Géométrie énumérative et théorie des cordes
Org:
Keshav Dasgupta et
Johannes Walcher (McGill)
[
PDF]
 PER BERGLUND, University of New Hampshire
Global Embeddings for Branes at Toric Singularities and Moduli Stabilization [PDF]

We discuss recent work on the realization of gauge theories from D3branes at toric singularities in compact CalabiYau manifolds. In particular, we show how a new type of Euclidean D3brane instanton supported on a nonSpin fourcycle in type IIB orientifolds can give rise to a nonperturbative contribution to the superpotential. This allows the Kähler moduli to be stabilized consistent with the assumption that the fourcycle vanishes for the toric singularity, while the overall volume of the CalabiYau manifold is exponentially large.
 VINCENT BOUCHARD, University of Alberta
Topological recursion and double Hurwitz numbers [PDF]

Double Hurwitz numbers count covers of the Riemann sphere by genus $g$ Riemann surfaces with arbitrary ramification over $0$ and $\infty$, and simple ramification elsewhere. We show that generating functions for certain classes of double Hurwitz numbers satisfy the EynardOrantin topological recursion, which completely determines them recursively through complex analysis on particularly simple spectral curves. We also argue that double Hurwitz numbers can be obtained in the "infinite framing" limit of GromovWitten invariants on certain orbifolds, in parallel to a similar limit relating simple Hurwitz numbers and GromovWitten invariants of $\mathbb{C}^3$. This is joint work with Dani Hernandez Serrano and Motohico Mulase.
 GUILLAUME LAPORTE, Mcgill University
Monodromy of an Inhomogeneous PicardFuchs Equation [PDF]

The global behaviour of the normal function associated with van Geemen's
family of lines on the mirror quintic is presented, as well as how the limiting value of the normal function at large complex structure is an irrational number expressible in terms of the dilogarithm.
 ARNAUD LEPAGEJUTIER, McGill
Smoothed Transitions in Higher Spin AdS Gravity [PDF]

We consider CFTs conjectured to be dual to higher spin theories of gravity in AdS${}_3$ and AdS${}_4$. Two dimensional CFTs with $W_N$ symmetry are considered in the $\lambda=0$ ($k \to \infty$) limit where they are described by continuous orbifolds. The torus partition function is computed, making reasonable assumptions, and equals that of a free field theory. We find no phase transition at temperatures of order one; the usual HawkingPage phase transition is removed by the highly degenerate light states associated with conical defect states in the bulk. Three dimensional ChernSimons Matter CFTs with vectorlike matter are considered on $T^3$, where the dynamics is described by an effective theory for the eigenvalues of the holonomies. Likewise, we find no evidence for a HawkingPage phase transition at large level $k$.
 SHUNJI MATSUURA, McGill University
Classification of gapless topological phases [PDF]

TBA
 RUXANDRA MORARU, University of Waterloo
Stable bundles on complex nilmanifolds [PDF]

Let $G$ be a connected, simply connected nilpotent Lie group, and let $\Gamma \subset G$ be a discrete, cocompact subgroup. The quotient manifold $\Gamma\backslash G$ is called a {\em nilmanifold}. If $N = \Gamma \backslash G$ is equipped with a complex structure $I$ induced by a leftinvariant complex structure on $G$, then $(N,I)$ is called a {\em complex nilmanifold}. Other than complex tori, examples of complex nilmanifolds are given by Kodaira surfaces and Iwasawa manifolds. Moreover, although all complex nilmanifolds have holomorphically trivial canonical bundles, only complex tori admit Kaehler metrics. Nonetheless, many nonKaehler complex nilmanifolds admit balanced metrics. In this talk, I will describe some of the interesting geometric properties that moduli spaces of stable bundles on nonKaehler complex nilmanifolds possess.
 JIHYE SEO, Physics Department, McGill University and CRM MathPhysics lab
Exactly stable nonBPS spinors in heterotic string theory on tori [PDF]

Considering SO(32) heterotic string theory compactified on tori,
stability of nonsupersymmetric states is studied. A nonsupersymmetric state with robust stability is constructed, and its exact stability is proven in a large region of moduli space against all the possible decay mechanisms allowed by charge conservation. Using various Tduality, we translate various selection rules about conserved charges
into simpler problems resembling partition and parity of integers.
 ALISHA WISSANJI, University of Alberta, Department of Mathematical and Statistical Sciences
IIA Perspective On Cascading Gauge Theory [PDF]

We study the N=1 supersymmetric cascading gauge theory found in type IIB string theory on p regular and M fractional D3branes at the tip of the conifold, using the Tdual type IIA description. We reproduce the supersymmetric vacuum structure of this theory, and show that the IIA analog of the nonsupersymmetric state found by Kachru, Pearson and Verlinde in the IIB description is metastable in string theory, but the barrier for tunneling to the supersymmetric vacuum goes to infinity in the field theory limit. We also comment on the N=2 supersymmetric gauge theory corresponding to regular and fractional D3branes on a nearsingular K3, and clarify the origin of the cascade in this theory.
© Société mathématique du Canada