Second-quantized mirror symmetry

Second-quantized Mirror Symmetry

We propose and give strong evidence for a duality relating Type II theories on CalabiYau spaces and heterotic strings on K3× T , both of which have N = 2 spacetime supersymmetry. Entries in the dictionary relating the dual theories are derived from an analysis of the soliton string worldsheet in the context of N = 2 orbifolds of dual N = 4 compactifications of Type II and heterotic strings. In ...

Log Mirror Symmetry and Local Mirror Symmetry

We study Mirror Symmetry of log Calabi-Yau surfaces. On one hand, we consider the number of “affine lines” of each degree in P\B, where B is a smooth cubic. On the other hand, we consider coefficients of a certain expansion of a function obtained from the integrals of dx/x ∧ dy/y over 2chains whose boundaries lie on Bφ, where {Bφ} is a family of smooth cubics. Then, for small degrees, they coin...

Second Quantized Frobenius Algebras

We show that given a Frobenius algebra there is a unique notion of its second quantization, which is the sum over all symmetric group quotients of n–th tensor powers, where the quotients are given by symmetric group twisted Frobenius algebras. To this end, we consider the setting of Frobenius algebras given by functors from geometric categories whose objects are endowed with geometric group act...

Mirror Symmetry and Localization

Meet Homological Mirror Symmetry

In this paper, we introduce the interested reader to homological mirror symmetry. After recalling a little background knowledge, we tackle the simplest cases of homological mirror symmetry: curves of genus zero and one. We close by outlining the current state of the field and mentioning what homological mirror symmetry has to say about other aspects of mirror symmetry.