Superconformal quantum field theory in curved spacetime

Abstract

By conformally coupling vector and hyper multiplets in Minkowski space, we obtain a class of field theories with extended rigid conformal supersymmetry on any Lorentzian four-manifold admitting twistor spinors. We construct the conformal symmetry superalgebras which describe classical symmetries of these theories and derive an appropriate BRST operator in curved spacetime. In the process, we elucidate the general framework of cohomological algebra which underpins the construction. We then consider the corresponding perturbative quantum field theories. In particular, we examine the conditions necessary for conformal supersymmetries to be preserved at the quantum level, i.e. when the BRST operator commutes with the perturbatively defined S-matrix, which ensures superconformal invariance of amplitudes. To this end, we prescribe a renormalization scheme for time-ordered products that enter the perturbative S-matrix and show that such products obey certain Ward identities in curved spacetime. These identities allow us to recast the problem in terms of the cohomology of the BRST operator. Through a careful analysis of this cohomology, and of the renormalization group in curved spacetime, we establish precise criteria which ensure that all conformal supersymmetries are preserved at the quantum level. As a by-product, we provide a rigorous proof that the beta-function for such theories is one-loop exact. We also briefly discuss the construction of chiral rings and the role of non-perturbative effects in curved spacetime.

53 pages, v3: more typos corrected, reference added, corrected remark at the end of section 2.3 and a note added in acknowledgments

References in corpus (8)

• Conformal symmetry classes for pp-wave spacetimes
• de Sitter Supersymmetry Revisited
• Supersymmetric Killing Structures
• Chiral Ring Of Sp(N) And SO(N) Supersymmetric Gauge Theory In Four Dimensions
• The twistor equation in Lorentzian spin geometry
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Cited by in corpus (13)

• Extended Supersymmetry on Curved Spaces
• Three-dimensional N=2 supergravity theories: From superspace to components
• de Sitter Supersymmetry Revisited
• Symmetries of curved superspace in five dimensions
• The Thermal Bath of de Sitter from Holography
• Anomalies in time-ordered products and applications to the BV-BRST formulation of quantum gauge theories
• Supergeometry in locally covariant quantum field theory
• Conformal superalgebras via tractor calculus
• Self-consistency of Conformally Coupled ABJM Theory at the Quantum Level
• Submaximal conformal symmetry superalgebras for Lorentzian manifolds of low dimension
• Supersymmetric Yang-Mills theory on conformal supergravity backgrounds in ten dimensions
• The Weyl anomaly in interacting quantum field theory on curved spacetimes
• Quantum fields in curved space-time, semiclassical gravity, quantum gravity phenomenology, and analogue models: Report on session D4 at GR20