Irreversibility of the renormalization group flow in non-unitary quantum field theory

Castro-Alvaredo, Olalla A.; Doyon, Benjamin; Ravanini, Francesco

doi:10.1088/1751-8121/aa8a10

Cited by 22 publications

(25 citation statements)

References 70 publications

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“…Still, we should point out that our non-unitary 4D theories described above have an avatar of 2D unitarity: a modified notion of reflection positivity exists in our theories. Related 2D constructions have played a role in recent work on non-unitary extensions of Zamolodchikov's c-theorem [42]. Such structures, involving "hidden" unitarity, may also shed more light on the question of which non-unitary theories in 2D are able to encode the unitary 4D physics in the original construction of [2].…”

Section: Discussionmentioning

confidence: 99%

Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories

Buican

Laczko

2018

Phys. Rev. Lett.

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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.

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Section: Discussionmentioning

confidence: 99%

Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories

Buican

Laczko

2018

Phys. Rev. Lett.

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“…In particular, m corresponds to the number of times the link wraps the longitude of the torus and n corresponds to the number of times the link wraps the meridian. 43 The links may be characterized by the components that make it up. In particular, we have…”

Section: Torus Links and Canonical Wordsmentioning

confidence: 99%

Galois conjugation and multiboundary entanglement entropy

Buican

Radhakrishnan

2020

J. High Energ. Phys.

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We revisit certain natural algebraic transformations on the space of 3D topological quantum field theories (TQFTs) called “Galois conjugations.” Using a notion of multiboundary entanglement entropy (MEE) defined for TQFTs on compact 3-manifolds with disjoint boundaries, we give these abstract transformations additional physical meaning. In the process, we prove a theorem on the invariance of MEE along orbits of the Galois action in the case of arbitrary Abelian theories defined on any link complement in S3. We then give a generalization to non-Abelian TQFTs living on certain infinite classes of torus link complements. Along the way, we find an interplay between the modular data of non-Abelian TQFTs, the topology of the ambient spacetime, and the Galois action. These results are suggestive of a deeper connection between entanglement and fusion.

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“…An other example in [53] terminates in a flow from the Yang-Lee edge singularity to the trivial c = 0 theory. Recently in [54] it was shown that it is possible to relax the requirement of unitary and still show the existence of a monotonic decreasing c-function along such flows. So the learning here is that it is not a manifest impossibility to conceive an RG flow between a non-unitary UV CFT and a unitary IR CFT.…”

Section: The Rg Behaviour When Not Restricted To the Integrable Locusmentioning

confidence: 99%

Classical and quantum aspects of Yang-Baxter Wess-Zumino models

Demulder

Driezen

Sevrin

et al. 2018

J. High Energ. Phys.

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Abstract:We investigate the integrable Yang-Baxter deformation of the 2d Principal Chiral Model with a Wess-Zumino term. For arbitrary groups, the one-loop β-functions are calculated and display a surprising connection between classical and quantum physics: the classical integrability condition is necessary to prevent new couplings being generated by renormalisation. We show these theories admit an elegant realisation of Poisson-Lie Tduality acting as a simple inversion of coupling constants. The self-dual point corresponds to the Wess-Zumino-Witten model and is the IR fixed point under RG. We address the possibility of having supersymmetric extensions of these models showing that extended supersymmetry is not possible in general.

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Irreversibility of the renormalization group flow in non-unitary quantum field theory

Cited by 22 publications

References 70 publications

Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories

Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories

Galois conjugation and multiboundary entanglement entropy

Classical and quantum aspects of Yang-Baxter Wess-Zumino models

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