• Open Access

Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories

Matthew Buican and Zoltan Laczko
Phys. Rev. Lett. 120, 081601 – Published 23 February 2018
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Abstract

In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories. On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow. In this Letter, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional N=2 superconformal field theories (SCFTs) by performing simple calculations involving sets of nonunitary free four-dimensional hypermultiplets. These free fields are distant cousins of the Majorana fermion underlying the two-dimensional Ising model and are not obviously connected to our interacting theories via an RG flow. Rather surprisingly, this construction gives us Lagrangians for particular observables in certain subsectors of many “non-Lagrangian” SCFTs by sacrificing unitarity while preserving the full N=2 superconformal algebra. As a by-product, we find relations between characters in unitary and nonunitary affine Kac-Moody algebras. We conclude by commenting on possible generalizations of our construction.

  • Received 7 December 2017

DOI:https://doi.org/10.1103/PhysRevLett.120.081601

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Particles & FieldsInterdisciplinary Physics

Authors & Affiliations

Matthew Buican and Zoltan Laczko

  • CRST and School of Physics and Astronomy Queen Mary University of London, London E1 4NS, United Kingdom

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Issue

Vol. 120, Iss. 8 — 23 February 2018

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