree-level scattering amplitudes are identical to those of local Einstein supergravity, confirming locality at the classical perturbative level.
• The nonlocal theory admits the same exact vacuum solutions as local supergravity, including the singular Schwarzschild metric, indicating that weak nonlocality does not resolve spacetime singularities.