Past String Theory Seminar

This is a report on an ongoing project to construct Calabi-Yau manifolds for which the Hodge numbers $(h^{11}, h^{21})$ are both relatively small. These manifolds are, in a sense, the simplest Calabi-Yau manifolds. I will report on joint work with Volker Braun, Andrei Constantin, Rhys Davies, Challenger Mishra and others.

The planar N=4 SYM is believed to be integrable. Following this thoroughly justified belief, its exact spectrum had been encoded recently into a quantum spectral curve (QSC). We can explicitly solve the QSC in various regimes; in particular, one can perform a highly-efficient weak coupling expansion.

I will explain how QSC looks like for the harmonic oscillator and then, using this analogy, introduce the QSC equations for the SYM spectrum. We will use these equations to compute a particular 6-loop conformal dimension in real time and then discuss explicit results (found up to 10-loop orders) as well as some general statements about the answer at any loop-order.

I will give an overview of ongoing joint work with R. Rubio and C. Tipler, in which we study the moduli problem for the Strominger system of equations. Building on the work of De la Ossa and Svanes and, independently, of Anderson, Gray and Sharpe, we construct an elliptic complex whose first cohomology group is the space of infinitesimal deformations of a solution of the strominger system. I will also discuss an intriguing link between this moduli problem and a moduli problem for holomorphic Courant algebroids over Calabi-Yau threefolds. Finally, we will see how the problem for the Strominger system embeds naturally in generalized geometry, and discuss some perspectives of this approach.

I will describe the computation of the supersymmetric Renyi entropy across an entangling 3-sphere for five-dimensional superconformal field theories. For a class of USp(2N) gauge theories I’ll also construct a holographic dual 1/2 BPS black hole solution of Euclidean Romans F(4) supergravity. The large N limit of the gauge theory results will be shown to agree perfectly with the supergravity computations.

I will discuss the implementation of explicit stabilisation of all closed string moduli in fluxed type IIB Calabi-Yau compactifications with chiral matter.  Using toric geometry we construct Calabi-Yau manifolds with del Pezzo singularities. D-branes located at such singularities can support the Standard Model gauge group and matter content. We consider Calabi-Yau manifolds with a discrete symmetry that reduces the effective number of complex structure moduli, which allows us to calculate the corresponding periods and find explicit flux vacua. We compute the values of the flux superpotential and the string coupling at these vacua. Starting from these explicit complex structure solutions, we obtain AdS and dS minima where the Kaehler moduli are stabilised by a mixture of D-terms, non-perturbative and perturbative alpha'-corrections as in the LARGE Volume Scenario.

I will discuss several recent developments regarding the construction of fluxes for F-theory on Calabi-Yau fourfolds. Of particular importance to the effective physics is the structure of the middle (co)homology groups, on which new results are presented. Fluxes dynamically drive the fourfold to Noether-Lefschetz loci in moduli space. While the structure of such loci is generally unknown for Calabi-Yau fourfolds, this problem can be answered in terms of arithmetic for K3 x K3 and a classification is possible.

In this talk, we discuss an analogue of the Hermitian-Einstein equations for generalized Kaehler manifolds proposed by N. Hitchin. We explain in particular how these equations are equivalent to a notion of stability, and that there is a Kobayahsi-Hitchin-type of correspondence between solutions of these equations and stable objects. The correspondence holds even for non-Kaehler manifolds, as long as they are endowed with Gauduchon metrics (which is always the case for generalized Kaehler structures on 4-manifolds).

This is joint work with Shengda Hu and Reza Seyyedali.