4,609 research outputs found
Universality for Shape Dependence of Casimir Effects from Weyl Anomaly
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 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.Comment: 19 pages, 1 figure and 3 tables, references added, accepted for
publication in JHE
Universality in the Shape Dependence of Holographic R\'enyi Entropy for General Higher Derivative Gravity
We consider higher derivative gravity and obtain universal relations for the
shape coefficients of the shape dependent universal part of
the R\'enyi entropy for four dimensional CFTs in terms of the parameters of two-point and three-point functions of stress tensors. As a
consistency check, these shape coefficients and satisfy the
differential relation as derived previously for the R\'enyi entropy.
Interestingly, these holographic relations also apply to weakly coupled
conformal field theories such as theories of free fermions and vectors but are
violated by theories of free scalars. The mismatch of for scalars has
been observed in the literature and is due to certain delicate boundary
contributions to the modular Hamiltonian. Interestingly, we find a combination
of our holographic relations which are satisfied by all free CFTs including
scalars. We conjecture that this combined relation is universal for general
CFTs in four dimensional spacetime. Finally, we find there are similar
universal laws for holographic R\'enyi entropy in general dimensions.Comment: 32 pages,0 figures, references added, appendix added, accepted for
publication in JHE
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