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Sharp Boundaries for the Swampland

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arxiv 2102.08951 v2 pith:7VFWIYPZ submitted 2021-02-17 hep-th

classification hep-th
keywords couplingstheoriescoupledderivativehigherorders-matrixallows
verification ladder T0 review T1 audit T2 compute T3 formal
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We reconsider the problem of bounding higher derivative couplings in consistent weakly coupled gravitational theories, starting from general assumptions about analyticity and Regge growth of the S-matrix. Higher derivative couplings are expected to be of order one in the units of the UV cutoff. Our approach justifies this expectation and allows to prove precise bounds on the order one coefficients. Our main tool are dispersive sum rules for the S-matrix. We overcome the difficulties presented by the graviton pole by measuring couplings at small impact parameter, rather than in the forward limit. We illustrate the method in theories containing a massless scalar coupled to gravity, and in theories with maximal supersymmetry.

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Cited by 27 Pith papers

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