10 research outputs found
Machine Learning Line Bundle Cohomologies of Hypersurfaces in Toric Varieties
Different techniques from machine learning are applied to the problem of
computing line bundle cohomologies of (hypersurfaces in) toric varieties. While
a naive approach of training a neural network to reproduce the cohomologies
fails in the general case, by inspecting the underlying functional form of the
data we propose a second approach. The cohomologies depend in a piecewise
polynomial way on the line bundle charges. We use unsupervised learning to
separate the different polynomial phases. The result is an analytic formula for
the cohomologies. This can be turned into an algorithm for computing analytic
expressions for arbitrary (hypersurfaces in) toric varieties.Comment: 8 pages, 6 figures, 5 tables; typos corrected, reference added,
clarifications adde
The Refined Swampland Distance Conjecture in Calabi-Yau Moduli Spaces
The Swampland Distance Conjecture claims that effective theories derived from
a consistent theory of quantum gravity only have a finite range of validity.
This will imply drastic consequences for string theory model building. The
refined version of this conjecture says that this range is of the order of the
naturally built in scale, namely the Planck scale. It is investigated whether
the Refined Swampland Distance Conjecture is consistent with proper field
distances arising in the well understood moduli spaces of Calabi-Yau
compactification. Investigating in particular the non-geometric phases of
Kahler moduli spaces of dimension , we always found
proper field distances that are smaller than the Planck-length.Comment: 71 pages, 11 figures, v2: refs added, typos correcte
A Spin-2 Conjecture on the Swampland
We consider effective theories with massive fields that have spins larger
than or equal to two. We conjecture a universal cutoff scale on any such theory
that depends on the lightest mass of such fields. This cutoff corresponds to
the mass scale of an infinite tower of states, signalling the breakdown of the
effective theory. The cutoff can be understood as the Weak Gravity Conjecture
applied to the St\"uckelberg gauge field in the mass term of the high spin
fields. A strong version of our conjecture applies even if the graviton itself
is massive, so to massive gravity. We provide further evidence for the
conjecture from string theory.Comment: 6 pages. v2. Added reference
Quantum Corrections in 4d N=1 Infinite Distance Limits and the Weak Gravity Conjecture
We study quantum corrections in four-dimensional theories with
supersymmetry in the context of Quantum Gravity Conjectures. According to the
Emergent String Conjecture, infinite distance limits in quantum gravity either
lead to decompactification of the theory or result in a weakly coupled string
theory. We verify this conjecture in the framework of supersymmetric
F-theory compactifications to four dimensions including perturbative
as well as non-perturbative corrections. After proving uniqueness of the
emergent critical string at the classical level, we show that quantum
corrections obstruct precisely those limits in which the scale of the emergent
critical string would lie parametrically below the Kaluza-Klein scale. Limits
in which the tension of the asymptotically tensionless string sits at the
Kaluza-Klein scale, by contrast, are not obstructed. In the second part of the
paper we study the effect of quantum corrections for the Weak Gravity
Conjecture away from the strict weak coupling limit. We propose that gauge
threshold corrections and mass renormalisation effects modify the
super-extremality bound in four dimensions. For the infinite distance limits in
F-theory the classical super-extremality bound is generically satisfied by a
sublattice of states in the tower of excitations of an emergent heterotic
string. By matching the F-theory corrections to gauge threshold
corrections of the dual heterotic theory we predict how the masses of this
tower must be renormalised in order for the Weak Gravity Conjecture to hold at
the quantum level.Comment: 75 pages, 7 figures; v2: references added, typos corrected, minor
clarifications; v3: references added, version accepted for publication in
JHE
String Phenomenology 2019
The KKLT scenario in a warped throat, if consistent, provides a concrete counterexample to both the AdS scale separation and the dS swampland conjectures. In this talk I will analyze the relevant effective field theory for the conifold modulus and the overall Kahler modulus that both have exponentially small masses. In particular, I will focus on KK modes that have masses below the mass scale set by the conifold modulus. We find that integrating out the KK modes leads to one-loop corrections to the moduli kinetic terms which are of the same functional form as their tree level values. Implications for the consistency of the KKLT scenario are discussed. Finally I will comment on the role of KK modes for the emergence of kinetic terms in quantum gravity