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List of abstracts
In the context of (0,2) gauged linear sigma models, we explore chains of perturbatively dual heterotic string compactifications. The notion of target space duality originates in non-geometric phases and can be used to generate distinct GLSMs with shared geometric phases leading to apparently identical target space theories. To date, this duality has mainly been explored at the level of counting states in the effective theories. We extend this analysis to the effective potential and loci of enhanced symmetry in dual theories. By engineering vector bundles with non-trivial constraints arising from slope-stability (i.e. D-terms) and holomorphy (i.e. F-terms) we are able to explore in detail the vacuum space of the dual theories.
I will consider N=(0,2) gauged linear sigma models (GLSMs) with a Coulomb branch, such as GLSMs with an N=(2,2) locus. For this restricted but interesting class of (0,2) gauge theories, one can apply recent supersymmetric localization techniques to the theory defined on a Riemann surface. I will explain a simple residue formula for correlations functions of `pseudo-chiral' Coulomb branch operators on the sphere (or on any closed orientable Riemann surface). This is particularly interesting for non-abelian gauge theories.
We will study and compare several notions of moduli in (0,2) theories, and will illustrate them with toric examples.
We investigate orbifold and smooth Calabi-Yau compactifications of the non-supersymmetric heterotic SO(16)xSO(16) string. We begin with reviewing some properties of this non-supersymmetric string and describe its relation to it supersymmetric cousins. We focus on some of the issues of non-supersymmetric theories, like tachyons. In particular, we argue that the N=0 theory never leads to tachyons on smooth Calabi-Yaus in the large volume approximation. As twisted tachyons may arise on certain singular orbifolds, we conjecture that such tachyonic states are lifted in the full blow-up. We perform model searches on selected orbifold and smooth Calabi-Yau geometries. In particular, we construct an explicit example of a Standard Model-like theory with three generations. Finally we develop some effective field theory description for the low energy limit of such non-supersymmetric string constructions. We use this to investigate some so far unknown possible symmetries of such non-supersymmetric string constructions. And finally using this language we investigate some properties of quantum corrections in this context.
I will review a variety of new results from the last year on compactification of heterotic theories on Calabi-Yau manifolds. This will include new geometric examples and advances in moduli identification.
In this talk, I will discuss holographic duals for various constructions of 2d (0,2) SCFTs and RG flows between them. As part of the solution we will need to develop a general and convenient framework based on 3d N=2 gauged supergravity, which has rather small amount of supersymmetry and, presumably for this reason, managed to escape attention in the supergravity literature. The talk is based in part on http://arxiv.org/pdf/1503.01474.pdf
I review recent progress on calculating the perturbative holomorphic Yukawa couplings in heterotic Calabi-Yau compactifications. It will be shown how these methods apply to specific examples and lead to explicit results for the Yukawa couplings, including their dependence on complex structure. I will also explain a topological vanishing theorem which implies certain Yukawa couplings, despite being allowed by symmetry, have to be zero. Finally, I will discuss some implications for Yukawa unification in heterotic standard models.
I will discuss some work in progress on 3-dimensional Minkowski vacua obtained from M-theory and perturbative heterotic compactifications. Some of the latter are realized as torus fibrations over K3, but there may well be more CFTs without a simple geometric realization.
We are considering heterotic N=(2,2) models that correspond to A^9_1 Gepner models. We classify all Abelian discrete quotients and compute the full massless matter spectrum at the Fermat locus. We find the set of models to be closed under mirror symmetry and satisfy a universal relation. Furthermore we give a prescription of how to compute all charges under all symmetries of the 4D theory. Using mirror symmetry we deform the Landau-Ginzburg (LG) models to other geometric phases and match those effects to the Higgs mechanism in 4D. In this way we can compute the presence/absence of discrete R-and non-R symmetries once we deform away from the LG point which we do in two concrete examples.
Abelian GLSMs have been an important tool for studying the SCFTs to which they flow in the IR. I will discuss some applications along these lines.
We compute the new supersymmetric index of a large class of heterotic compactifications with torsion, corresponding to principal two-torus bundles over warped K3 surfaces with H-flux. Starting from a UV description as a (0,2) gauged linear sigma-model with torsion, we use supersymmetric localization techniques to provide an explicit expression of the index as a sum over the Jeffrey-Kirwan residues of the one-loop determinant. We finally propose a geometrical formula that gives the new supersymmetric index in terms of bundle data, regardless of any particular choice of underlying two-dimensional theory.
I will re-derive some of the recent developments in the heterotic moduli story from the Gukov-Vafa-Witten superpotential. Focusing on compact geometries whose zeroth order smooth Calabi-Yau limit exists, I will show an interesting relation between the number of lifted moduli through the preservation of holomorphic bundles, and the anomaly cancellation condition. This gives a lower bound on the number of lifted moduli. If time, I will also discuss some results in this direction when considering G2 compactifications to three dimensions.
We study the local moduli space of solutions to the Strominger system. We will introduce some mathematical tools coming from generalized geometry, that are helpful to understand the moduli problem. We show that infinitesimal solutions to the Strominger system that are compatible with flux quantization correspond to infinitesimal solutions to generalized Killing spinors equations on a Courant algebroid.
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