Constraint on Defect and Boundary Renormalization Group Flows

We reveal elegant relations between the shape dependence of the Casimir effects and Weyl anomaly in boundary conformal field theories (BCFT). We show that for any BCFT which has a description in terms of an effective action, the near boundary divergent behavior of the renormalized stress tensor is completely determined by the central charges of the theory. These relations are verified by free BCFTs. We also test them with holographic models of BCFT and find exact agreement. We propose that these relations between Casimir coefficients and central charges hold for any BCFT. With the holographic models, we reproduce not only the precise form of the near boundary divergent behavior of the stress tensor, but also the surface counter term that is needed to make the total energy finite. As they are proportional to the central charges, the near boundary divergence of the stress tensor must be physical and cannot be dropped by further artificial renormalization. Our results thus provide affirmative support on the physical nature of the divergent energy density near the boundary, whose reality has been a long-standing controversy in the literature.

Section: Jhep03(2018)046mentioning

confidence: 99%

Universality for shape dependence of Casimir effects from Weyl anomaly

Miao

Chu

2018

“…By using instead the boundary conditions K = d+1 d T , the relations q = a = f α (π/2) have been obtained [72][73][74]. Notice that the relation q = a is not true for a free scalar [49,56,65].…”

Section: Jhep11(2017)076mentioning

confidence: 99%

“…They have been computed for some free models in [49,56,65]. The quantity T i i has been studied also in BCFT 4 [51,52].…”

Section: Jhep11(2017)076mentioning

confidence: 99%

“…The space of the boundary conditions which preserve the conformal invariance depends on the underlying model. In BCFT 3 , the presence of the boundary leads to a Weyl anomaly which is non vanishing only on the boundary and this allows to introduce two boundary charges [49,50]. In BCFT 4 , the Weyl anomaly is the sum of a well known term on the bulk and a term due to the occurrence of the boundary [49][50][51][52].…”

Section: Introductionmentioning

confidence: 99%

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Corner contributions to holographic entanglement entropy in AdS4/BCFT3

Seminara

Sisti

Tonni

2017

Abstract:We study the holographic entanglement entropy of spatial regions with corners in the AdS 4 /BCFT 3 correspondence by considering three dimensional boundary conformal field theories whose boundary is a timelike plane. We compute analytically the corner function corresponding to an infinite wedge having one edge on the boundary. A relation between this corner function and the holographic one point function of the stress tensor is observed. An analytic expression for the corner function of an infinite wedge having only its tip on the boundary is also provided. This formula requires to find the global minimum among two extrema of the area functional. The corresponding critical configurations of corners are studied. The results have been checked against a numerical analysis performed by computing the area of the minimal surfaces anchored to some finite domains containing corners.

“…It would also be important to try to generalize our approach to higher dimensions and different defects. Recent work in higher dimensions includes [31,32]. Moreover, it would be interesting to explore the connection with holographic results on defect entropy [9,10,[33][34][35].…”

Section: Jhep10(2016)140mentioning

confidence: 99%

The g-theorem and quantum information theory

Casini

Landea

Torroba

2016

130

158

Abstract:We study boundary renormalization group flows between boundary conformal field theories in 1 + 1 dimensions using methods of quantum information theory. We define an entropic g-function for theories with impurities in terms of the relative entanglement entropy, and we prove that this g-function decreases along boundary renormalization group flows. This entropic g-theorem is valid at zero temperature, and is independent from the gtheorem based on the thermal partition function. We also discuss the mutual information in boundary RG flows, and how it encodes the correlations between the impurity and bulk degrees of freedom. Our results provide a quantum-information understanding of (boundary) RG flow as increase of distinguishability between the UV fixed point and the theory along the RG flow.