| Convexity of scaling dimensions over conformal manifolds |
| Nat Levine |
| Event Type: Informal HEP Talk |
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| Time: 2:00 PM - 3:15 PM |
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| Location: 726 Broadway, 940, CCPP Seminar |
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| Abstract: We study d-dimensional conformal field theories (CFTs) with exactly marginal couplings and the property that the finite part of the sphere partition function is unambiguous. This class includes all odd-dimensional CFTs with conformal manifolds, and sufficiently supersymmetric even-dimensional ones. We prove that the scaling dimension of the lightest unprotected scalar operator with fixed quantum numbers is a concave function. More generally, the sum of the lowest n such scaling dimensions is concave for any n. These results hold with respect to a dressed Riemannian metric on the conformal manifold: the standard Zamolodchikov metric multiplied by the sphere partition function. We show how these convexity statements can imply monotonicity in the context of holographic CFTs, assuming the unprotected states decouple in the weakly coupled gravity limit. We test our results in N=4 super Yang-Mills theory in both the planar and non-planar regimes. Link to the Event Video |