On the computation of non‐perturbative effective potentials in the string theory landscape – IIB/F‐theory perspective –

Abstract

Abstract:We discuss a number of issues arising when computing non-perturbative effects systematically across the string theory landscape. In particular, we cast the study of fairly generic physical properties into the language of computability/number theory and show that this amounts to solving systems of diophantine equations. In analogy to the negative solution to Hilbert's 10th problem, we argue that in such systematic studies there may be no algorithm by which one can determine all physical effects. We take large volume type IIB compactifications as an example, with the physical property of interest being the low-energy non-perturbative F-terms of a generic compactification. A similar analysis is expected to hold for other kinds of string vacua, and we discuss in particular the extension of our ideas to F-theory. While these results imply that it may not be possible to systematically answer certain physical questions about generic type IIB compactifications, we identify particular Calabi-Yau manifolds in which the diophantine equations become linear, and thus can be systematically solved.As part of the study of the required systematics of F-terms, we develop technology for computing Z 2 equivariant line bundle cohomology on toric varieties, which determines the presence of particular instanton zero modes via the Koszul complex. This is of general interest for realistic IIB model building on complete intersections in toric ambient spaces.

Exceptional N = 3 $$ \mathcal{N}=3 $$ theories

“…This setup appears naturally in the A N −1 case, where the resulting N = 4 theories with duality defects are useful for understanding aspects of the physics of euclidean D3-branes in F-theory language [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]. There is no known corresponding notion of an "exceptional instanton", but the abstract study of the generalization of such duality defects to exceptional theories should be interesting in any case, and the non-geometric backgrounds described in this note give one way of explicitly constructing such setups.…”

Branes with brains: exploring string vacua with deep reinforcement learning

“…1 In fact, in 1986 it was already anticipated [6] that there are over 10 1500 consistent chiral heterotic compactifications. As examples of complexity, finding small cosmological constants in the Bousso-Polchinski model is NP-complete [7], constructing scalar potentials in string theory and finding minima are both computationally hard [8], and the diversity of Diophantine equations that arise in string theory (for instance, in index calculations) raises the issue of undecidability in the landscape [9] by analogy to the negative solution to Hilbert's 10 th problem. Finally, in addition to difficulties posed by size and complexity, there are also critical formal issues related to the lack of a complete definition of string theory and M-theory.…”

Estimating Calabi-Yau hypersurface and triangulation counts with equation learners

“…For example, dynamical vacuum selection [8] on a network of string geometries [9] in a well-studied bubble cosmology [10] selects models with large numbers of gauge groups and axions, as well as strong coupling. However, concrete studies of the landscape are difficult due to its enormity [11,12,13,14,9,15], computational complexity [16,17,18,19,20], and undecidability [17]. It is therefore natural to expect that, in addition to the formal progress that is clearly required, data science techniques such as supervised machine learning will be necessary to understand the landscape; see for initial works [21,22,8,23] in this directions and [24,25,26,27,28,29,30] for additional promising results.…”