Displacement Operators and Constraints on Boundary Central Charges

Herzog, Christopher P.; Huang, Kuo-Wei; Jensen, Kristan

doi:10.1103/physrevlett.120.021601

Cited by 69 publications

(113 citation statements)

References 39 publications

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“…defined through the variational rule (2.5) is physical so we do not expect it to acquire any divergences or anomalous dimension). Another interesting object we can compute is the two-point function of the displacement operator, whose coefficient is related to a B−type conformal anomaly (a central charge) at the boundary in d = 3 (see [36], [37] for more details). In our case this two-point function reads Note that the d = 3 expression agrees with the free-field computation of [38].…”

Section: Displacement Operatormentioning

confidence: 99%

Composite operators near the boundary

Prochazka

Söderberg

2020

J. High Energ. Phys.

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We use renormalization group methods to study composite operators existing at a boundary of an interacting conformal field theory. In particular we relate the data on boundary operators to short-distance (near-boundary) divergences of bulk two-point functions. We further argue that in the presence of running couplings at the boundary the anomalous dimensions of certain composite operators can be computed from the relevant beta functions and remark on the implications for the boundary (pseudo) stress-energy tensor. We apply the formalism to a scalar field theory in d = 3 − dimensions with a quartic coupling at the boundary whose beta function we determine to the first non-trivial order. We study the operators in this theory and compute their conformal data using −expansion at the Wilson-Fisher fixed point of the boundary renormalization group flow. We find that the model possesses a non-zero boundary stress-energy tensor and displacement operator both with vanishing anomalous dimensions. The boundary stress tensor decouples at the fixed point in accordance with Cardy's condition for conformal invariance. We end the main part of the paper by discussing the possible physical significance of this fixed point for various values of . A. General form of a bulk-boundary correlator 32 B. Four-point correlator 33 C. Master integral 34 D. Stress-energy tensor correlator at orderĝ 35

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Section: Displacement Operatormentioning

confidence: 99%

Composite operators near the boundary

Prochazka

Söderberg

2020

J. High Energ. Phys.

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“…For a free scalar field, c = 1 and a = ±1 for Dirichlet (+) and Neumann (−) boundary conditions, and c = 2, a = 0 for a free Dirac fermion with mixed boundary conditions. Recently [42,67], c has been connected to two other boundary charges, namely A T and c nn , where c nn is the charge in the two-point function of the displacement operator. Then, with eq.…”

Section: A Comments On Bulk and Boundary Chargesmentioning

confidence: 99%

“…It is known that b 1 = c = 3π 4 C T for free fields. In [67], it was proven that b 1 is related to the coefficient c nn in the displacement operator two-point function as b 1 = 2π 4 c nn . Further, in [42] b 1 has been connected to A T via b 1 = −240π 2 A T .…”

Section: A Comments On Bulk and Boundary Chargesmentioning

confidence: 99%

Relating bulk to boundary entanglement

Berthiere

Witczak-Krempa

2019

Phys. Rev. B

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Quantum field theories have a rich structure in the presence of boundaries. We study the groundstates of conformal field theories (CFTs) and Lifshitz field theories in the presence of a boundary through the lens of the entanglement entropy. For a family of theories in general dimensions, we relate the universal terms in the entanglement entropy of the bulk theory with the corresponding terms for the theory with a boundary. This relation imposes a condition on certain boundary central charges. For example, in 2 + 1 dimensions, we show that the corner-induced logarithmic terms of free CFTs and certain Lifshitz theories are simply related to those that arise when the corner touches the boundary. We test our findings on the lattice, including a numerical implementation of Neumann boundary conditions. We also propose an ansatz, the boundary Extensive Mutual Information model, for a CFT with a boundary whose entanglement entropy is purely geometrical. This model shows the same bulk-boundary connection as Dirac fermions and certain supersymmetric CFTs that have a holographic dual. Finally, we discuss how our results can be generalized to all dimensions as well as to massive quantum field theories. Contents

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“…In addition to traditional field theory techniques, see, e.g. [63,65,[69][70][71][72][73][74], the need of a non-perturbative approach using symmetries or dualities is evident. A non-perturbative holographic dual description to BCFT was initiated by Takayanagi in [54] and later developed for general shape of boundary geometry in [55,56].…”

Section: Holographic Boundary Conformal Field Theorymentioning

confidence: 99%

Weyl Anomaly and Vacuum Magnetization Current of M5‐brane in Background Flux

Chu

2019

Fortschritte der Physik

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It was recently discovered that for a boundary system in the presence of a background magnetic field, the quantum fluctuation of the vacuum would create a non‐uniform magnetization density for the vacuum and a magnetization current is induced in the vacuum. It was also shown that this ‘magnetic Casimir effect’ of the vacuum is closely related to another quantum effect of the vacuum, the Weyl anomaly. Furthermore, the phenomena can be understood in terms of the holography of the boundary system. In this article, we review the derivation of this phenomena from QFT as well as the derivation of it using AdS/BCFT. We then generalize this four dimensional effect to six‐dimensions. We use the AdS/BCFT holography to show that in the presence of a 3‐form magnetic field strength H, a string current is induced in a six‐dimensional boundary conformal field theory. This allows us to determine the gauge field contribution to the Weyl anomaly in six‐dimensional conformal field theory in a H‐flux background. For the (2,0) superconformal field theory of N M5‐branes, the current has a magnitude proportional to N3 for large N. This suggests that the degree of freedoms scales as N3 in the (2,0) superconformal theory of N multiple M5‐branes. Our result for the Weyl anomaly is a new prediction for the (2,0) theory.

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Displacement Operators and Constraints on Boundary Central Charges

Cited by 69 publications

References 39 publications

Composite operators near the boundary

Composite operators near the boundary

Relating bulk to boundary entanglement

Weyl Anomaly and Vacuum Magnetization Current of M5‐brane in Background Flux

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