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Scale Invariance vs. Conformal Invariance: Holographic Two-Point Functions in Horndeski Gravity
We consider Einstein-Horndeski gravity with a negative bare constant as a
holographic model to investigate whether a scale invariant quantum field theory
can exist without the full conformal invariance. Einstein-Horndeski gravity can
admit two different AdS vacua. One is conformal, and the holographic two-point
functions of the boundary energy-momentum tensor are the same as the ones
obtained in Einstein gravity. The other AdS vacuum, which arises at some
critical point of the coupling constants, preserves the scale invariance but
not the special conformal invariance due to the logarithmic radial dependence
of the Horndeski scalar. In addition to the transverse and traceless graviton
modes, the theory admits an additional trace/scalar mode in the scale invariant
vacuum. We obtain the two-point functions of the corresponding boundary
operators. We find that the trace/scalar mode gives rise to an non-vanishing
two-point function, which distinguishes the scale invariant theory from the
conformal theory. The two-point function vanishes in , where the full
conformal symmetry is restored. Our results indicate the strongly coupled scale
invariant unitary quantum field theory may exist in without the full
conformal symmetry. The operator that is dual to the bulk trace/scalar mode
however violates the dominant energy condition.Comment: Latex, 28 pages, comments and references adde
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Wnt Signaling in Neural Crest Ontogenesis and Oncogenesis.
Neural crest (NC) cells are a temporary population of multipotent stem cells that generate a diverse array of cell types, including craniofacial bone and cartilage, smooth muscle cells, melanocytes, and peripheral neurons and glia during embryonic development. Defective neural crest development can cause severe and common structural birth defects, such as craniofacial anomalies and congenital heart disease. In the early vertebrate embryos, NC cells emerge from the dorsal edge of the neural tube during neurulation and then migrate extensively throughout the anterior-posterior body axis to generate numerous derivatives. Wnt signaling plays essential roles in embryonic development and cancer. This review summarizes current understanding of Wnt signaling in NC cell induction, delamination, migration, multipotency, and fate determination, as well as in NC-derived cancers
More on Heavy-Light Bootstrap up to Double-Stress-Tensor
We investigate the heavy-light four-point function up to
double-stress-tensor, supplementing 1910.06357. By using the OPE coefficients
of lowest-twist double-stress-tensor in the literature, we find the Regge
behavior for lowest-twist double-stress-tensor in general even dimension within
the large impact parameter regime. In the next, we perform the Lorentzian
inversion formula to obtain both the OPE coefficients and anomalous dimensions
of double-twist operators with finite spin
in . We also extract the anomalous dimensions of double-twist
operators with finite spin in general dimension, which allows us to address the
cases that is specified to the poles in lowest-twist
double-stress-tensors where certain double-trace operators
mix with lowest-twist
double-stress-tensors. In particular, we verify and discuss the Residue
relation that determines the product of the mixed anomalous dimension and the
mixed OPE. We also present the double-trace and mixed OPE coefficients
associated with poles in . In the end, we turn to discuss
CFT, we verify the uniqueness of double-stress-tensor that is consistent
with Virasoso symmetry.Comment: latex, 44 pages, 1 figur
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