Tameness, Strings, and the Distance Conjecture

Grimm, Thomas W.; Lanza, Stefano; Li, Chongchuo

doi:10.1007/jhep09(2022)149

Cited by 14 publications

(24 citation statements)

References 70 publications

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“…The highest Mordell-Weil rank obtained so far for elliptic threefolds is rmax = 10 [82]. 21 We thank Wati Taylor for pointing this out to us.…”

Section: Jhep03(2023)197mentioning

confidence: 89%

“…Indeed, it is certainly possible to violate the bound set by r F (e) max in explicit Weierstrass models. 21 For example, consider the maximal possible gauge group of type E n 1 6 × E n 2 7 by engineering the various gauge group factors on separate divisors in class H. Compatibility 20 The upper bound (6.31) is the analogue, on fourfolds, of the bound n(U(1)) ≤ 32 for F-theory compactifications to six dimensions on an elliptic three-fold over base P 2 [11]. The highest Mordell-Weil rank obtained so far for elliptic threefolds is rmax = 10 [82].…”

Section: Jhep03(2023)197mentioning

confidence: 99%

“…The original motivation in studying such strings was the conjecture of [18,19] that any infinite distance limit in four dimensions can be obtained as the endpoint of an RG flow induced by the backreaction of an EFT string. This idea has been investigated further in [20][21][22] from various perspectives.…”

Section: Introductionmentioning

confidence: 99%

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Quantum gravity bounds on $$ \mathcal{N} $$ = 1 effective theories in four dimensions

Martucci

Risso

Weigand

2023

J. High Energ. Phys.

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We propose quantum gravitational constraints on effective four-dimensional theories with $$ \mathcal{N} $$ N = 1 supersymmetry. These Swampland constraints arise by demanding consistency of the worldsheet theory of a class of axionic, or EFT, strings whose existence follows from the Completeness Conjecture of quantum gravity. Modulo certain assumptions, we derive positivity bounds and quantization conditions for the axionic couplings to the gauge and gravitational sector at the two- and four-derivative level, respectively. We furthermore obtain general bounds on the rank of the gauge sector in terms of the gravitational couplings to the axions. We exemplify how these bounds rule out otherwise consistent effective supergravity theories as theories of quantum gravity. Our derivations of the quantum gravity bounds are tested and further motivated in concrete string theoretic settings. In particular, this leads to a sharper version of the bound on the gauge group rank in F-theory on elliptic four-folds with a smooth base, which improves the known geometrical Kodaira bounds. We furthermore provide a detailed derivation of the EFT string constraints in heterotic string compactifications including higher derivative corrections to the effective action and apply the bounds to M-theory compactifications on G2 manifolds.

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“…The highest Mordell-Weil rank obtained so far for elliptic threefolds is rmax = 10 [82]. 21 We thank Wati Taylor for pointing this out to us.…”

Section: Jhep03(2023)197mentioning

confidence: 89%

Section: Jhep03(2023)197mentioning

confidence: 99%

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Quantum gravity bounds on $$ \mathcal{N} $$ = 1 effective theories in four dimensions

Martucci

Risso

Weigand

2023

J. High Energ. Phys.

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“…Indeed, in different regions of the moduli space different infinite towers may first break down the effective theory, for they are the lightest ones in those regions, and the mass of their lightest state may serve as cutoff. This phenomenon is common to several effective theories stemming from string theory -see [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] for a sample of works. In general, however, it is not clear how many towers are needed in order to realize the Distance Conjecture throughout the moduli space, and how to systematically partition the moduli space according to the regions where each of these towers is relevant.…”

Section: Introductionmentioning

confidence: 91%

Machine learning the breakdown of tame effective theories

Lanza

2024

Eur. Phys. J. C

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Effective field theories endowed with a nontrivial moduli space may be broken down by several, distinct effects as the energy scales that are probed increase. These may include the appearance of a finite number of new states, or the emergence of an infinite tower of states, as predicted by the Distance Conjecture. Consequently, the moduli space can be partitioned according to which kind of state first breaks down the effective description, and the effective-theory cutoff has to be regarded as a function of the moduli that may abruptly vary in form across the components of the partition. In this work we characterize such a slicing of the moduli space, induced by the diverse breakdown mechanisms, in a two-fold way. Firstly, employing the recently formulated Tameness Conjecture, we show that the partition of the moduli space so constructed is composed only of a finite number of distinct components. Secondly, we illustrate how this partition can be concretely constructed by means of supervised machine learning techniques, with minimal bottom-up information.

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“…It is an interesting question in how far tameness, with the sharpened notion discussed in this work, is related to a coupling to gravity. It was suggested in [2], and further explored in [4,34], that o-minimality is a necessary condition for an effective theory to admit a UV completion with gravity. It is not expected, however, that it is also a sufficient condition.…”

Section: Jhep05(2024)001mentioning

confidence: 99%

Complexity in tame quantum theories

Grimm,

Schlechter,

van Vliet

2024

J. High Energ. Phys.

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Inspired by the notion that physical systems can contain only a finite amount of information or complexity, we introduce a framework that allows for quantifying the amount of logical information needed to specify a function or set. We then apply this methodology to a variety of physical systems and derive the complexity of parameter-dependent physical observables and coupling functions appearing in effective Lagrangians. In order to implement these ideas, it is essential to consider physical theories that can be defined in an o-minimal structure. O-minimality, a concept from mathematical logic, encapsulates a tameness principle. It was recently argued that this property is inherent to many known quantum field theories and is linked to the UV completion of the theory. To assign a complexity to each statement in these theories one has to further constrain the allowed o-minimal structures. To exemplify this, we show that many physical systems can be formulated using Pfaffian o-minimal structures, which have a well-established notion of complexity. More generally, we propose adopting sharply o-minimal structures, recently introduced by Binyamini and Novikov, as an overarching framework to measure complexity in quantum theories.

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Tameness, Strings, and the Distance Conjecture

Cited by 14 publications

References 70 publications

Quantum gravity bounds on $$ \mathcal{N} $$ = 1 effective theories in four dimensions

Quantum gravity bounds on $$ \mathcal{N} $$ = 1 effective theories in four dimensions

Machine learning the breakdown of tame effective theories

Complexity in tame quantum theories

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