Abstract Hodge Decomposition and Minimal Models for Cyclic Algebras

AbstractWe formulate a ℤk-parafermionization/bosonization scheme for one-dimensional lattice models and field theories on a torus, starting from a generalized Jordan-Wigner transformation on a lattice, which extends the Majorana-Ising duality atk= 2. The ℤk-parafermionization enables us to investigate the critical theories of parafermionic chains whose fundamental degrees of freedom are parafermionic, and we find that their criticality cannot be described by any existing conformal field theory. The modular transformations of these parafermionic low-energy critical theories as general consistency conditions are found to be unconventional in that their partition functions on a torus transform differently from any conformal field theory whenk >2. Explicit forms of partition functions are obtained by the developed parafermionization for a large class of critical ℤk-parafermionic chains, whose operator contents are intrinsically distinct from any bosonic or fermionic model in terms of conformal spins and statistics. We also use the parafermionization to exhaust all the ℤk-parafermionic minimal models, complementing earlier works on fermionic cases.

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Defects and perturbation

Journal of High Energy Physics ◽

10.1007/jhep04(2021)300 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Enrico M. Brehm

Keyword(s):

Entanglement Entropy ◽

Topological Defects ◽

Field Theories ◽

Two Dimensional ◽

Conformal Field Theories ◽

Minimal Models ◽

Conformal Field

Abstract We investigate perturbatively tractable deformations of topological defects in two-dimensional conformal field theories. We perturbatively compute the change in the g-factor, the reflectivity, and the entanglement entropy of the conformal defect at the end of these short RG flows. We also give instances of such flows in the diagonal Virasoro and Super-Virasoro Minimal Models.

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Hodge decomposition of string topology

Forum of Mathematics Sigma ◽

10.1017/fms.2021.26 ◽

2021 ◽

Vol 9 ◽

Author(s):

Yuri Berest ◽

Ajay C. Ramadoss ◽

Yining Zhang

Keyword(s):

Lie Algebras ◽

General Theorem ◽

Hodge Decomposition ◽

String Topology ◽

Free Loop Space ◽

Oriented Manifold ◽

Universal Enveloping Algebras ◽

Finite Dimensional ◽

Equivariant Homology ◽

Simply Connected

Abstract Let X be a simply connected closed oriented manifold of rationally elliptic homotopy type. We prove that the string topology bracket on the $S^1$ -equivariant homology $ {\overline {\text {H}}}_\ast ^{S^1}({\mathcal {L}} X,{\mathbb {Q}}) $ of the free loop space of X preserves the Hodge decomposition of $ {\overline {\text {H}}}_\ast ^{S^1}({\mathcal {L}} X,{\mathbb {Q}}) $ , making it a bigraded Lie algebra. We deduce this result from a general theorem on derived Poisson structures on the universal enveloping algebras of homologically nilpotent finite-dimensional DG Lie algebras. Our theorem settles a conjecture of [7].

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The ScotoSinglet Model: a scalar singlet extension of the Scotogenic Model

Journal of High Energy Physics ◽

10.1007/jhep06(2021)136 ◽

2021 ◽

Vol 2021 (6) ◽

Author(s):

Ankit Beniwal ◽

Juan Herrero-García ◽

Nicholas Leerdam ◽

Martin White ◽

Anthony G. Williams

Keyword(s):

Parameter Space ◽

Direct Detection ◽

Neutrino Masses ◽

Minimal Models ◽

Flavour Violation ◽

The One ◽

Relic Abundance ◽

Electroweak Precision ◽

Scalar Singlet ◽

Lepton Flavour

Abstract The Scotogenic Model is one of the most minimal models to account for both neutrino masses and dark matter (DM). In this model, neutrino masses are generated at the one-loop level, and in principle, both the lightest fermion singlet and the lightest neutral component of the scalar doublet can be viable DM candidates. However, the correct DM relic abundance can only be obtained in somewhat small regions of the parameter space, as there are strong constraints stemming from lepton flavour violation, neutrino masses, electroweak precision tests and direct detection. For the case of scalar DM, a sufficiently large lepton-number-violating coupling is required, whereas for fermionic DM, coannihilations are typically necessary. In this work, we study how the new scalar singlet modifies the phenomenology of the Scotogenic Model, particularly in the case of scalar DM. We find that the new singlet modifies both the phenomenology of neutrino masses and scalar DM, and opens up a large portion of the parameter space of the original model.

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