Analytic continuation and supersymmetry

TL;DR

This paper explores how various complex parameter continuations in quantum field and string theories can be realized through supersymmetric quantum field or M-theory, often involving softly broken supersymmetry near defects.

Contribution

It demonstrates that many analytic continuations of parameters in quantum theories can be achieved within supersymmetric frameworks, providing a unified perspective.

Findings

Analytic continuations can be realized with supersymmetry.

Supersymmetry is softly broken near defects supporting the continuation.

Various parameters like coupling constants and spacetime dimensions can be continued.

Abstract

Real-valued parameters of quantum field theory, such as Planck constant, coupling constants, temperature and spacetime metric, chemical potentials or background gauge fields can be made complex. In perturbative string theory, the worldsheet metric is sometime Lorentzian, somewhere Euclidean, and likely complex in between. Less often, integral, or quantized, parameters, such as the number of flavors or species (as in replica method), the number of colors (as in matrix models, master field), spacetime dimension (dimensional regularization), or angular momentum (Regge poles) are continued to complex values. We observe that many, if not all of these analytic continuations can be realized with conventional supersymmetric quantum field (or M-) theory. The supersymmetry is softly broken near a defect supporting the theory being analytically continued in some of its parameters.