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Bounding scalar operator dimensions in 4D CFT | | Riccardo Rattazzi
; Vyacheslav S. Rychkov
; Erik Tonni
; Alessandro Vichi
; | | Date: |
1 Jul 2008 | | Abstract: | In an arbitrary unitary 4D CFT we consider a scalar operator phi, and the
operator phi^2 defined as the lowest dimension scalar which appears in the OPE
phi imesphi with a nonzero coefficient. Using general considerations of OPE,
conformal block decomposition, and crossing symmetry, we derive a
theory-independent inequality [phi^2] leq f([phi]) for the dimensions of
these two operators. The function f(d) entering this bound is computed
numerically. For d->1 we have f(d)=2+O(sqrt{d-1}), which shows that the free
theory limit is approached continuously. We perform some checks of our bound.
We find that the bound is satisfied by all weakly coupled 4D conformal fixed
points that we are able to construct. The Wilson-Fischer fixed points violate
the bound by a constant O(1) factor, which must be due to the subtleties of
extrapolating to 4-epsilon dimensions. We use our method to derive an
analogous bound in 2D, and check that the Minimal Models satisfy the bound,
with the Ising model nearly-saturating it. Derivation of an analogous bound in
3D is currently not feasible because the explicit conformal blocks are not
known in odd dimensions. We also discuss the main phenomenological motivation
for studying this set of questions: constructing models of dynamical
ElectroWeak Symmetry Breaking without flavor problems. | | Source: | arXiv, 0807.0004 | | Services: | Forum | Review | PDF | Favorites | |
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