Mirror symmetry

About: Mirror symmetry is a research topic. Over the lifetime, 2422 publications have been published within this topic receiving 90786 citations.

Examples of bundles on Calabi–Yau 3-folds for string theory compactifications

Abstract: Simple examples are given of bundles on Calabi-Yau 3-folds satisfying 8 out of 9 conditions required for a realistic compactification of string theory to 4 dimensions.

Mirror symmetry for moduli spaces of Higgs bundles via p-adic integration

Abstract: We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type $\operatorname{SL}_n$ and $\operatorname{PGL}_n$. More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generically fibred into dual abelian varieties. Our proof utilises p-adic integration relative to the fibres, and interprets canonical gerbes present on these moduli spaces as characters on the Hitchin fibres using Tate duality. Furthermore we prove for $d$ coprime to $n$, that the number of rank $n$ Higgs bundles of degree $d$ over a fixed curve defined over a finite field, is independent of $d$. This proves a conjecture by Mozgovoy--Schiffman in the coprime case.

Symmetries, asymmetries, and the world of particles

Abstract: Discusses mirror symmetry, a symmetries, time reversal, vacuum as a physical medium, spontaneous symmetry breaking, particles, and quarks.

Negative Branes, Supergroups and the Signature of Spacetime

Abstract: We study the realization of supergroup gauge theories using negative branes in string theory. We show that negative branes are intimately connected with the possibility of timelike compactification and exotic spacetime signatures previously studied by Hull. Isolated negative branes dynamically generate a change in spacetime signature near their worldvolumes, and are related by string dualities to a smooth M-theory geometry with closed timelike curves. Using negative D3 branes, we show that $SU(0|N)$ supergroup theories are holographically dual to an exotic variant of type IIB string theory on $dS_{3,2} \times \bar S^5$, for which the emergent dimensions are timelike. Using branes, mirror symmetry and Nekrasov's instanton calculus, all of which agree, we derive the Seiberg-Witten curve for $\mathcal N=2 ~SU(N|M)$ gauge theories. Together with our exploration of holography and string dualities for negative branes, this suggests that supergroup gauge theories may be non-perturbatively well-defined objects, though several puzzles remain.