Welcome to my personal homepage! In this website you can learn a bit more about me or have a look at a complete list of my publications. My most recent papers are presented below. You can always send me an email for more information.
KALEIDOSCOPES, WAVES AND THE PREPOTENTIAL
with Fabian Ruehle
Abstract
Isomorphic flops are topology-changing transitions connecting two diffeomorphic families of Calabi-Yau threefolds. They correspond to the generators of certain Coxeter groups acting on the moduli space. As a consequence of these symmetries, the prepotential of 4D Type IIA compactifications on such varieties must assemble into Coxeter-invariant functions. We construct a database of all Coxeter symmetries from isomorphic flops in Kähler-favorable CICYs. The action of the Coxeter group on the Kähler moduli space leaves a symmetric bilinear form invariant, which we interpret as a metric and construct its associated Laplace-Beltrami operator. We argue that the Coxeter-invariant functions featured in the prepotential solve the Helmholtz equation with this Laplacian, and that the prepotential can then be resummed into a decomposition in terms of eigenfunctions of the Laplace-Beltrami operator. The convergence rate of the raw orbit sums of worldsheet instanton contributions and the resummed expressions are complementary, with the latter sharply localizing around the first few terms in the interior of the moduli space.
HARMONIC ANALYSIS OF THE INSTANTON PREPOTENTIAL
with Fabian Ruehle
Abstract
Discrete symmetries of Calabi-Yau moduli spaces, generated by isomorphic flops, constrain the instanton expansion of the 4D Type IIA prepotential. We show that the Coxeter-invariant functions into which the prepotential organizes are eigenfunctions of a Laplace-Beltrami operator built from the Coxeter-invariant symmetric bilinear form on the moduli space. This means that the Gromov-Witten expansion can be interpreted as a superposition of waves propagating on the Coxeter quotient of the moduli space, and its resummation is the corresponding spectral decomposition. For the dihedral Coxeter groups, separation of variables in the eigenvalue equation explains from first principles why special modified Bessel functions, ordinary Bessel functions and Jacobi theta functions appear as the natural building blocks of the prepotential, depending on whether the Coxeter rotation acts hyperbolically, elliptically, or parabolically. The resulting spectral representations converge efficiently in the interior of the moduli space, complementing the standard large-volume instanton expansion.
OPEN STRINGS AND HETEROTIC INSTANTONS
with Christian Kneißl, Jacob M. Leedom and Nicole Righi
Abstract
Motivated by closed string perturbation theory arguments by S. Shenker, we consider non-perturbative effects of characteristic strength , with the closed string coupling constant, in supersymmetric critical heterotic string theories. We argue that in 10D such effects arise from heterotic “D-instantons,” i.e. heterotic disk diagrams, whose existence relies on a non-trivial interplay between worldsheet and spacetime degrees of freedom. In compactifications of the heterotic string, we argue that similar effects can arise from wrapped Euclidean non-BPS “D-strings.” Two general principles arise: The first is that the consistency of those heterotic branes on which the fundamental string can end relies on an inflow mechanism for spacetime degrees of freedom. The second is that Shenker’s argument, taken to its logical conclusion, implies that all closed string theories must exhibit open strings as well.
NON-MINIMAL ELLIPTIC THREEFOLDS AT INFINITE DISTANCE II: ASYMPTOTIC PHYSICS
with Seung-Joo Lee and Timo Weigand
Abstract
We interpret infinite-distance limits in the complex structure moduli space of F-theory compactifications to six dimensions in the light of general ideas in quantum gravity. The limits we focus on arise from non-minimal singularities in the elliptic fiber over curves in a Hirzebruch surface base, which do not admit a crepant resolution. Such degenerations take place along infinite directions in the non-perturbative brane moduli space in F-theory. A blow-up procedure, detailed generally in Part I of this project, gives rise to an internal space consisting of a union of log Calabi-Yau threefolds glued together along their boundaries. We geometrically classify the resulting configurations for genus-zero single infinite-distance limits. Special emphasis is put on the structure of singular fibers in codimension zero and one. As our main result, we interpret the central fiber of these degenerations as endpoints of a decompactification limit with six-dimensional defects. The conclusions rely on an adiabatic limit to gain information on the asymptotically massless states from the structure of vanishing cycles. We also compare our analysis to the heterotic dual description where available. Our findings are in agreement with general expectations from quantum gravity and provide further evidence for the Emergent String Conjecture.
