A bstract The Distance Conjecture holds that any infinitedistance limit in the scalar field moduli space of a consistent theory of quantum gravity must be accompanied by a tower of light particles whose masses scale exponentially with proper field distance ‖ ϕ ‖ as m ~ exp(− λ ‖ ϕ ‖), where λ is orderone in Planck units. While the evidence for this conjecture is formidable, there is at present no consensus on which values of λ are allowed. In this paper, we propose a sharp lower bound for the lightest tower in a given infinitedistance limit in d dimensions: λ ≥ $$ 1/\sqrt{d2} $$ 1 / d − 2 . In support of this proposal, we show that (1) it is exactly preserved under dimensional reduction, (2) it is saturated in many examples of string/Mtheory compactifications, including maximal supergravity in d = 4 – 10 dimensions, and (3) it is saturated in many examples of minimal supergravity in d = 4 – 10 dimensions, assuming appropriate versions of the Weak Gravity Conjecture. We argue that towers with λ < $$ 1/\sqrt{d2} $$ 1 / d − 2 discussed previously in the literature are always accompanied by even lighter towersmore »
A CFT distance conjecture
A bstract We formulate a series of conjectures relating the geometry of conformal manifolds to the spectrum of local operators in conformal field theories in d > 2 spacetime dimensions. We focus on conformal manifolds with limiting points at infinite distance with respect to the Zamolodchikov metric. Our central conjecture is that all theories at infinite distance possess an emergent higherspin symmetry, generated by an infinite tower of currents whose anomalous dimensions vanish exponentially in the distance. Stated geometrically, the diameter of a noncompact conformal manifold must diverge logarithmically in the higherspin gap. In the holographic context our conjectures are related to the Distance Conjecture in the swampland program. Interpreted gravitationally, they imply that approaching infinite distance in moduli space at fixed AdS radius, a tower of higherspin fields becomes massless at an exponential rate that is bounded from below in Planck units. We discuss further implications for conformal manifolds of superconformal field theories in three and four dimensions.
 Award ID(s):
 1915093
 Publication Date:
 NSFPAR ID:
 10376823
 Journal Name:
 Journal of High Energy Physics
 Volume:
 2021
 Issue:
 10
 ISSN:
 10298479
 Sponsoring Org:
 National Science Foundation
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