Machine learning line bundle cohomologies of hypersurfaces in toric varieties

Klaewer, Daniel; Schlechter, Lorenz

doi:10.1016/j.physletb.2019.01.002

Cited by 75 publications

(75 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let us illustrate the process of finding the region boundaries for the example dP 4 . The Picard number of this space is five, so a two-dimensional slice misses the behaviour of a boundary in the remaining three directions.…”

Section: Regions and Polynomials For Del Pezzo Surfacesmentioning

confidence: 99%

See 1 more Smart Citation

Index Formulae for Line Bundle Cohomology on Complex Surfaces

Brodie

Constantin

Deen

et al. 2020

Fortschritte der Physik

View full text Add to dashboard Cite

We conjecture and prove closed-form index expressions for the cohomology dimensions of line bundles on del Pezzo and Hirzebruch surfaces. Further, for all compact toric surfaces we provide a simple algorithm which allows expression of any line bundle cohomology in terms of an index. These formulae follow from general theorems we prove for a wider class of surfaces. In particular, we construct a map that takes any effective line bundle to a nef line bundle while preserving the zeroth cohomology dimension. For complex surfaces, these results explain the appearance of piecewise polynomial equations for cohomology and they are a first step towards understanding similar formulae recently obtained for Calabi-Yau three-folds.The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/prop.201900086 1 The first non-trivial instance of a line bundle cohomology formula appeared in the earlier work [2,3], in which generic hypersurfaces of type (2,2,2,2) in a product of four complex projective spaces were studied.

show abstract

Section: Regions and Polynomials For Del Pezzo Surfacesmentioning

confidence: 99%

“…For dP 4 , the normal vectors have the same structure as for dP 3 but with the other obvious permutations included. The same is true for dP 5 , except, additionally, the new vector v = (2, −1, −1, −1, −1, −1) appears.…”

Section: A Compact Formula For Del Pezzo Surfacesmentioning

confidence: 99%

Index Formulae for Line Bundle Cohomology on Complex Surfaces

Brodie

Constantin

Deen

et al. 2020

Fortschritte der Physik

View full text Add to dashboard Cite

show abstract

“…Supervised learning was also utilized [11] to predict a central charges in 4d N = 1 SCFTs via volume minimization in gravity duals with toric descriptions. In mathematical directions that are also relevant for string vacua, supervised learning yielded an estimated upper bound on the number of Calabi-Yau threefolds realized as hypersurfaces in a large class of toric varieties [5], and has also led to accurate predictions for line bundle cohomology [12,14]. See [15][16][17][18][19][20] for additional works in string theory that use supervised learning.…”

Section: Contentsmentioning

confidence: 99%

Branes with brains: exploring string vacua with deep reinforcement learning

Halverson

Nelson

Ruehle

2019

J. High Energ. Phys.

View full text Add to dashboard Cite

We propose deep reinforcement learning as a model-free method for exploring the landscape of string vacua. As a concrete application, we utilize an artificial intelligence agent known as an asynchronous advantage actor-critic to explore type IIA compactifications with intersecting D6-branes. As different string background configurations are explored by changing D6-brane configurations, the agent receives rewards and punishments related to string consistency conditions and proximity to Standard Model vacua. These are in turn utilized to update the agent's policy and value neural networks to improve its behavior. By reinforcement learning, the agent's performance in both tasks is significantly improved, and for some tasks it finds a factor of O(200) more solutions than a random walker. In one case, we demonstrate that the agent learns a human-derived strategy for finding consistent string models. In another case, where no human-derived strategy exists, the agent learns a genuinely new strategy that achieves the same goal twice as efficiently per unit time. Our results demonstrate that the agent learns to solve various string theory consistency conditions simultaneously, which are phrased in terms of non-linear, coupled Diophantine equations.

show abstract

“…The discrete landscape can be viewed as the complement of a continuum of seemingly consistent low-energy effective field theories (EFTs) that cannot descend from a string compactification, deemed the swampland [22,23]. While the latter has received much attention in recent years, progress in data science might allow for systematic studies of [24] and machine learning [25][26][27][28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Searching the landscape of flux vacua with genetic algorithms

Cole

Schachner

Shiu

2019

J. High Energ. Phys.

View full text Add to dashboard Cite

In this paper, we employ genetic algorithms to explore the landscape of type IIB flux vacua. We show that genetic algorithms can efficiently scan the landscape for viable solutions satisfying various criteria. More specifically, we consider a symmetric T 6 as well as the conifold region of a Calabi-Yau hypersurface. We argue that in both cases genetic algorithms are powerful tools for finding flux vacua with interesting phenomenological properties. We also compare genetic algorithms to algorithms based on different breeding mechanisms as well as random walk approaches.

show abstract

Machine learning line bundle cohomologies of hypersurfaces in toric varieties

Cited by 75 publications

References 13 publications

Index Formulae for Line Bundle Cohomology on Complex Surfaces

Index Formulae for Line Bundle Cohomology on Complex Surfaces

Branes with brains: exploring string vacua with deep reinforcement learning

Searching the landscape of flux vacua with genetic algorithms

Contact Info

Product

Resources

About