Related papers: Modular Invariance in Superstring on Calabi-Yau n-…
An overview is given of the construction of a differential polynomial ring of functions on the moduli space of Calabi-Yau threefolds. These rings coincide with the rings of quasi modular forms for geometries with duality groups for which…
We discover a modular property of supersymmetric partition functions of supersymmetric theories with R-symmetry in four dimensions. This modular property is, in a sense, the generalization of the modular invariance of the supersymmetric…
We show that B-model topological strings on local Calabi-Yau threefolds are large N duals of matrix models, which in the planar limit naturally give rise to special geometry. These matrix models directly compute F-terms in an associated N=1…
We exploit the presence of moduli fields in the ${\rm AdS}_3\times { S}^3\times CY_2$, where $CY_2=T^4$ or $K3$, solution to Type IIB superstring theory, to construct a U-fold solution with geometry ${\rm AdS}_2\times S^1\times {\rm…
We study the moduli spaces of heterotic/type II dual pairs in four dimensions with N=2 supersymmetry corresponding to non-geometric Calabi-Yau backgrounds on the type II side and to T-fold compactifications on the heterotic side. The vector…
We discuss the period geometry and the topological string amplitudes on elliptically fibered Calabi-Yau fourfolds in toric ambient spaces. In particular, we describe a general procedure to fix integral periods. Using some elementary facts…
In this note we examine the supermembrane action on Calabi-Yau 3-folds. We write down the Dirac-Born-Infeld part of the action, and show that it is invariant under the rigid spacetime supersymmetry.
In this contribution to the Proceedings of the Conference on Analysis, Complex Geometry, and Mathematical Physics, an expository overview of superstring perturbation theory to two loop order is presented to an audience of mathematicians and…
We apply the coset character identities (generalization of Jacobi's abstruse identity) to compact and noncompact Gepner models. In the both cases, we prove that the partition function actually vanishes due to the spacetime supersymmetry. In…
It is shown that the model X_{14}(7,3,2,1,1) has two Calabi--Yau phases.
F-theory compactifications on Calabi-Yau fivefolds give rise to two-dimensional N=(0,2) supersymmetric field theories coupled to gravity. We explore the dilaton supergravity defined by the moduli sector of such compactifications. The…
A system containing a pair of non-BPS D-strings of type IIA string theory on an orbifold, representing a single D2-brane wrapped on a nonsupersymmetric 2-cycle of a Calabi-Yau 3-fold with $(h^{(1,1)},h^{(1,2)})$ = (11,11), is analyzed. In…
We give a representation, in terms of iterated Mellin-Barnes integrals, of periods on multi-moduli Calabi-Yau manifolds arising in superstring theory. Using this representation and the theory of multidimensional residues, we present a…
This work deals with the topological classification of germs of singular foliations on $(\mathbb C^{2},0)$. Working in a suitable class of foliations we fix the topological invariants given by the separatrix set, the Camacho-Sad indices and…
We introduce unsupervised machine learning techniques in order to identify toric phases of 4d N=1 supersymmetric gauge theories corresponding to the same toric Calabi-Yau 3-fold. These 4d N=1 supersymmetric gauge theories are worldvolume…
We give a short overview over recent work on finding constraints on partition functions of 2d CFTs from modular invariance. We summarize the constraints on the spectrum and their connection to Calabi-Yau compactifications.
We study the quantum volume of D-branes wrapped around various cycles in Calabi-Yau manifolds, as the manifold's moduli are varied. In particular, we focus on the behaviour of these D-branes near phase transitions between distinct low…
We review a general paradigm for constructing U-fold backgrounds in (dimensionally reduced) Type IIB superstring theory, of the form ${\rm AdS}_{d-1}\times S^1\times S^d$, with a monodromy along $S^1$ in the string-duality group. We also…
Non-perturbative corrections and modular properties of four-dimensional type IIB Calabi-Yau orientifolds are discussed. It is shown that certain non-perturbative alpha' corrections survive in the large volume limit of the orientifold and…
This is the author's PhD thesis. Two main sections address various aspects of mirror symmetry for compact Calabi-Yau threefolds and the roles that classically modular varieties play in string theory compactifications. The main results…