Self-dual 
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 bosonic quantum Hall state in mixed-dimensional QED

Hsiao, Wei-Han; Son, D.

doi:10.1103/physrevb.100.235150

Cited by 17 publications

(24 citation statements)

References 34 publications

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“…The duality implies a inverse relation between the conductivities of the two theories, as discussed in Section 2.4.1 [9]. The same results is obtained in the case of electrodynamics of scalar particles [21]; there is a difference of a factor of two in the relation (2.50), i.e. π → π/2, stemming from the duality transformations (2.31) and (2.37).…”

Section: )supporting

confidence: 63%

Quantization of a self-dual conformal theory in (2 + 1) dimensions

Andreucci

Cappelli

Maffi

2020

J. High Energ. Phys.

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Compact nonlocal Abelian gauge theory in (2 + 1) dimensions, also known as loop model, is a massless theory with a critical line that is explicitly covariant under duality transformations. It corresponds to the large N F limit of self-dual electrodynamics in mixed three-four dimensions. It also provides a bosonic description for surface excitations of three-dimensional topological insulators. Upon mapping the model to a local gauge theory in (3 + 1) dimensions, we compute the spectrum of electric and magnetic solitonic excitations and the partition function on the three torus T 3 . Analogous results for the S 2 × S 1 geometry show that the theory is conformal invariant and determine the manifestly self-dual spectrum of conformal fields, corresponding to order-disorder excitations with fractional statistics.

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Section: )supporting

confidence: 63%

Quantization of a self-dual conformal theory in (2 + 1) dimensions

Andreucci

Cappelli

Maffi

2020

J. High Energ. Phys.

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“…Mixed QED has a large although perhaps little known footprint in the literature. See refs [17][18][19][20][21][22][23]. for several examples where these theories appear.…”

mentioning

confidence: 99%

On marginal operators in boundary conformal field theory

Herzog

Shamir

2019

J. High Energ. Phys.

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The presence of a boundary (or defect) in a conformal field theory allows one to generalize the notion of an exactly marginal deformation. Without a boundary, one must find an operator of protected scaling dimension ∆ equal to the space-time dimension d of the conformal field theory, while with a boundary, as long as the operator dimension is protected, one can make up for the difference d − ∆ by including a factor z ∆−d in the deformation where z is the distance from the boundary. This coordinate dependence does not lead to a reduction in the underlying SO(d, 1) global conformal symmetry group of the boundary conformal field theory. We show that such terms can arise from boundary flows in interacting field theories. Ultimately, we would like to be able to characterize what types of boundary conformal field theories live on the orbits of such deformations. As a first step, we consider a free scalar with a conformally invariant mass term z −2 φ 2 , and a fermion with a similar mass. We find a connection to double trace deformations in the AdS/CFT literature.

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“…II B) of the "fermionic dual" to the XY model in (2.1) results in selfdual transport. How this symmetry might be realized quantum mechanically is unclear [55]. This question is related to the emergent time-reversal symmetry of this "fermionic dual" at zero Dirac composite fermion density.…”

Section: Discussionmentioning

confidence: 99%

“…(1.1) and (1.3). We discuss their implementation [18,19,[54][55][56] in the dual Lagrangian (2.1) at N f = 1 at criticality m = 0.…”

Section: B Discrete Symmetry At N F =mentioning

confidence: 99%

Scaling and diffusion of Dirac composite fermions

Lee¹,

Mulligan²

2020

Phys. Rev. Research

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We study the effects of quenched disorder and a dissipative Coulomb interaction on an anyon gas in a periodic potential undergoing a quantum phase transition. We use a (2 + 1)-dimensional low-energy effective description that involves N f = 1 Dirac fermion coupled to a U (1) Chern-Simons gauge field at level (θ − 1/2). When θ = 1/2 the anyons are free Dirac fermions that exhibit an integer quantum Hall transition; when θ = 1 the anyons are bosons undergoing a superconductor-insulator transition in the universality class of the three-dimensional XY model. Using the large N f approximation we perform a renormalization-group analysis. We find the Coulomb interaction to be an irrelevant perturbation of the clean fixed point for any θ. The dissipative Coulomb interaction allows for two classes of IR stable fixed points in the presence of disorder: those with a finite nonzero Coulomb coupling and dynamical critical exponent z = 1 and those with an effectively infinite Coulomb coupling and 1 < z < 2. At θ = 1/2 the clean fixed point is stable to charge-conjugation preserving (random mass) disorder, while a line of diffusive fixed points is obtained when the product of charge-conjugation and time-reversal symmetries is preserved. At θ = 1 we find a finite disorder fixed point with unbroken charge-conjugation symmetry whether or not the Coulomb interaction is present. Other cases result in runaway flows. We comment on the relation of our results to other theoretical studies and the relevancy to experiment.

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Self-dual ν=1 bosonic quantum Hall state in mixed-dimensional QED

Cited by 17 publications

References 34 publications

Quantization of a self-dual conformal theory in (2 + 1) dimensions

Quantization of a self-dual conformal theory in (2 + 1) dimensions

On marginal operators in boundary conformal field theory

Scaling and diffusion of Dirac composite fermions

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