Related papers: A counterexample to the CFT convexity conjecture
It is shown the antisymmetric part of the metric tensor is the potential for the spin field. Various metricity conditions are discussed and comparisons are made to other theories, including Einstein's. It is shown in the weak field limit…
The Weak Gravity Conjecture predicts that in quantum gravity there should exist overcharged states, that is states with charge larger than their mass. Extending this to large masses and charges, we are expecting similar overcharged…
We give an explicit counterexample to an entanglement inequality suggested in a recent paper [quant-ph/0005126] by Benatti and Narnhofer. The inequality would have had far-reaching consequences, including the additivity of the entanglement…
We consider the problem of identifying the CFT's that may be dual to pure gravity in three dimensions with negative cosmological constant. The c-theorem indicates that three-dimensional pure gravity is consistent only at certain values of…
We study the Weak Gravity Conjecture in the presence of scalar fields. The Weak Gravity Conjecture is a consistency condition for a theory of quantum gravity asserting that for a U(1) gauge field, there is a particle charged under this…
The black hole weak gravity conjecture (WGC) is a set of linear inequalities on the four-derivative corrections to Einstein--Maxwell theory. Remarkably, in four dimensions, these combinations appear in the $2 \to 2$ photon amplitudes,…
Conformal symmetry is broken by a flat or spherical defect operator $\mathcal{D}$. We show that this defect operator, may be identified as a pair of twist operators which are inserted at the tips of its causal diamond. Any $k-$point…
We prove a strengthened form of convexity for operator monotone decreasing positive functions defined on the positive real numbers. This extends Ando and Hiai's work to allow arbitrary positive maps instead of states (or the identity map),…
The clockwork is a mechanism for generating light particles with exponentially suppressed interactions in theories which contain no small parameters at the fundamental level. We develop a general description of the clockwork mechanism valid…
The weak lower semicontinuity of the functional $$ F(u)=\int_{\Omega}f(x,u,\nabla u)\, dx$$ is a classical topic that was studied thoroughly. It was shown that if the function $f$ is continuous and convex in the last variable, the…
The concept of convex compactness, weaker than the classical notion of compactness, is introduced and discussed. It is shown that a large class of convex subsets of topological vector spaces shares this property and that is can be used in…
In this paper, we prove the convexity of trace functionals $$(A,B,C)\mapsto \text{Tr}|B^{p}AC^{q}|^{s},$$ for parameters $(p,q,s)$ that are best possible, where $B$ and $C$ are any $n$-by-$n$ positive definite matrices, and $A$ is any…
Considering theories in sectors of large global charge $Q$ results in a semiclassical effective field theory (EFT) description for some strongly-coupled conformal field theories (CFTs) with continuous global symmetries. Hence, when studying…
We examine the AdS/CFT correspondence when the gauge theory is considered on a compactified space with supersymmetry breaking boundary conditions. We find that the corresponding supergravity solution has a negative energy, in agreement with…
The main result (roughly) is that if (H_i) converges weakly to H and if also f(H_i) converges weakly to f(H), for a single strictly convex continuous function f, then (H_i) must converge strongly to H. One application is that if f(pr(H)) =…
This paper concerns three classes of real-valued functions on intervals, operator monotone functions, operator convex functions, and strongly operator convex functions. Strongly operator convex functions were previously treated in [3] and…
Conformal symmetry is broken in physical QCD; nevertheless, one can use conformal symmetry as a template, systematically correcting for its nonzero $\beta$ function as well as higher-twist effects. For example, commensurate scale relations…
We study the three dimensional Einstein gravity conformally coupled to a scalar field. Solutions of this theory are geometries with vanishing scalar curvature. We consider solutions with a constant scalar field which corresponds to an…
A key idea in convex optimization theory is to use well-structured affine functions to approximate general functions, leading to impactful developments in conjugate functions and convex duality theory. This raises the question: what are the…
We discuss several aspects of the proposed correspondence between quantum gravity on de Sitter spaces and Euclidean conformal field theories. The central charge appearing in the asymptotic symmetry algebra of three-dimensional de Sitter…