Deformed WZW models and Hodge theory. Part I

Grimm, Thomas W.; Jeroen, Monnee,

doi:10.1007/jhep05(2022)103

Cited by 6 publications

(5 citation statements)

References 148 publications

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“…This operator-based approach has been explored in more detail in[26,31,32]: for (3.14) one can introduce a corresponding charge operator with H p,q ∞ as eigenspaces; for the sl(2)-triples one can rotate to a complex basis such that the generators commute with the charge operator. This thereby allows for a simultaneous decomposition into eigenstates, which -although we do not use these operators explicitly in this work -is described in this subsection 8.…”

mentioning

confidence: 99%

The tadpole conjecture in asymptotic limits

Graña

Grimm

Heisteeg

et al. 2022

J. High Energ. Phys.

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The tadpole conjecture suggests that the complete stabilization of complex structure deformations in Type IIB and F-theory flux compactifications is severely obstructed by the tadpole bound on the fluxes. More precisely, it states that the stabilization of a large number of moduli requires a flux background with a tadpole that scales linearly in the number of stabilized fields. Restricting to the asymptotic regions of the complex structure moduli space, we give the first conceptual argument that explains this linear scaling setting and clarifies why it sets in only for a large number of stabilized moduli. Our approach relies on the use of asymptotic Hodge theory. In particular, we use the fact that in each asymptotic regime an orthogonal sl(2)-block structure emerges that allows us to group fluxes into sl(2)-representations and decouple complex structure directions. We show that the number of stabilized moduli scales with the number of sl(2)-representations supported by fluxes, and that each representation fixes a single modulus. Furthermore, we find that for Calabi-Yau four-folds all but one representation can be identified with representations occurring on two-folds. This allows us to discuss moduli stabilization explicitly and establish the relevant scaling constraints for the tadpole.

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mentioning

confidence: 99%

The tadpole conjecture in asymptotic limits

Graña

Grimm

Heisteeg

et al. 2022

J. High Energ. Phys.

Self Cite

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show abstract

“…We assume that this procedure can be replicated at several, different spacetime points, corresponding to different points in the moduli space. The set of the moduli space points {ϕ A k } probed in this way, along with the types Type J k of the states 5 For instance, the presence of dynamical objects such as black holes [20], cosmic strings [14,21] and domain walls [13] may be the source of a nontrivial change of the vev's of the moduli throughout spacetime. that first break down the effective theory at the point ϕ A k constitute the data that we will be focusing on and which we will feed to the machine learning algorithm:…”

Section: Bottom-up Viewpoint I: Partitioning the Moduli Space Via A K...mentioning

confidence: 99%

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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“…The physics of these near-boundary EFTs can be studied in detail by means of asymptotic Hodge Theory. Established in [10], asymptotic Hodge Theory has proven to be a powerful tool for examining the structure of string vacua and characteristics of the BPS spectrum in the asymptotic regions of moduli space [11,12,[15][16][17][18][19][49][50][51][52][53]. A brief overview of asymptotic Hodge Theory is contained in appendix B, where we further highlight how the couplings of the vector multiplet sector can be studied in full generality exploiting the tools that the Hodge theory provides.…”

Section: Global Symmetries In the Rigid Case And One-modulus Asymptot...mentioning

confidence: 99%

Global symmetry-breaking and generalized theta-terms in Type IIB EFTs

Grimm,

Lanza,

van Vuren

2023

J. High Energ. Phys.

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A longstanding conjecture states that global symmetries should be absent in quantum gravity. By investigating large classes of Type IIB four-dimensional $$ \mathcal{N} $$ N = 2 effective field theories, we enlist the potential generalized global symmetries that could be present and explore how they are avoided. Crucial ingredients that arise in such effective field theories are generalized θ-terms. These introduce non-linear couplings between axion fields and topological terms quadratic in the gauge field strengths which break a large subset of the global symmetries. Additional residual global symmetries may further be broken by assuming the existence of some charged states. However, we illustrate that the presence of generalized θ-terms leads to a generalized Witten effect, which implies that the spectrum of charged states is constituted by an infinitely populated lattice. We further show that such a lattice is generated by the action of the monodromy transformation that characterizes the moduli space boundary near which the effective theory is defined.

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Deformed WZW models and Hodge theory. Part I

Cited by 6 publications

References 148 publications

The tadpole conjecture in asymptotic limits

The tadpole conjecture in asymptotic limits

Machine learning the breakdown of tame effective theories

Global symmetry-breaking and generalized theta-terms in Type IIB EFTs

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