NON-MINIMAL ELLIPTIC THREEFOLDS AT INFINITE DISTANCE I: LOG CALABI-YAU RESOLUTIONS
with Seung-Joo Lee and Timo Weigand
Abstract
We study infinite-distance limits in the complex structure moduli space of elliptic Calabi-Yau threefolds. In F-theory compactifications to six dimensions, such limits include infinite-distance trajectories in the non-perturbative open string moduli space. The limits are described as degenerations of elliptic threefolds whose central elements exhibit non-minimal elliptic fibers, in the Kodaira sense, over curves on the base. We show how these non-crepant singularities can be removed by a systematic sequence of blow-ups of the base, leading to a union of log Calabi-Yau spaces glued together along their boundaries. We identify criteria for the blow-ups to give rise to open chains or more complicated trees of components and analyse the blow-up geometry. While our results are general and applicable to all non-minimal degenerations of Calabi-Yau threefolds in codimension one, we exemplify them in particular for elliptic threefolds over Hirzebruch surface base spaces. We also explain how to extract the gauge algebra for F-theory probing such reducible asymptotic geometries. This analysis is the basis for a detailed F-theory interpretation of the associated infinite-distance limits that will be provided in a companion paper.
MEMBRANE LIMITS IN QUANTUM GRAVITY
with Daniel Kläwer and Timo Weigand
Abstract
It is expected that infinite distance limits in the moduli space of quantum gravity are accompanied by a tower of light states. In view of the emergent string conjecture, this tower must either induce a decompactification or correspond to the emergence of a tensionless critical string. We study the consistency conditions implied by this conjecture on the asymptotic behavior of quantum gravity under dimensional reduction. If the emergent string descends from a (2+1)-dimensional membrane in a higher-dimensional theory, we find that such a membrane must parametrically decouple from the Kaluza-Klein scale. We verify this censorship against emergent membrane limits, where the membrane would sit at the Kaluza-Klein scale, in the hypermultiplet moduli space of Calabi-Yau 3-fold compactifications of string/M-theory. At the classical level, a putative membrane limit arises, up to duality, from an M5-brane wrapping the asymptotically shrinking special Lagrangian 3-cycle corresponding to the Strominger-Yau-Zaslow fiber of the Calabi-Yau. We show how quantum corrections in the moduli space obstruct such a limit and instead lead to a decompactification to 11 dimensions, where the role of the M5- and M2-branes are interchanged.
ANALYTIC PERIODS VIA TWISTED SYMMETRIC SQUARES
with Lorenz Schlechter
Abstract
We study the symmetric square of Picard-Fuchs operators of genus one curves and the thereby induced generalized Clausen identities. This allows the computation of analytic expressions for the periods of all one-parameter K3 manifolds in terms of elliptic integrals. The resulting expressions are globally valid throughout the moduli space and allow the explicit inversion of the mirror map and the exact computation of distances, useful for checks of the Swampland Distance Conjecture. We comment on the generalization to multi-parameter models and provide a two-parameter example.
SWAMPLAND CONJECTURES FOR AN ALMOST TOPOLOGICAL GRAVITY THEORY
with Ralph Blumenhagen, Christian Kneißl, Andriana Makridou and Lorenz Schlechter
Abstract
We analyze AdS and dS swampland conjectures in a three-dimensional higher spin theory with self-interacting matter, which contains conformal gravity and is almost topological. A theory of a similar type was proposed as the effective theory in the high energy phase of non-critical M-theory in 3D. With some details differing from the usual string theory story, it is found that the resulting effective theory, namely topologically massive gravity, fits well into the web of the proposed swampland conjectures. Supporting a recent proposal, in particular we find that this 3D theory gives rise to a quantum break time that scales like .
SMALL FLUX SUPERPOTENTIALS FOR TYPE IIB FLUX VACUA CLOSE TO A CONIFOLD
with Ralph Blumenhagen, Max Brinkmann and Lorenz Schlechter
Abstract
We generalize the recently proposed mechanism by Demirtas, Kim, McAllister and Moritz arXiv:1912.10047 for the explicit construction of type IIB flux vacua with to the region close to the conifold locus in the complex structure moduli space. For that purpose tools are developed to determine the periods and the resulting prepotential close to such a codimension one locus with all the remaining moduli still in the large complex structure regime. As a proof of principle we present a working example for the Calabi-Yau manifold .