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Relative Entropy and Proximity of Quantum Field Theories

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arxiv 1410.6809 v2 pith:EN5IOBQL submitted 2014-10-24 hep-th cond-mat.dis-nn

Relative Entropy and Proximity of Quantum Field Theories

Vijay Balasubramanian , Jonathan J. Heckman , Alexander Maloney This is my paper
classification hep-th cond-mat.dis-nn
keywords fieldtheoriesdistinguishentropyleadsproximityquantifiesquantum
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We study the question of how reliably one can distinguish two quantum field theories (QFTs). Each QFT defines a probability distribution on the space of fields. The relative entropy provides a notion of proximity between these distributions and quantifies the number of measurements required to distinguish between them. In the case of nearby conformal field theories, this reduces to the Zamolodchikov metric on the space of couplings. Our formulation quantifies the information lost under renormalization group flow from the UV to the IR and leads us to a quantification of fine-tuning. This formalism also leads us to a criterion for distinguishability of low energy effective field theories generated by the string theory landscape.

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Cited by 3 Pith papers

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  1. Notes on Wasserstein distance and wormholes

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    Defines Boltzmann-Wasserstein distance on quantum theories via optimal W2 transport of Boltzmann-weighted spectra, equates it to thermal correlators, and constructs a Schwinger-Keldysh wormhole saddle that reproduces ...

  2. Optimal paths across potentials on scalar field space

    hep-th 2026-04 unverdicted novelty 7.0

    Optimal transport yields a generalized Wasserstein distance on field space, obtained from a WKB expansion of a Schrödinger equation and extended to dynamical gravity via the Wheeler-DeWitt equation in the ADM formalism.

  3. Naturalness and Fisher Information

    hep-th 2026-03 unverdicted novelty 7.0

    A fine-tuning measure is defined from the eigenvalues of a rescaled Fisher information matrix on parameter space, with a geometric interpretation as the pullback of the Euclidean metric from observable space.